Random Walker Rankings

Post-Bowl Rankings

2012-01-29T10:38:00.000-05:00

Better late than never, if I don't get these posted here by the end of January I think I would completely forget about them. Anyway, here we are. I've never been a fan of running the post-bowl rankings. I believe if you look back through my track record of when I usually get around to posting them, my typically long delay represents this lack of enthusiasm in most cases.

This year, I had a gut feeling how it was going to work out even before I ran the calculation. Put simply, our algorithm treats the BCS Championship Game just like any other football game. There is no special indication putting more weight on this game nor is there even any input into the ranking that this game occurred after LSU's earlier victory over Alabama. To top it off, we do not include margin of victory either. So the direct information used about LSU-Alabama is restricted to the fact that they split their two games. The net result is that Alabama isn't selected as the #1 team at any of the bias parameter values, as seen in the plot below.

Is this a clear sign of a flaw? I think that depends on your philosophy in both creating and using such rankings. Once we've all agreed that there is a "championship game" then the outcome is decided on the field, not what some formula says after the fact. Could we modify the rankings to include the date of game or margin of victory or phase of the moon? Sure, but that would be counter to our stated philosophy in making the ranking system simple. Alabama won it all on the field and that's what matters.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through December 3rd

2011-12-04T10:48:00.002-05:00

The regular season and conference championships are in the books. The BCS Championship pairing is now largely in the hands of the voters: Oklahoma State throttled Oklahoma but the computer rankings do not include margin of victory information, though of course Oklahoma State will still be helped greatly in the computers by the win over another highly-ranked team. We'll know soon whether it was enough to get them back in the Championship picture or if we'll have an Alabama-LSU rematch.

The other BCS bowls hinge on some details of the BCS selection procedures. For instance (as discussed here), does TCU get high enough in the Standings to get an automatic bid, and does Michigan qualify for an at-large bid? And then ultimately the BCS bowls make their own choices within those constraints.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 26th

2011-11-27T08:45:00.000-05:00

With the dominant ways that both LSU and Alabama won this weekend, the BCS Championship game is all but set. The Hang Up and Listen podcast team wonderfully admonished everyone to stay away from the phrase "BCS chaos" from now on; but it's now unnecessary advice for the rest of this year's discussion about the championship game. We're going to get LSU and Alabama. The talking heads are even all about how LSU could lose next week to Georgia and still make the BCS Championship game (unlinked because I'm confident you've heard it already from somewhere).

Looking at the rest of the BCS bowl games, hopeful projections currently count on Houston winning the Conference USA Championship next weekend, which will translate into an automatic BCS bowl game berth (under #3A of the automatic qualification piece of the current BCS selection procedures). Meanwhile, Boise State could end up higher ranked in the BCS Standings (they were last week) but be left out of the BCS bowls for not winning their conference title (see the same selection procedures linked above). [Why do I care? I don't know. Maybe I just like to cheer for the underdog?]

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 19th

2011-11-20T08:50:00.004-05:00

One week later, and everything has changed. Your guess about what happens next is as good as mine (or probably better). As we just saw many ways this weekend, anything can happen.

The big surprise (at least to me) in the RWFL rankings plotted below is that Oklahoma State is still ranked in the top two throughout here.

While the RWFL rankings have nothing to do with the official BCS Standings, we sometimes talk about using this family of rankings as a proxy for the different ways that the computer component of the BCS might turn out. In this case, however, we need to stress one important difference: the RWFL rankings as calculated here do not use the dates of the games at all, unlike some of the computer rankings in the BCS. That is, these rankings treat the games of this past weekend no differently than a game in September (e.g., when Arkansas lost to Alabama). The dates of the games could be easily incorporated to weight more recent games more heavily if one wanted to do so; but that's another coefficient that would need to be picked, counter to our keep-it-simple philosophy here. So it is an important way that we do not mimic the computer component of the BCS Standings.

Looking at the computer components of last week's BCS Standings, where Arkansas was 6th (and three teams above them lost), I fully expect to see them much higher when the Standings come out tonight, further emphasizing the importance of their upcoming game with LSU.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 12th

2011-11-13T08:28:00.001-05:00

And then there were... three? No, sorry Houston, there's no way you're going to be part of the BCS discussion; but they nevertheless deserve congratulations for being one of the few undefeated FBS teams remaining at this point.

As long as LSU and Oklahoma State keep winning, they will play for the championship. But their winning out is far from certain. Obviously, they can't look past anyone, and they have particularly tough tests before the end of the season, with LSU playing Arkansas and a tough SEC Championship opponent, and Oklahoma State still has Oklahoma on their schedule.

While we wait for those tests, we call attention to the sharp changes on the right edge of the plot below of this week's RWFL rankings. This gives us an opportunity to recall some of the features of this family of rankings as we consider different values of p. As p approaches 1 on the right edge of the plot (the last point plotted is p=0.9999), going undefeated trumps everything else. Houston climbs quickly to #3 near the edge and undefeated FCS Sam Houston State (not shown, but you can see the gap that none of the plotted teams is ranked #5 at p=0.9999 [click the plot to see a larger version]) rises quickly on the right edge from even deeper in the rankings, eventually passing all of the 1-loss teams at p even closer to 1. But at the middle ranges of p we consider (typically p=0.75), the game outcomes are naturally balanced with a notion of strength of schedule, with Houston at #17 for p=0.75 and falling as low as #21 in the left half of the plot (as p gets closer to 0.5).

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 5th

2011-11-06T07:56:00.000-05:00

For a brief moment, the potential BCS Championship picture looks simple: LSU & Oklahoma State.

But both teams have difficult tests remaining in the next month. If either stumbles, the rankings below would appear to indicate we could have BCS chaos; however, it is important to look at last week's BCS Standings and conclude that the polls would help propel Stanford into the championship game if they stay undefeated and either of the top two teams stumble. If two top BCS teams stumble and Boise State stays undefeated, though, I'm not so certain of the outcome. But such possibilities are still a long way away...

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 29th

2011-10-30T08:11:00.001-04:00

Clemson and Kansas State have now dropped from the undefeated ranks, further depleting the teams making bids for the top two spots, setting us up nicely for November.

We'll obviously lose at least one more undefeated next week, with LSU traveling to Alabama. We could be running low on undefeated AQ teams soon, and that's when the controversy usually starts to heat up.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 22nd

2011-10-23T10:33:00.000-04:00

Even with losses by Oklahoma and Wisconsin now on the books, we still have a traffic jam near the top of the RWFL rankings. Six undefeated teams crowd the top (with two other undefeateds joining them in the plot below). LSU, Oklahoma St, and Alabama each take turns in the top spot as one considers different values of the bias parameter p.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 15th

2011-10-16T12:24:00.000-04:00

With a fleet of undefeateds still out there, the observation of the week is about how jumbled the RWFL rankings are, both this week and compared with previous weeks. As seen in the plot below, four different teams appear in our top two for some values of the parameter p: Oklahoma State, Clemson, Alabama, and Oklahoma.

Contrast this with the plots from previous weeks, when we of course had less game data. In particular, it's worth mentioning again that these rankings are based only on the final information about who won and who lost. No scores, no stats, no scouting. Just wins and losses. That is, just like the computer systems in the BCS Standings. So strong conclusions are necessarily made from limited information. But we'll have more of that information every week. And of course the other undefeateds are ready to move up if given the chance.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 8th

2011-10-09T08:37:00.001-04:00

With so many undefeated teams at this stage of the season, the questions are all about comparing measures of strength of schedule. The plot below shows just one way of varying the meaning of strength of schedule from the game results we have so far this season. This will all get a lot more interesting as the number of undefeated teams falls.

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 1st

2011-10-02T09:01:00.003-04:00

Last evening was the first time this season it was cool enough for a good fire pit, adding to my personal sense that Fall is here and further inspiring me to start the Random Walker First-Last (RWFL) rankings for the 2011 college football season.

We are once again enormously grateful to both Peter Wolfe and Kenneth Massey for making this task easier on all of us. Both are part of the official Bowl Championship Series standings. Wolfe provides the data in an easy-to-process form. Massey publishes the College Football Ranking Comparison.

We have nothing to do with the official Bowl Championship Series standings. We provide these rankings for fun as an example of how the teams might be ranked using a simple "my team beat your team" argument. As described in our papers and elsewhere on this blog and its links, the RWFL ranking system has one "free parameter" p which loosely speaking relates to the balance between strength of schedule and overall record. When p is close to 1/2 (the left edge of the figure below), quality of opponent plays a strong role. As p increases towards 1 (the right edge), single-game victories and going undefeated matter more.

We will continue to post plots representing the placement of the top-ranked teams as we vary the p parameter in the RWFL rankings. Looking at different values of p is of course just one of many ways to modify the rankings; but they sometimes lead to a quick observation about how sensitive rankings are to different ways of valuing the importance of strength of schedule. That said, such changes have elaborate follow-on effects---changing the ranking of one school impacts the rankings of all of the schools they played, and so on---so that it is often difficult to make quick sense of why this one change affects the rankings. Looking at the figure below, Clemson is ranked #1 at almost all values of p, except very close to p=1 where Alabama slides into the top spot. There are some large movements in the figure, with Illinois ranked at #16 near the left edge but moving up to #5 near the right edge. Why do these changes occur? One could try to weave a story, but with so many undefeated teams right now it might just be easiest to wait for more football to be played.

The RWFL rankings at p=0.75 run on the full network of connected teams should appear in Massey's comparisons for this season starting this week (where the rankings are broken out separately for the FBS and FCS). The rankings on the restricted network including only the FBS teams are equivalent to Eugene Potemkin's "E-Rating" that sometimes appears there too.

Now I can pay attention to football...

2011-09-29T20:06:00.000-04:00

Though my passport from the Red Sox Nation has faded in a decade away from Boston living, I still feel gutted by the just completed September swoon. Nate Silver beautifully quantifies the epic level of the Red Sox collapse this year. Even as he notes that the estimate is not at all mathematically rigorous, it's a twisted kind of fun to have a numerical narrative building to the claim of "about one chance in 278 million of all these events coming together in quite this way." For even casual Red Sox fans, those numbers are believable in our gut.

Looking for the silver lining on this cloud, I now plan to see whether I can get the Random Walker Rankings for the 2011 college football season running soon...

Random Walker Brackets

2011-03-16T19:27:00.001-04:00

For those looking for some last-minute algorithmic help filling out their brackets (if your pool doesn't count the first four games), I got word today that Mark McClure has performed the random walker rankings for college basketball this year. In my limited experience looking at such rankings in previous years, one of the issues with this approach applied to college basketball is that there appears to be a well-established home court advantage, at least insofar as typically appears looking at intra-conference home-at-home series. Joel Sokol at Georgia Tech uses a system with similar mathematical features that takes into account such issues.

The 2011 NCAA brackets via random walkers (Mark McClure)
Profs' Picks (Joel Sokol)

Final 2010-11 RWFL Rankings

2011-01-11T11:11:00.001-05:00

It came down to the final seconds of the BCS National Championship game, but we have a champion.

My dreams for this blog have run head first this Fall into my administrative duties. Obviously, we all have to make choices based on our priorities, and making this an active blog has fallen to the wayside under other pressures. But I remain committed to running the random walker rankings and posting the results here. Additionally, our rankings for the full FBS and FCS will continue to be available on Kenneth Massey's College Football Ranking Comparison.

Rankings through December 4th

2010-12-05T11:16:00.001-05:00

There will be little or no argument about which two teams most deserve to appear in the national championship game under the BCS rules: Auburn and Oregon.

But what about undefeated TCU? When we vary our bias parameter, as a proxy for various algorithmic ranking choices, TCU ranks between 3rd and 6th (as represented in the figure below). Oklahoma, Stanford, and Missouri each rank ahead of TCU under some of the parameter values.

Do you know the last time TCU lost a regular season game? November 6th, 2008, by three points after giving up a last-minute TD to a Utah team that finished that season undefeated with a Sugar Bowl victory over Alabama. TCU went 11-2 that year, with their only other loss at the hands of Oklahoma, who finished that season losing in the BCS National Championship game. TCU then finished the 2009 season with a 12-1 record after losing the Fiesta Bowl to an undefeated Boise State, who broke the 4th quarter tie thanks in part to a gutsy fake punt. And now they're 12-0 in 2010.

Irrespective of whether TCU ends up undefeated after their bowl game, can't we just have playoffs already?

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 27th

2010-11-28T09:04:00.002-05:00

With three undefeated teams left, the college football weekend that just concluded either set the table for BCS Championship clarity or chaos, as we await next week's SEC Championship and Oregon versus Oregon State. As has been clear for weeks now, if Auburn and Oregon win out, they'll meet for the Championship. If one of them loses, however, it's time for controversy: should TCU be given a shot at the title? But unless Auburn or Oregon lose next week, that will just be an academic argument (insert joke here about how that should be right up my alley).

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 20th

2010-11-21T08:20:00.000-05:00

With the top four teams in the BCS all off for the weekend, one doesn't expect much of a change at the top of the rankings. With most of the other highly-ranked teams winning, except Nebraska (previously BCS#8), there seems even less reason for change in algorithmic rankings. Yes, the debate continues about the relative rankings of the other one-loss teams, but the computer rankings used by the BCS don't factor in margin of victory (neither do we here).

So it is something of a surprise that the top of the plot below is so different from last week's figure. Obviously, we expect Nebraska to fall with a loss; but LSU used to be ahead of both TCU and Boise State for a wide range of "p values" (our bias parameter which influences the importance of strength of schedule and which serves as a very rough proxy for some different ranking systems). That range where the strength of schedule of LSU, Stanford, and Missouri is enough here to put them ahead of Boise State has now narrowed in the left edge of the figure. This is presumably in part because each of them beat teams with incoming records at .500 and below in conference this weekend; but I also suspect a variety of indirect effects in the developing network of wins and losses between teams.

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 13th

2010-11-14T10:49:00.000-05:00

Before another week went in the books, it briefly seemed not just possible but likely that BCS chaos was upon us, that is, before both Oregon and Auburn prevailed in their respective games. As long as they both keep winning, the national championship picture will remain simple; but we saw again that a stumble is always possible, and both teams have two solid challenges in front of them. As the saying goes, that's why they play the games. If one or both indeed stumble, the "BCS busters" and the one-loss teams will all be there trying to stake their claims on a title shot.

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through November 6th

2010-11-07T08:10:00.002-05:00

As we make ourselves comfortable here in the month of November, the narratives of different possibilities start becoming clearer and the lobbying to get teams into the BCS championship ramps up. The big results of the weekend impacting the top of the rankings include the wins by Oregon, TCU, and LSU.

Last week we linked to Ivan Maisel's argument that Oregon's seemingly poor computer ranking would be remedied down the stretch. Again, we have nothing to do with the official BCS Standings; but the consideration of the whole family of random walker rankings (across various values of the bias parameter p) is an imperfect proxy for weighting outcomes and schedule strength in the computer rankings. Comparing last week's plot of rank versus p with the plot from this week, Oregon is already in a much stronger position with the algorithms, and that's still before playing any of the three teams Maisel highlights.

Keep in mind that these rankings do not consider margin of victory (nor do any of the official computer rankings in the BCS Standings, by edict). So indeed, Oregon would appear to hold their fate in their own hands. Meanwhile, TCU did what they could to solidify their case, by knocking off previously undefeated Utah, while LSU continues to make itself part of the conversation. If either Auburn or Oregon stumble down the stretch, we're going to have another season of BCS chaos.

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 30th

2010-10-31T08:22:00.000-04:00

And then there were five left. Five undefeated teams, that is. The drama will continue to be the discrepancies between the polls and the computer rankings, at least in the short term. Ivan Maisel makes the argument that the relatively poor ranking Oregon currently has in the computers will be at least partially remedied down the stretch when they play Cal, Arizona, and Oregon State. Of course, they have to keep winning, and their mascot has to keep up with the push-ups.

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 23rd

2010-10-24T07:36:00.002-04:00

The rankings appear to tighten up a little with some more teams encountering their first losses of the season this weekend. The most interesting items in the plot below are the bias parameters (the values of p) at which one-loss Oklahoma and LSU are ranked ahead of undefeated Boise State, Oregon, and Utah. That said, other than making the observation, we're happy to just sit back and watch more football right now. We continue to post our rankings for the full FBS and FCS on Kenneth Massey's College Football Ranking Comparison.

Rankings through October 16th

2010-10-17T11:30:00.002-04:00

Another week, another defeat for a #1 team. We still have a lot of football to play, and plenty of undefeated teams left. The first official BCS Standings for the year are released tonight, and much attention will rightly be paid to these rankings to see who has the proverbial pole position to possibly reach the championship game.

Meanwhile, check out Fuzzy math by the BCS by Jon Solomon, bringing to light some of the potential problems with the fact that most of the computer systems used by the BCS are black boxes. Don't get me wrong, I think that the service provided by the authors of these systems should be rewarded (and not just with the hate mail they all get). Colley and Massey once did me the favor of speaking at a minisymposium at a math conference, and I know they do this out of love of the game. But the built-in verification that would come with greater transparency would be most welcome.

As an aside, regarding the actual error of changing team lists noted in the article, we made the same error at a bookkeeping level last week. That is, our current calculations here are independent of such lists because we work on the full connected component of teams connected to one another by games played. But when we sent in our lists of FBS and FCS teams to Kenneth Massey, he caught that we didn't send him the correct lists. It's a completely understandable error, demonstrating the value of the verification that would come with greater transparency.

In the plots below, the order of the undefeated teams jumbles around as you vary p, the bias parameter value. Full "Random Walker FL" rankings of the FBS and FCS for the week will be posted on Kenneth Massey's College Football Ranking Comparison.

Random Walker Rankings, 2010 Edition

2010-10-10T09:37:00.004-04:00

The college football season is already well along and it's past time to bring back the random walker rankings. Of course, college football is understandably a touchy subject at Carolina this season. Ignoring those important issues for the purposes of this blog, we focus back on the rankings, which just became more interesting near the top with Alabama's loss. So, hey, hey, they're the monkeys, let's see what they've got to say this year.

As always, we're grateful to Peter Wolfe for providing the data in an easy-to-process form, and to Kenneth Massey for publishing the College Football Ranking Comparison. We have nothing to do with the official Bowl Championship Series standings. We provide these rankings as an example of how the teams might be ranked using a "my team beat your team" argument. The Random Walker First-Last rankings (at bias parameter p=0.75) on the full network of connected teams appears in Massey's comparisons for this season starting this week. The rankings on the restricted network of FBS teams are equivalent to Eugene Potemkin's "E-Rating" that sometimes appears there too.

Because the full rank order of teams is provided in the comparisons, this season we will only post here the graphical representation of the top-ranked teams across different bias parameter p values, focusing on any interesting changes found there. Looking at different values of p is of course just one of many ways to modify the rankings. Loosely speaking, the overall strength of schedule is more emphasized at p close to 1/2 (the left edge of the figures below), while p close to 1 emphasizes going undefeated and single-game outcomes.

The plot below, including the top 16 teams at p=0.75 for all games played through Saturday October 9th, shows how the rank order changes with varying bias parameter p. For example, slightly above 0.9, Boise State and Auburn swap places #2 and #3 in these rankings. (Click on the figure to see a larger version.)

At this stage of the season, algorithmic rankings remain at a severe disadvantage because of the relatively limited amount of data available. As more games are played, it will be interesting to see the week-to-week changes in the rankings.

Final 2009 Season Rankings

2010-01-16T09:55:00.003-05:00

We have finally run the RWFL calculation on the season that ended over a week ago with Alabama's victory over Texas. Of course, that left us with two undefeated FBS teams: Alabama and Boise State. Unfortunately, the nature of the BCS is that we'll never see the last game necessary to eliminate one of these teams from the ranks of the undefeated.

The RWFL-based bowl predictions were magnificently bad this year. I haven't analyzed anything in depth in the discrepancy between what was predicted and what happened. Of course, there are many reasons why teams may do better or worse in bowl games than they "should" in whatever sense one takes that word here. However, particularly per my interest in communities in networks, I'm always keen to see if there are conference-based patterns in the mispredictions. Last year, I recall that the bowl games appeared to indicate that the RWFL had left the Big 12 under-ranked. This year, that conference may have been the Big Ten, with many RWFL predictions of Big 10 bowl defeats that went awry. But that is admittedly just a first impression.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Thursday January 7th 2010:
1. Alabama (14-0) [1.8099]
2. Florida (13-1) [1.3544]
3. Boise St (14-0) [1.0583]
4. Cincinnati (12-1) [1.0386]
5. Texas (13-1) [1.0197]
6. Ohio State (11-2) [0.9994]
7. TCU (12-1) [0.9500]
8. Iowa (11-2) [0.9438]
9. Georgia Tech (11-3) [0.8511]
10. Oregon (10-3) [0.8504]
11. Virginia Tech (10-3) [0.8148]
12. Penn State (11-2) [0.7775]
13. LSU (9-4) [0.7300]
14. Brigham Young (11-2) [0.7263]
15. Pittsburgh (10-3) [0.7029]
16. Southern Cal (9-4) [0.6760]
17. Miami FL (9-4) [0.6628]
18. Wisconsin (10-3) [0.6541]
19. Mississippi (9-4) [0.6376]
20. Georgia (8-5) [0.6211]
21. West Virginia (9-4) [0.6155]
22. Arkansas (8-5) [0.6150]
23. Auburn (8-5) [0.6058]
24. Clemson (9-5) [0.5853]
25. Utah (10-3) [0.5713]
26. Arizona (8-5) [0.5699]
27. North Carolina (8-5) [0.5604]
28. Oklahoma St (9-4) [0.5513]
29. Nebraska (10-4) [0.5486]
30. Stanford (8-5) [0.5434]
31. South Carolina (7-6) [0.5359]
32. Florida St (7-6) [0.5327]
33. Oregon St (8-5) [0.5163]
34. Tennessee (7-6) [0.5073]
35. California (8-5) [0.4993]
36. Texas Tech (9-4) [0.4913]
37. Central Michigan (12-2) [0.4882]
38. Navy (10-4) [0.4847]
39. Connecticut (8-5) [0.4834]
40. Oklahoma (8-5) [0.4809]
41. Kentucky (7-6) [0.4682]
42. Northwestern (8-5) [0.4641]
43. Boston College (8-5) [0.4539]
44. Houston (10-4) [0.4534]
45. Rutgers (9-4) [0.4530]
46. South Florida (8-5) [0.4430]
47. Mississippi St (5-7) [0.4403]
48. East Carolina (9-5) [0.4392]
49. Missouri (8-5) [0.4136]
50. UCLA (7-6) [0.4120]
51. Washington (5-7) [0.3980]
52. Troy (9-4) [0.3955]
53. Fresno St (8-5) [0.3932]
54. Notre Dame (6-6) [0.3923]
55. Minnesota (6-7) [0.3874]
56. Air Force (8-5) [0.3815]
57. Nevada (8-5) [0.3750]
58. Middle Tennessee St (10-3) [0.3740]
59. SMU (8-5) [0.3659]
60. Central Florida (8-5) [0.3550]
61. Temple (9-4) [0.3482]
62. Wyoming (7-6) [0.3470]
63. Purdue (5-7) [0.3419]
64. Idaho (8-5) [0.3362]
65. Michigan St (6-7) [0.3358]
66. Iowa St (7-6) [0.3240]
67. Wake Forest (5-7) [0.3215]
68. Texas A&M (6-7) [0.3186]
69. Marshall (7-6) [0.3166]
70. North Carolina St (5-7) [0.3096]
71. Ohio U. (9-5) [0.2929]
72. Syracuse (4-8) [0.2839]
73. Kansas St (6-6) [0.2823]
74. Bowling Green (7-6) [0.2727]
75. Michigan (5-7) [0.2610]
76. Hawai`i (6-7) [0.2602]
77. Virginia (3-9) [0.2576]
78. Southern Miss (7-6) [0.2571]
79. Kansas (5-7) [0.2565]
80. UNLV (5-7) [0.2539]
81. Duke (5-7) [0.2534]
82. Arizona St (4-8) [0.2520]
83. Baylor (4-8) [0.2359]
84. Louisville (4-8) [0.2348]
85. Illinois (3-9) [0.2261]
86. Indiana (4-8) [0.2197]
87. Utah St (4-8) [0.2140]
88. Louisiana-Monroe (6-6) [0.2116]
89. Colorado (3-9) [0.2102]
90. Louisiana-Lafayette (6-6) [0.2080]
91. Louisiana Tech (4-8) [0.2078]
92. Northern Illinois (7-6) [0.2076]
93. Alabama-Birmingham (5-7) [0.2075]
94. San Diego St (4-8) [0.1991]
95. Colorado St (3-9) [0.1891]
96. Tulsa (5-7) [0.1885]
97. Vanderbilt (2-10) [0.1876]
98. UTEP (4-8) [0.1847]
99. Maryland (2-10) [0.1810]
100. Toledo (5-7) [0.1802]
101. Florida Int'l (3-9) [0.1792]
102. Florida Atlantic (5-7) [0.1776]
103. Buffalo (5-7) [0.1703]
104. Washington St (1-11) [0.1631]
105. New Mexico St (3-10) [0.1517]
106. Tulane (3-9) [0.1502]
107. San Jose St (2-10) [0.1459]
108. Kent St (5-7) [0.1429]
109. Army (5-7) [0.1389]
110. Western Michigan (5-7) [0.1305]
111. Arkansas St (4-8) [0.1270]
112. Rice (2-10) [0.1188]
113. New Mexico (1-11) [0.1147]
114. Memphis (2-10) [0.1090]
115. Miami OH (1-11) [0.1041]
116. Akron (3-9) [0.1037]
117. North Texas (2-10) [0.0886]
118. Ball St (2-10) [0.0652]
119. Eastern Michigan (0-12) [0.0021]
120. Western Kentucky (0-12) [0.0003]
Conference Rankings (Average Per Team):
SEC 0.7094
BigEast 0.5319
Big10 0.5101
Pac10 0.4880
ACC 0.4820
Big12 0.4277
MWC 0.4148
WAC 0.3492
FBSInd 0.3386
CUSA 0.2622
SunBelt 0.1957
MAC 0.1930
Non-FBS -0.0830

From the self-deprecation department

2009-12-26T12:49:00.005-05:00

This year was the first year that I followed our web traffic at any level of detail. The normal pattern has been that traffic spikes on Sundays during the regular season. But that traffic has dropped off dramatically following the big spike on BCS Selection Sunday. Right now, maybe that looks like a positive development (smile) seeing how poorly we're doing so far in our now annual use of the RWFL rankings to try to pick the bowl games. This year's RWFL-based selections have correctly picked 1 of the 6 bowl games so far this season, putting us currently at the 9.9th percentile in ESPN's College Bowl Mania. That's right, more than 90% of entries are currently performing better than our picks. Impressive! But there are a lot of games left to play, so we'll see how it shakes out in the long run. After all, our entry can't drop much lower.

Last Minute Bowl Game Preparations

2009-12-19T11:28:00.002-05:00

The first bowl games are only hours away, so it's time to get ready! No, I don't mean chili and guacamole (though that sounds good). I mean our third annual attempt to use the rankings to predict the bowl games. We'll once again be playing over at ESPN's College Bowl Mania (not endorsing it, it's just where I'm signed up), which requires predictions of outcomes and rank-ordering of confidence in those predictions. The 2007 random walker bowl predictions turned out pretty well, placing above the 75th percentile of all entries, which I believe is good for a fully automated system. The 2008 bowl predictions, however, really missed the mark. But that doesn't stop us from coming back to try again.

The big caveats up front are that we definitely do not recommend these rankings for anything beyond entertainment. The underlying rankings are not intended to be best in any sense, except that they are relatively simple to explain. And the methodology used to assign predictive probabilities here is fundamentally flawed. The general principle we use is that we assign a probability to a victory by the higher-ranked team such that the addition of a mythical fractional-outcome game split according to those probabilities does not change the existing rankings. However, this simple principle is fabulously erroneous for many reasons, not the least of which is that it can algebraically return a greater-than-100% chance of victory. You might think a mathematician would bother to fix such a problem, but there are so many other flaws in trying to use these rankings to predict upcoming games that it's unclear whether further detailed work would yield anything useful.

Like past years, we used the full-component RWFL predictions at p=0.75 (see other parts of this site for those details). Each game selection is specified by predicting the higher-ranked team will beat the lower-ranked team. The games are presented in order of confidence (highest to lowest), determined by the mean of the stated probability spread (obtained individually by the first-place votes and the last-place votes). I'm happy to discuss such details further, though I warn again that it is a relatively crude model. And since I'm assuming visitors just want the results, let's get to the predictions.

----
International
South Florida (7-5) over Northern Illinois (7-5)
70-82%
----
AdvoCare V100 Independence
Georgia (7-5) over Texas A&M (6-6)
67-79%
----
Chick-fil-A
Virginia Tech (9-3) over Tennessee (7-5)
69-76%
----
Emerald
Southern Cal (8-4) over Boston College (8-4)
65-70%
----
Rose Bowl Game presented by Citi
Oregon (10-2) over Ohio State (10-2)
61-71%
----
Brut Sun
Stanford (8-4) over Oklahoma (7-5)
63-69%
----
Insight
Minnesota (6-6) over Iowa St (6-6)
65-67%
----
Konica Minolta Gator
West Virginia (9-3) over Florida St (6-6)
65-67%
----
New Mexico
Fresno St (8-4) over Wyoming (6-6)
65-66%
----
Pacific Life Holiday
Arizona (8-4) over Nebraska (9-4)
65-66%
----
EagleBank
UCLA (6-6) over Temple (9-3)
56-70%
----
Outback
Auburn (7-5) over Northwestern (8-4)
61-62%
----
Papajohns.com
South Carolina (7-5) over Connecticut (7-5)
61-62%
----
Valero Alamo
Texas Tech (8-4) over Michigan St (6-6)
57-66%
----
Champs Sports
Miami FL (9-3) over Wisconsin (9-3)
56-67%
----
Sheraton Hawaii
Nevada (8-4) over SMU (7-5)
56-65%
----
Bell Helicopter Armed Forces
Houston (10-3) over Air Force (7-5)
47-75%
----
FedEx Orange
Georgia Tech (11-2) over Iowa (10-2)
56-61%
----
Citi BCS National Championship Game
Alabama (13-0) over Texas (13-0)
47-70%
----
Texas
Missouri (8-4) over Navy (8-4)
54-60%
----
Gaylord Hotels Music City
Clemson (8-5) over Kentucky (7-5)
57-58%
----
St. Petersburg
Central Florida (8-4) over Rutgers (8-4)
50-65%
----
R+L Carriers New Orleans
Middle Tennessee St (9-3) over Southern Miss (7-5)
56-57%
----
S.D. County Credit Union Poinsettia
California (8-4) over Utah (9-3)
53-59%
----
AT&T Cotton
Oklahoma St (9-3) over Mississippi (8-4)
52-59%
----
Allstate Sugar
Florida (12-1) over Cincinnati (12-0)
52-59%
----
Capital One
LSU (9-3) over Penn State (10-2)
50-60%
----
Tostitos Fiesta
TCU (12-0) over Boise St (13-0)
53-55%
----
Roady's Humanitarian
Idaho (7-5) over Bowling Green (7-5)
50-58%
----
GMAC
Central Michigan (11-2) over Troy (9-3)
54-54%
----
Little Caesars
Ohio U. (9-4) over Marshall (6-6)
52-53%
----
AutoZone Liberty
Arkansas (7-5) over East Carolina (9-4)
44-55%
----
MAACO Las Vegas
Oregon St (8-4) over Brigham Young (10-2)
49-50%
----
Meineke Car Care
North Carolina (8-4) over Pittsburgh (9-3)
39-51%
----

Note, in particular, the toss-up nature in the last picks above. Meanwhile, even some of the more confident calls include probability spreads that dip below 50%, including the call for the BCS National Championship Game.

By the way, we get a LOT more visitors than comments on this site. Feel free to express your opinion about the accuracy (or better yet, the stupidity) of these predictions!

Rankings through December 5th

2009-12-06T08:25:00.003-05:00

Every time you changed the channel yesterday, there was another wild game on. Alabama rolled Florida. Texas survived last-second confusion and won on a last-second FG. Cincy came back from 21 down and won by the difference of Pitt's botched extra point attempt following a perhaps too-early TD. GT won a back-and-forth match with Clemson. And Fresno State beat Illinois on a stretch into the endzone in the last seconds, followed by a fluke tip drill two-point conversion. Okay, so that last one has zero implication for the BCS bowls, and most of us probably only saw it on SportsCenter; but it was crazy.

Cincy and TCU fans are probably steaming this morning that Texas got that second back. And Texas will probably lose a few votes in the BCS Standings, but the conventional wisdom seems to be that their lead over TCU last week was so large that it won't matter: Texas will play Alabama for the championship.

TCU will get the non-AQ group automatic qualification. The three remaining BCS at-large bids are up to the bowls themselves, but it seems certain that Florida will get one, and it seems likely that Boise State and either Iowa or Penn State will get the other. That is, unless a bowl game chooses to go to a three-loss team, it's just a matter of which team goes where; Brad Edwards at ESPN concisely breaks the process down and makes predictions.

Finally, on to our own rankings. Note the figure below the rank ordering of the 120 teams, because it says something interesting this week. Specifically, it plots the order of the top teams under varying the single "p value" bias parameter in our ranking system, which is a highly imperfect proxy for exploring other ranking systems that work under the same limiting assumptions (notably no margin of victory and no information about dates of games). While Alabama remains the undisputed #1 as the bias varies between its allowed values, Cincy, Florida, and Texas each make appearances at #2.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday December 5th:
1. Alabama (13-0) [1.6882]
2. Florida (12-1) [1.2422]
3. Cincinnati (12-0) [1.2000]
4. Texas (13-0) [1.1248]
5. TCU (12-0) [1.0198]
6. Oregon (10-2) [1.0023]
7. Georgia Tech (11-2) [0.9651]
8. Boise St (13-0) [0.9495]
9. Virginia Tech (9-3) [0.8073]
10. Ohio State (10-2) [0.7910]
11. LSU (9-3) [0.7865]
12. Iowa (10-2) [0.7746]
13. Miami FL (9-3) [0.7666]
14. West Virginia (9-3) [0.6841]
15. Arizona (8-4) [0.6710]
16. Southern Cal (8-4) [0.6678]
17. Stanford (8-4) [0.6546]
18. North Carolina (8-4) [0.6454]
19. Penn State (10-2) [0.6447]
20. Pittsburgh (9-3) [0.6344]
21. Oregon St (8-4) [0.6244]
22. Brigham Young (10-2) [0.6235]
23. Georgia (7-5) [0.6216]
24. Oklahoma St (9-3) [0.6175]
25. California (8-4) [0.6021]
26. Mississippi (8-4) [0.5896]
27. South Carolina (7-5) [0.5764]
28. Clemson (8-5) [0.5750]
29. Arkansas (7-5) [0.5734]
30. Auburn (7-5) [0.5696]
31. Tennessee (7-5) [0.5425]
32. Wisconsin (9-3) [0.5406]
33. Houston (10-3) [0.5280]
34. East Carolina (9-4) [0.5162]
35. Kentucky (7-5) [0.4978]
36. Utah (9-3) [0.4977]
37. Nebraska (9-4) [0.4903]
38. Boston College (8-4) [0.4878]
39. Florida St (6-6) [0.4825]
40. Texas Tech (8-4) [0.4599]
41. Missouri (8-4) [0.4591]
42. Central Michigan (11-2) [0.4558]
43. Northwestern (8-4) [0.4454]
44. Connecticut (7-5) [0.4429]
45. Oklahoma (7-5) [0.4380]
46. Washington (5-7) [0.4369]
47. South Florida (7-5) [0.4368]
48. Mississippi St (5-7) [0.4327]
49. Troy (9-3) [0.4211]
50. Central Florida (8-4) [0.4205]
51. Fresno St (8-4) [0.4197]
52. UCLA (6-6) [0.4193]
53. Rutgers (8-4) [0.4184]
54. Navy (8-4) [0.4175]
55. Nevada (8-4) [0.4011]
56. Notre Dame (6-6) [0.3973]
57. Minnesota (6-6) [0.3862]
58. Temple (9-3) [0.3607]
59. SMU (7-5) [0.3477]
60. Middle Tennessee St (9-3) [0.3437]
61. Wake Forest (5-7) [0.3422]
62. Michigan St (6-6) [0.3296]
63. Texas A&M (6-6) [0.3279]
64. Ohio U. (9-4) [0.3254]
65. Air Force (7-5) [0.3141]
66. North Carolina St (5-7) [0.3131]
67. Purdue (5-7) [0.3102]
68. Marshall (6-6) [0.3034]
69. Wyoming (6-6) [0.3017]
70. Idaho (7-5) [0.3011]
71. Southern Miss (7-5) [0.2985]
72. Bowling Green (7-5) [0.2968]
73. Arizona St (4-8) [0.2795]
74. Iowa St (6-6) [0.2771]
75. Virginia (3-9) [0.2765]
76. Syracuse (4-8) [0.2763]
77. Kansas St (6-6) [0.2736]
78. Duke (5-7) [0.2680]
79. Kansas (5-7) [0.2590]
80. UNLV (5-7) [0.2453]
81. Hawai`i (6-7) [0.2430]
82. Baylor (4-8) [0.2417]
83. Louisville (4-8) [0.2379]
84. Michigan (5-7) [0.2319]
85. Alabama-Birmingham (5-7) [0.2182]
86. Illinois (3-9) [0.2168]
87. Louisiana-Monroe (6-6) [0.2137]
88. Colorado (3-9) [0.2120]
89. Northern Illinois (7-5) [0.2065]
90. Louisiana-Lafayette (6-6) [0.2039]
91. Utah St (4-8) [0.1998]
92. Louisiana Tech (4-8) [0.1984]
93. UTEP (4-8) [0.1947]
94. Indiana (4-8) [0.1935]
95. Vanderbilt (2-10) [0.1921]
96. Tulsa (5-7) [0.1912]
97. San Diego St (4-8) [0.1860]
98. Washington St (1-11) [0.1816]
99. Colorado St (3-9) [0.1813]
100. Maryland (2-10) [0.1808]
101. Buffalo (5-7) [0.1735]
102. Florida Atlantic (5-7) [0.1715]
103. Toledo (5-7) [0.1697]
104. Florida Int'l (3-9) [0.1677]
105. Tulane (3-9) [0.1555]
106. Kent St (5-7) [0.1471]
107. San Jose St (2-10) [0.1420]
108. New Mexico St (3-10) [0.1388]
109. Army (5-6) [0.1341]
110. Rice (2-10) [0.1262]
111. Western Michigan (5-7) [0.1256]
112. Memphis (2-10) [0.1172]
113. Arkansas St (4-8) [0.1162]
114. Miami OH (1-11) [0.1088]
115. New Mexico (1-11) [0.1048]
116. Akron (3-9) [0.1004]
117. North Texas (2-10) [0.0838]
118. Ball St (2-10) [0.0634]
119. Eastern Michigan (0-12) [-0.0003]
120. Western Kentucky (0-12) [-0.0032]
Conference Rankings (Average Per Team):
SEC 0.6927
Pac10 0.5540
BigEast 0.5414
ACC 0.5092
Big10 0.4422
Big12 0.4317
MWC 0.3860
WAC 0.3326
FBSInd 0.3163
CUSA 0.2848
MAC 0.1949
SunBelt 0.1909
Non-FBS -0.0829

Rankings through November 28th

2009-11-29T08:09:00.004-05:00

With only one week left before the bowl bids, the teams at the very top just keep on winning. Meanwhile, losses among BCS bid hopefuls Oklahoma State and Pitt have helped to slightly clarify the at-large possibilities.

First, the obvious: the winner of the SEC Championship game next weekend between Florida and Alabama will appear in the National Championship game. The loser will get one of the three BCS at-large bids. Texas will be the other half of the National Championship game if they beat Nebraska for the Big 12 Championship. TCU will get a non-AQ-group automatic bid to a BCS bowl, leaving only two at-large bids left up for grabs.

If Texas loses next weekend, they will certainly get an at-large bid, and we're going to hear lots of controversy about who should play in the National Championship game: Texas, TCU, Cincinnati (if they beat Pitt in the de facto Big East title game), or Boise State (if they win their final regular season game).

Will Boise State get an at-large bid? Let's break it down very quickly by assuming for the present argument that no three-loss team is going to get a BCS bowl bid this year (though that assumption might not be safe). This way, we take Oregon, GT, and Pitt out of at-large contention: if they win, they win the automatic bids from their respective conferences. The remaining variables then are Texas, Cincinnati, the Big Ten at-large hopefuls, and of course, Boise State has to win their regular season finale (otherwise this discussion is moot).

Assuming Boise State wins next weekend and no three-loss team gets an at-large bid, the remaining scenarios are:

If Texas and Cincy both lose next weekend, they very likely take the two remaining at-large bids, though Boise State, Iowa & Penn State fans might not be too pleased with the Cincinnati selection. More importantly, the bowl games (who ultimately make the selections) might decide a different selection is more lucrative. In any case, this scenario is bad for Boise State.

If Cincy wins and Texas loses, Texas certainly takes an at-large bid, leaving one left to go to either Boise State, Iowa, or Penn State. If the split goes the other way (Texas wins and Cincy loses), then perhaps the Cincy selection isn't quite so certain, leaving two at-large bids to split among these teams. Does Boise State get one under this scenario? I have no idea. Note this might also end up depending on the other conference championship games, in that it might be hard to rationalize an Iowa/PennSt selection over a Boise State squad ranked, say, five spots higher in the BCS Standings; but if other teams fall, the rank-order gap might narrow significantly.

Finally, the good news for Boise State: if Texas and Cincy both win next weekend, they take their respective conferences' automatic bids, leaving two at-large bids remaining. In this scenario, an undefeated Boise State is all but certain to grab a BCS bid, since the Big Ten can only take one at-large bid (to either Iowa or Penn State). The only way to deny Boise State in this scenario is to give an at-large bid to a three-loss team. So the Broncos will be cheering for the Longhorns and Bearcats, and if all three win, it looks like we'll see two non-AQ group schools in the BCS games for the first time.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 28th:
1. Alabama (12-0) [1.4900]
2. Florida (12-0) [1.4155]
3. Cincinnati (11-0) [1.1452]
4. Texas (12-0) [1.0918]
5. TCU (12-0) [1.0246]
6. Boise St (12-0) [0.9648]
7. Oregon (9-2) [0.9501]
8. Georgia Tech (10-2) [0.9121]
9. Ohio State (10-2) [0.7874]
10. Virginia Tech (9-3) [0.7827]
11. LSU (9-3) [0.7669]
12. Miami FL (9-3) [0.7656]
13. Southern Cal (8-3) [0.7645]
14. Iowa (10-2) [0.7552]
15. Pittsburgh (9-2) [0.6931]
16. Oregon St (8-3) [0.6788]
17. California (8-3) [0.6785]
18. Stanford (8-4) [0.6565]
19. Penn State (10-2) [0.6446]
20. West Virginia (8-3) [0.6358]
21. Brigham Young (10-2) [0.6218]
22. North Carolina (8-4) [0.6187]
23. Oklahoma St (9-3) [0.6181]
24. Georgia (7-5) [0.6170]
25. Clemson (8-4) [0.6148]
26. Houston (10-2) [0.5983]
27. Arizona (7-4) [0.5967]
28. South Carolina (7-5) [0.5749]
29. Mississippi (8-4) [0.5728]
30. Arkansas (7-5) [0.5678]
31. Auburn (7-5) [0.5456]
32. Tennessee (7-5) [0.5430]
33. Wisconsin (8-3) [0.5170]
34. Nebraska (9-3) [0.5057]
35. Utah (9-3) [0.4952]
36. Kentucky (7-5) [0.4924]
37. Florida St (6-6) [0.4890]
38. South Florida (7-4) [0.4845]
39. Boston College (8-4) [0.4844]
40. Texas Tech (8-4) [0.4635]
41. Rutgers (8-3) [0.4605]
42. Missouri (8-4) [0.4569]
43. East Carolina (8-4) [0.4418]
44. Northwestern (8-4) [0.4401]
45. Oklahoma (7-5) [0.4367]
46. Troy (9-3) [0.4295]
47. Mississippi St (5-7) [0.4284]
48. Central Florida (8-4) [0.4237]
49. Navy (8-4) [0.4199]
50. UCLA (6-6) [0.4165]
51. Central Michigan (10-2) [0.4135]
52. Connecticut (6-5) [0.4011]
53. Fresno St (7-4) [0.3965]
54. Nevada (8-4) [0.3957]
55. Notre Dame (6-6) [0.3933]
56. Minnesota (6-6) [0.3872]
57. Washington (4-7) [0.3808]
58. Temple (9-3) [0.3637]
59. Ohio U. (9-3) [0.3557]
60. Middle Tennessee St (9-3) [0.3467]
61. SMU (7-5) [0.3434]
62. Wake Forest (5-7) [0.3420]
63. Texas A&M (6-6) [0.3256]
64. Michigan St (6-6) [0.3248]
65. North Carolina St (5-7) [0.3189]
66. Air Force (7-5) [0.3135]
67. Purdue (5-7) [0.3067]
68. Marshall (6-6) [0.3017]
69. Bowling Green (7-5) [0.2987]
70. Southern Miss (7-5) [0.2975]
71. Wyoming (6-6) [0.2968]
72. Idaho (7-5) [0.2954]
73. Syracuse (4-8) [0.2801]
74. Iowa St (6-6) [0.2788]
75. Arizona St (4-8) [0.2766]
76. Kansas St (6-6) [0.2754]
77. Virginia (3-9) [0.2729]
78. Duke (5-7) [0.2676]
79. Kansas (5-7) [0.2584]
80. Hawai`i (6-6) [0.2518]
81. UNLV (5-7) [0.2469]
82. Baylor (4-8) [0.2397]
83. Louisville (4-8) [0.2378]
84. Michigan (5-7) [0.2292]
85. Illinois (3-8) [0.2262]
86. Alabama-Birmingham (5-7) [0.2129]
87. Louisiana-Monroe (6-6) [0.2109]
88. Colorado (3-9) [0.2088]
89. Louisiana-Lafayette (6-6) [0.2051]
90. Northern Illinois (7-5) [0.2041]
91. UTEP (4-8) [0.1987]
92. Utah St (4-8) [0.1975]
93. Vanderbilt (2-10) [0.1936]
94. Indiana (4-8) [0.1921]
95. Tulsa (5-7) [0.1916]
96. Maryland (2-10) [0.1891]
97. Florida Int'l (3-8) [0.1875]
98. San Diego St (4-8) [0.1832]
99. Washington St (1-11) [0.1824]
100. Louisiana Tech (3-8) [0.1811]
101. Colorado St (3-9) [0.1793]
102. Buffalo (5-7) [0.1768]
103. Toledo (5-7) [0.1691]
104. San Jose St (2-9) [0.1567]
105. Tulane (3-9) [0.1565]
106. Florida Atlantic (4-7) [0.1515]
107. Kent St (5-7) [0.1509]
108. Army (5-6) [0.1361]
109. Rice (2-10) [0.1264]
110. Western Michigan (5-7) [0.1248]
111. New Mexico St (3-9) [0.1220]
112. Memphis (2-10) [0.1167]
113. Arkansas St (3-8) [0.1092]
114. Miami OH (1-11) [0.1084]
115. New Mexico (1-11) [0.1035]
116. Akron (3-9) [0.1004]
117. North Texas (2-10) [0.0790]
118. Ball St (2-10) [0.0631]
119. Western Kentucky (0-11) [0.0062]
120. Eastern Michigan (0-12) [-0.0022]
Conference Rankings (Average Per Team):
SEC 0.6840
Pac10 0.5581
BigEast 0.5423
ACC 0.5048
Big10 0.4373
Big12 0.4300
MWC 0.3850
WAC 0.3290
FBSInd 0.3164
CUSA 0.2841
MAC 0.1944
SunBelt 0.1917
Non-FBS -0.0825

Rankings through November 21st

2009-11-22T08:08:00.002-05:00

Another week of wins at the top of last week's BCS Standings. The most prominent loss near the top of the Standings was LSU's confused clock management thriller at Ole Miss. Of course, other losses by Notre Dame, Kansas and Michigan make big news because coaching jobs might be on the line, but we're now most interested in the BCS Bowl bids here.

All signs continue to point to a probable Alabama/Florida v. Texas National Championship Game, though of course that might depend on teams continuing to win. That said, it's becoming conceivable that Texas could lose a game down the stretch and still appear in the National Championship (the earliest compelling argument I heard for this was on Slate's Hang Up and Listen podcast). So I continue to be most interested right now in whether Boise State will get a BCS at-large bid this year.

Without repeating yesterday's post, the LSU loss possibly hurts Boise State a little, simply because LSU wasn't going to get a BCS Bowl bid anyway (assuming Florida and Alabama get them, with only two allowed per conference). So LSU will fall from their current BCS#8 spot, and someone else who might be in the running for an at-large bid will be able to make a stronger case. Maybe I'm splitting hairs here worrying on Boise State's behalf about one loss by LSU. But there could be a lot of teams making a respectable case for an at-large bid if they don't win their conference championships: Texas plays Nebraska, GT faces Clemson, Cincy gets Pitt, and Oregon hosts Oregon State in the now de facto Pac-10 championship game. Again, we take it as a given that the loser of Florida/Alabama will get an at-large bid, and we assume that TCU will get the non-AQ-group automatic berth if they beat New Mexico next week. That leaves two at-large bids remaining, some of which could disappear to losers of the conference championship games, or even to the Big Ten.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 21st:
1. Alabama (11-0) [1.3873]
2. Florida (11-0) [1.2604]
3. Cincinnati (10-0) [1.2062]
4. Georgia Tech (10-1) [1.1521]
5. TCU (11-0) [1.1169]
6. Texas (11-0) [1.0729]
7. Oregon (9-2) [0.9538]
8. Boise St (11-0) [0.9062]
9. Pittsburgh (9-1) [0.8839]
10. Ohio State (10-2) [0.8350]
11. Virginia Tech (8-3) [0.7996]
12. Miami FL (8-3) [0.7874]
13. Iowa (10-2) [0.7809]
14. North Carolina (8-3) [0.7454]
15. Southern Cal (7-3) [0.7449]
16. Clemson (8-3) [0.7240]
17. Penn State (10-2) [0.6923]
18. California (8-3) [0.6850]
19. Oklahoma St (9-2) [0.6742]
20. Oregon St (8-3) [0.6731]
21. LSU (8-3) [0.6490]
22. Stanford (7-4) [0.6206]
23. Mississippi (8-3) [0.6025]
24. Houston (9-2) [0.5948]
25. Arizona (6-4) [0.5763]
26. Arkansas (7-4) [0.5670]
27. West Virginia (7-3) [0.5627]
28. Utah (9-2) [0.5575]
29. South Florida (7-3) [0.5547]
30. Brigham Young (9-2) [0.5481]
31. Wisconsin (8-3) [0.5401]
32. Florida St (6-5) [0.5242]
33. Auburn (7-4) [0.5063]
34. Navy (8-3) [0.5059]
35. Kentucky (7-4) [0.5029]
36. Boston College (7-4) [0.4981]
37. South Carolina (6-5) [0.4919]
38. Georgia (6-5) [0.4811]
39. Nebraska (8-3) [0.4753]
40. Rutgers (7-3) [0.4727]
41. Northwestern (8-4) [0.4598]
42. Temple (9-2) [0.4448]
43. Tennessee (6-5) [0.4446]
44. Notre Dame (6-5) [0.4387]
45. Missouri (7-4) [0.4333]
46. UCLA (6-5) [0.4262]
47. Texas Tech (7-4) [0.4256]
48. East Carolina (7-4) [0.4150]
49. Central Florida (7-4) [0.4123]
50. Minnesota (6-6) [0.4084]
51. Central Michigan (9-2) [0.4007]
52. Troy (8-3) [0.3985]
53. Connecticut (5-5) [0.3958]
54. Nevada (8-3) [0.3955]
55. Fresno St (7-4) [0.3857]
56. Washington (3-7) [0.3645]
57. Mississippi St (4-7) [0.3637]
58. Oklahoma (6-5) [0.3586]
59. Michigan St (6-6) [0.3419]
60. Wake Forest (4-7) [0.3372]
61. Southern Miss (7-4) [0.3362]
62. Marshall (6-5) [0.3341]
63. Idaho (7-4) [0.3291]
64. SMU (6-5) [0.3276]
65. Middle Tennessee St (8-3) [0.3266]
66. Purdue (5-7) [0.3241]
67. Air Force (7-5) [0.3215]
68. Syracuse (4-7) [0.3196]
69. Virginia (3-8) [0.3158]
70. Duke (5-6) [0.3154]
71. Texas A&M (6-5) [0.3116]
72. Ohio U. (8-3) [0.3014]
73. North Carolina St (4-7) [0.2844]
74. Wyoming (5-6) [0.2841]
75. Iowa St (6-6) [0.2825]
76. Arizona St (4-7) [0.2815]
77. Kansas (5-6) [0.2761]
78. Bowling Green (6-5) [0.2736]
79. Louisville (4-7) [0.2728]
80. Kansas St (6-6) [0.2699]
81. Baylor (4-7) [0.2485]
82. Michigan (5-7) [0.2481]
83. Northern Illinois (7-4) [0.2280]
84. UNLV (4-7) [0.2276]
85. Alabama-Birmingham (5-6) [0.2244]
86. Louisiana-Monroe (6-5) [0.2230]
87. Illinois (3-7) [0.2219]
88. Colorado (3-8) [0.2155]
89. Louisiana-Lafayette (6-5) [0.2121]
90. Maryland (2-9) [0.2100]
91. San Diego St (4-7) [0.2051]
92. Indiana (4-8) [0.2047]
93. Colorado St (3-8) [0.1993]
94. Hawai`i (5-6) [0.1967]
95. Toledo (5-6) [0.1940]
96. Washington St (1-10) [0.1870]
97. Vanderbilt (2-10) [0.1809]
98. Florida Int'l (3-8) [0.1781]
99. Kent St (5-6) [0.1717]
100. Louisiana Tech (3-8) [0.1702]
101. Tulsa (4-7) [0.1675]
102. Buffalo (4-7) [0.1650]
103. UTEP (3-8) [0.1637]
104. Tulane (3-8) [0.1588]
105. Utah St (3-8) [0.1586]
106. Western Michigan (5-6) [0.1557]
107. Army (5-6) [0.1415]
108. Florida Atlantic (3-7) [0.1384]
109. San Jose St (1-9) [0.1352]
110. New Mexico St (3-8) [0.1303]
111. Memphis (2-9) [0.1249]
112. Rice (2-9) [0.1204]
113. Miami OH (1-11) [0.1152]
114. Akron (2-9) [0.0997]
115. Arkansas St (2-8) [0.0908]
116. North Texas (2-9) [0.0851]
117. New Mexico (1-10) [0.0814]
118. Ball St (1-10) [0.0415]
119. Western Kentucky (0-10) [0.0134]
120. Eastern Michigan (0-11) [0.0131]
Conference Rankings (Average Per Team):
SEC 0.6198
BigEast 0.5836
ACC 0.5578
Pac10 0.5513
Big10 0.4597
Big12 0.4203
MWC 0.3935
FBSInd 0.3620
WAC 0.3119
CUSA 0.2816
MAC 0.2003
SunBelt 0.1851
Non-FBS -0.0831

Breaking Down the BCS Bowl Bids

2009-11-20T16:41:00.005-05:00

Last year in this space, we watched anxiously throughout November as Boise State tried to make its case for a BCS Bowl bid on the field, and in the Standings, only to have the last at-large bowl bid go to a lesser-ranked Ohio State team. Anyone else getting a sense of deja vu here?

Wait, you say, Boise State is currently #6 in the BCS Standings, and there are 10 BCS Bowl bids (Fiesta, Orange, Rose, Sugar, and the National Championship Game). Ah, but how do teams qualify for BCS games? In the rules, Boise State is what the latest politically correct college football language deems a "non-AQ group" school (that is, they are not from a conference with an Automatic Qualifier). A non-AQ group school can earn an automatic BCS berth if they do well enough in the Standings; but the rules are also very explicit that "No more than one such team from the non-AQ group shall earn an automatic berth in any year." Last year, that berth went to Utah. This year, if both TCU and Boise State win out, it will almost certainly go to TCU.

So does Boise State have any shot at getting an at-large selection this year? First, it obviously depends on their winning out; if they lose, their BCS bid is finished. Second, it depends on who wins the AQ conferences, because those winners take 6 of the 10 spots. If TCU wins out, they'll almost certainly take a 7th automatic qualification (and if they don't, then the discussion simplifies because an undefeated Boise State would get it instead). So who will get the other three at-large spots? The SEC runner-up, definitely a given. If Texas doesn't win the Big 12, they would almost certainly still be in the running for a bid. So there may be either one or two more slots for Boise State to try to take.

Remembering that BCS at-large bids do not need to follow the BCS Standings beyond a top-14 requirement (as when Ohio State was selected over Boise State last year), it's perhaps still reasonable to look at the top teams in the Standings to see who else might legitimately get selected over a non-automatic Boise State. In the Big East, Cincinnati is currently #5 and Pitt is #9, and obviously only one of them will win that conference. At #7, Georgia Tech might be a candidate for an at-large bid if they fail to win the ACC. Luckily for Boise State, #8 LSU is not a worry right now because each conference can only get two bids, and we already counted two to the SEC. Meanwhile, #10 Ohio State has already wrapped up the Big Ten, which is also good for Boise State. In contrast, #11 Oregon is still fighting in the Pac-10, and #12 Oklahoma State won last night to increase their chances. And the financial incentives for the bowl games built into the at-large selections might cause one to look at a second Big Ten school, with Iowa at #13 and Penn State at #14.

That's a lot of teams fighting for at most two spots. While some of the confusion might clarify this weekend or next, much might remain unresolved until the conference championships.

----

Unsurprisingly, we aren't the only ones who have been talking about Boise State's BCS at-large chances. See also:

PR firm hired to make push for Boise St.

Boise State still in line for at-large

Boise State fans need to pull for Texas, root against Oklahoma State

A backlog of Trent McCotter's columns

2009-11-18T03:47:00.002-05:00

Apparently Trent McCotter's brief stint writing thought-provoking articles about stats and sports for the News & Observer has come to an end. I'm disappointed by this, because I enjoyed each of his columns (not just the two we previously linked to from here). Indeed, I've been asking him every week for the past month whether a new one was coming or not. His columns were concise, and I know Trent well enough to know that he could have found a lot more to write about each topic. I'm certain it can't be an easy task to condense such thoughts into the strictly allotted newspaper space.

Trent's stories that appeared are still online:

How to fix the 'perfect game'

Zimmerman best in state at hitting streaks

'Tiger-proofing' golf courses yields surprises

Time to monkey around with BCS?

Ichiro a version of Wee Willie Keeler

The 'hot hand' in basketball: Does it exist?

Statistics gaffes highlight sports history

When is a conversion worth the risk?

Rankings through November 14th

2009-11-15T08:16:00.003-05:00

No big changes at the top of the RWFL rankings this week.

TCU solidified their position across various p bias values---if you look at the plot below the list of ranks, their win against Utah definitely helps in general, but still leaves them in fourth-place at the selected p=0.75 value posted here. This might help solidify TCU's narrowly-held #4 position in the BCS Standings, since they were already ahead of Cincinnati in both polls and should now do better than before in the computer component. But of course TCU will still be behind Texas in the BCS Standings, since they were already ahead of Texas in the composite of the computers and were still well behind Texas in the Standings.

That is, unless someone loses, we seem to be on course for a championship game between Texas and the winner of the Florida-Alabama "semifinal" SEC Championship game. TCU is on course for an automatic BCS bowl game berth; in contrast, Boise State's relatively weaker strength of schedule continues to leave them later in the discussion. Because of the wrinkles in the rules that only give one automatic BCS bid to the "non-AQ group", Boise State will possibly be hoping for one of the at-large bids, and those at-large bids do not have to follow the BCS Standings, as Boise State learned all too well last year when they watched a lower-rated Ohio State team take the last BCS bid.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 14th:
1. Alabama (10-0) [1.4580]
2. Florida (10-0) [1.3715]
3. Cincinnati (10-0) [1.1665]
4. TCU (10-0) [1.1513]
5. Georgia Tech (10-1) [1.1157]
6. Texas (10-0) [1.0832]
7. Boise St (10-0) [0.9626]
8. Oregon (8-2) [0.9185]
9. Pittsburgh (9-1) [0.8749]
10. Ohio State (9-2) [0.8747]
11. Iowa (9-2) [0.8048]
12. LSU (8-2) [0.7904]
13. Southern Cal (7-3) [0.7818]
14. Virginia Tech (7-3) [0.7656]
15. Miami FL (7-3) [0.7521]
16. Stanford (7-3) [0.7219]
17. Clemson (7-3) [0.7040]
18. Oregon St (7-3) [0.6998]
19. Oklahoma St (8-2) [0.6666]
20. Penn State (9-2) [0.6635]
21. Arizona (6-3) [0.6618]
22. Wisconsin (8-2) [0.6567]
23. North Carolina (7-3) [0.6480]
24. California (7-3) [0.6326]
25. Houston (8-2) [0.6094]
26. Utah (8-2) [0.5507]
27. Boston College (7-3) [0.5498]
28. Georgia (6-4) [0.5491]
29. Arkansas (6-4) [0.5351]
30. Navy (8-3) [0.5326]
31. Rutgers (7-2) [0.5299]
32. Brigham Young (8-2) [0.5200]
33. Mississippi (7-3) [0.5192]
34. Notre Dame (6-4) [0.5182]
35. West Virginia (7-3) [0.5174]
36. South Florida (6-3) [0.5016]
37. Auburn (7-4) [0.4948]
38. Florida St (5-5) [0.4892]
39. South Carolina (6-5) [0.4885]
40. Kentucky (6-4) [0.4662]
41. Nebraska (7-3) [0.4464]
42. Tennessee (5-5) [0.4407]
43. Temple (8-2) [0.4321]
44. Minnesota (6-5) [0.4253]
45. UCLA (5-5) [0.4175]
46. Central Michigan (8-2) [0.4161]
47. Northwestern (7-4) [0.4023]
48. Nevada (7-3) [0.4020]
49. Missouri (6-4) [0.4008]
50. Mississippi St (4-6) [0.4004]
51. Troy (7-3) [0.3978]
52. Washington (3-7) [0.3974]
53. Oklahoma (6-4) [0.3954]
54. Fresno St (6-4) [0.3905]
55. Central Florida (6-4) [0.3814]
56. Texas Tech (6-4) [0.3731]
57. SMU (6-4) [0.3699]
58. Michigan St (6-5) [0.3674]
59. Idaho (7-4) [0.3505]
60. East Carolina (5-4) [0.3505]
61. Air Force (7-4) [0.3443]
62. Wake Forest (4-7) [0.3439]
63. Connecticut (4-5) [0.3345]
64. Purdue (4-7) [0.3231]
65. Virginia (3-7) [0.3212]
66. Arizona St (4-6) [0.3201]
67. Middle Tennessee St (7-3) [0.3143]
68. Duke (5-5) [0.3137]
69. Southern Miss (6-4) [0.3070]
70. Iowa St (6-5) [0.3040]
71. North Carolina St (4-6) [0.2888]
72. Marshall (5-5) [0.2861]
73. Kansas St (6-5) [0.2809]
74. Texas A&M (5-5) [0.2760]
75. Baylor (4-6) [0.2692]
76. Ohio U. (7-3) [0.2686]
77. Northern Illinois (7-3) [0.2680]
78. Louisville (4-6) [0.2678]
79. Kansas (5-5) [0.2672]
80. Wyoming (5-5) [0.2672]
81. Michigan (5-6) [0.2657]
82. Bowling Green (5-5) [0.2629]
83. Syracuse (3-7) [0.2547]
84. Louisiana-Monroe (6-4) [0.2545]
85. Alabama-Birmingham (5-5) [0.2298]
86. Colorado St (3-7) [0.2291]
87. Indiana (4-7) [0.2266]
88. UNLV (4-7) [0.2246]
89. Illinois (3-7) [0.2220]
90. Maryland (2-8) [0.2139]
91. San Diego St (4-6) [0.2120]
92. Colorado (3-7) [0.2109]
93. Washington St (1-9) [0.1993]
94. Tulsa (4-5) [0.1976]
95. UTEP (3-7) [0.1941]
96. Toledo (4-6) [0.1931]
97. Vanderbilt (2-9) [0.1914]
98. Louisiana-Lafayette (5-5) [0.1894]
99. Hawai`i (4-6) [0.1863]
100. Louisiana Tech (3-7) [0.1856]
101. Kent St (5-5) [0.1831]
102. Tulane (3-7) [0.1678]
103. San Jose St (1-8) [0.1599]
104. Western Michigan (5-6) [0.1574]
105. Florida Int'l (3-7) [0.1571]
106. Buffalo (3-7) [0.1481]
107. Utah St (3-7) [0.1453]
108. Florida Atlantic (3-6) [0.1425]
109. New Mexico St (3-7) [0.1328]
110. Army (4-6) [0.1321]
111. Miami OH (1-10) [0.1248]
112. Memphis (2-8) [0.1102]
113. Akron (2-8) [0.1020]
114. North Texas (2-8) [0.0981]
115. Rice (1-9) [0.0951]
116. Arkansas St (2-7) [0.0923]
117. New Mexico (0-10) [0.0460]
118. Ball St (1-9) [0.0344]
119. Eastern Michigan (0-10) [0.0140]
120. Western Kentucky (0-10) [0.0125]
Conference Rankings (Average Per Team):
SEC 0.6421
Pac10 0.5751
BigEast 0.5559
ACC 0.5422
Big10 0.4756
Big12 0.4145
FBSInd 0.3943
MWC 0.3939
WAC 0.3239
CUSA 0.2749
MAC 0.2004
SunBelt 0.1843
Non-FBS -0.0836

Rankings through November 7th

2009-11-08T05:08:00.002-05:00

Two key losses this week effectively eliminate the title hopes of both Iowa and Oregon. Whatever our own rankings say below, it seems clear that the BCS is on a likely trajectory to a championship game between Texas and the winner of the Florida-Alabama "national semi-final" SEC Championship Game. Of course, if someone stumbles, Cincinnati, TCU & Boise State are all there waiting and hoping...

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 7th:
1. Alabama (9-0) [1.4886]
2. Florida (9-0) [1.3796]
3. Cincinnati (9-0) [1.1104]
4. TCU (9-0) [1.0754]
5. Georgia Tech (9-1) [1.0749]
6. Texas (9-0) [1.0623]
7. Iowa (9-1) [0.9969]
8. Boise St (9-0) [0.9968]
9. Oregon (7-2) [0.9503]
10. Southern Cal (7-2) [0.8936]
11. Miami FL (7-2) [0.8435]
12. LSU (7-2) [0.8376]
13. Ohio State (8-2) [0.7920]
14. Pittsburgh (8-1) [0.7876]
15. Arizona (6-2) [0.7793]
16. Virginia Tech (6-3) [0.7577]
17. Houston (8-1) [0.7383]
18. Penn State (8-2) [0.6932]
19. Wisconsin (7-2) [0.6782]
20. Clemson (6-3) [0.6766]
21. Stanford (6-3) [0.6530]
22. Oregon St (6-3) [0.6506]
23. Oklahoma St (7-2) [0.5992]
24. South Florida (6-2) [0.5860]
25. Utah (8-1) [0.5841]
26. Notre Dame (6-3) [0.5727]
27. West Virginia (7-2) [0.5629]
28. Auburn (7-3) [0.5611]
29. California (6-3) [0.5426]
30. Brigham Young (7-2) [0.5242]
31. North Carolina (6-3) [0.5139]
32. Arkansas (5-4) [0.5073]
33. Navy (7-3) [0.5064]
34. Boston College (6-3) [0.5047]
35. Georgia (5-4) [0.4917]
36. Tennessee (5-4) [0.4911]
37. South Carolina (6-4) [0.4844]
38. Kentucky (5-4) [0.4713]
39. Mississippi (6-3) [0.4702]
40. Washington (3-6) [0.4643]
41. Troy (7-2) [0.4590]
42. Fresno St (6-3) [0.4577]
43. Temple (7-2) [0.4420]
44. Florida St (4-5) [0.4358]
45. UCLA (4-5) [0.4302]
46. Northwestern (6-4) [0.4300]
47. Texas Tech (6-3) [0.4225]
48. Rutgers (6-2) [0.4216]
49. Minnesota (5-5) [0.4131]
50. Nebraska (6-3) [0.4129]
51. Central Michigan (7-2) [0.4061]
52. Mississippi St (4-5) [0.4012]
53. Oklahoma (5-4) [0.3762]
54. Idaho (7-3) [0.3761]
55. Purdue (4-6) [0.3604]
56. Wake Forest (4-6) [0.3598]
57. Michigan St (5-5) [0.3564]
58. Missouri (5-4) [0.3527]
59. SMU (5-4) [0.3354]
60. Kansas St (6-4) [0.3331]
61. Nevada (5-3) [0.3309]
62. Arizona St (4-5) [0.3285]
63. Marshall (5-4) [0.3240]
64. Virginia (3-6) [0.3201]
65. East Carolina (5-4) [0.3191]
66. Air Force (6-4) [0.3105]
67. Connecticut (4-5) [0.3095]
68. Michigan (5-5) [0.3061]
69. Texas A&M (5-4) [0.3045]
70. Duke (5-4) [0.2961]
71. Middle Tennessee St (6-3) [0.2948]
72. Kansas (5-4) [0.2913]
73. Syracuse (3-6) [0.2911]
74. Central Florida (5-4) [0.2905]
75. Iowa St (5-5) [0.2848]
76. North Carolina St (4-5) [0.2840]
77. Northern Illinois (6-3) [0.2838]
78. Ohio U. (6-3) [0.2678]
79. Southern Miss (5-4) [0.2672]
80. Louisiana-Monroe (5-4) [0.2636]
81. Bowling Green (4-5) [0.2630]
82. Indiana (4-6) [0.2499]
83. Baylor (4-5) [0.2470]
84. Illinois (3-6) [0.2449]
85. Wyoming (4-5) [0.2381]
86. Colorado (3-6) [0.2381]
87. UTEP (3-6) [0.2364]
88. San Diego St (4-5) [0.2363]
89. Louisville (3-6) [0.2342]
90. UNLV (4-6) [0.2334]
91. Louisiana-Lafayette (5-4) [0.2290]
92. Colorado St (3-7) [0.2200]
93. San Jose St (1-6) [0.2162]
94. Toledo (4-5) [0.2149]
95. Alabama-Birmingham (4-5) [0.2137]
96. Washington St (1-8) [0.2132]
97. Tulane (3-6) [0.2061]
98. Tulsa (4-5) [0.2033]
99. Maryland (2-7) [0.1981]
100. Vanderbilt (2-8) [0.1888]
101. Kent St (5-5) [0.1836]
102. Louisiana Tech (3-6) [0.1767]
103. Hawai`i (3-6) [0.1746]
104. Western Michigan (4-6) [0.1652]
105. Buffalo (3-6) [0.1614]
106. New Mexico St (3-6) [0.1511]
107. Florida Int'l (2-7) [0.1494]
108. Miami OH (1-9) [0.1402]
109. Florida Atlantic (2-6) [0.1293]
110. Utah St (2-7) [0.1288]
111. Army (3-6) [0.1255]
112. North Texas (2-7) [0.1241]
113. Arkansas St (2-6) [0.1226]
114. Memphis (2-7) [0.1217]
115. Akron (2-7) [0.1106]
116. Rice (0-9) [0.0540]
117. Ball St (1-8) [0.0483]
118. New Mexico (0-9) [0.0421]
119. Western Kentucky (0-9) [0.0270]
120. Eastern Michigan (0-9) [0.0251]
Conference Rankings (Average Per Team):
SEC 0.6477
Pac10 0.5906
BigEast 0.5379
ACC 0.5221
Big10 0.5019
Big12 0.4104
FBSInd 0.4016
MWC 0.3849
WAC 0.3343
CUSA 0.2758
MAC 0.2086
SunBelt 0.1999
Non-FBS -0.0842

Rankings through October 31st

2009-11-01T08:51:00.003-05:00

The undefeated teams all won again, with Iowa adding to their catalog of close calls. That said, you have to give the Hawkeyes credit: wins are wins. We have a lot of football left to play this season, so virtually anything can happen. Certainly Iowa has some big games left on their schedule. However, if Iowa continues to win and there's any BCS controversy down the stretch, I'd expect the off-season BCS discussions to include reconsideration of the rules which prevent computer rankings from including margin of victory.

In the meantime, I'd be surprised if Iowa falls much in this week's official BCS Standings, if at all, since they were already only #8 in both polls last week. Oregon, after their impressive victory over USC, is the obvious candidate to potentially pass Iowa. TCU, Boise State, and Cincinnati were each already ahead of Iowa in the polls, but behind Iowa in the total standings because of the computer ranking component, and it's hard for me to see how that will change.

Speaking of the remaining BCS busters, we have double intrigue waiting for the official BCS Standings this week. First, I'm interested to see whether BCS#6 TCU stays ahead of BCS#7 Boise State in this week's Standings. Boise State, already ahead of TCU in both polls last week, is likely to get a small boost in the computer rankings from the follow-on effect of Oregon's victory over USC, given Boise State's season-opening win over Oregon. Will it be enough to pass TCU in the official Standings? Second, we eagerly wait to see the relative rankings between Oregon and Boise State. The Ducks will undoubtedly get a big boost across all the BCS components this week, but will it be enough to pass the Broncos, the only team to beat them on the field this season?

Using the random walker rankings across various p values as an imperfect proxy for other rankings, the closeness of these questions regarding Boise State are evident in the figure presented here below the p=0.75 rankings. Boise State is ranked higher than TCU for p > 0.7 (approximately) and higher than Oregon for p > 0.8. In other words, very slight changes in the methodology (e.g., changing the p value) can reasonably have big effects in the rank ordering in this situation.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 31st:
1. Florida (8-0) [1.5226]
2. Iowa (9-0) [1.3781]
3. Alabama (8-0) [1.3288]
4. Oregon (7-1) [1.2656]
5. Boise St (8-0) [1.1549]
6. Texas (8-0) [1.1480]
7. TCU (8-0) [1.0819]
8. Cincinnati (8-0) [1.0588]
9. Georgia Tech (8-1) [1.0200]
10. LSU (7-1) [0.9699]
11. Southern Cal (6-2) [0.9276]
12. Penn State (8-1) [0.8159]
13. Miami FL (6-2) [0.7950]
14. Arizona (5-2) [0.7487]
15. Houston (7-1) [0.7412]
16. Pittsburgh (7-1) [0.7346]
17. Virginia Tech (5-3) [0.7173]
18. Notre Dame (6-2) [0.7120]
19. Wisconsin (6-2) [0.6726]
20. Utah (7-1) [0.6687]
21. California (6-2) [0.6666]
22. Ohio State (7-2) [0.6604]
23. Oklahoma St (6-2) [0.6069]
24. Clemson (5-3) [0.5981]
25. South Florida (6-2) [0.5667]
26. Auburn (6-3) [0.5600]
27. Washington (3-5) [0.5577]
28. West Virginia (6-2) [0.5328]
29. Oregon St (5-3) [0.5319]
30. South Carolina (6-3) [0.5292]
31. Brigham Young (6-2) [0.5189]
32. Georgia (4-4) [0.5091]
33. Boston College (6-3) [0.5045]
34. Stanford (5-3) [0.5002]
35. Tennessee (4-4) [0.4980]
36. Troy (6-2) [0.4887]
37. Kentucky (4-4) [0.4732]
38. North Carolina (5-3) [0.4711]
39. Florida St (4-4) [0.4556]
40. Arkansas (4-4) [0.4500]
41. Minnesota (5-4) [0.4463]
42. Idaho (7-2) [0.4406]
43. Oklahoma (5-3) [0.4341]
44. Texas Tech (6-3) [0.4313]
45. Mississippi (5-3) [0.4245]
46. Fresno St (5-3) [0.4179]
47. Central Michigan (7-2) [0.4109]
48. Missouri (5-3) [0.4108]
49. Rutgers (6-2) [0.4092]
50. Temple (6-2) [0.4047]
51. Mississippi St (4-5) [0.4026]
52. Michigan (5-4) [0.4012]
53. Navy (6-3) [0.3883]
54. UCLA (3-5) [0.3765]
55. Nebraska (5-3) [0.3680]
56. Kansas (5-3) [0.3633]
57. Texas A&M (5-3) [0.3633]
58. Michigan St (4-5) [0.3583]
59. Marshall (5-3) [0.3572]
60. Nevada (5-3) [0.3554]
61. Arizona St (4-4) [0.3493]
62. Duke (5-3) [0.3388]
63. SMU (4-4) [0.3271]
64. Virginia (3-5) [0.3258]
65. Iowa St (5-4) [0.3229]
66. Wake Forest (4-5) [0.3193]
67. Purdue (3-6) [0.3192]
68. East Carolina (5-3) [0.3141]
69. Kansas St (5-4) [0.3081]
70. Air Force (5-4) [0.3060]
71. Connecticut (4-4) [0.2868]
72. UTEP (3-5) [0.2821]
73. Northern Illinois (5-3) [0.2799]
74. Syracuse (3-5) [0.2797]
75. Northwestern (5-4) [0.2788]
76. Ohio U. (6-3) [0.2776]
77. Middle Tennessee St (5-3) [0.2723]
78. Bowling Green (3-5) [0.2686]
79. Louisiana-Monroe (4-4) [0.2655]
80. Indiana (4-5) [0.2628]
81. Wyoming (4-4) [0.2608]
82. Colorado St (3-6) [0.2544]
83. North Carolina St (3-5) [0.2542]
84. Southern Miss (5-4) [0.2541]
85. Louisville (3-5) [0.2489]
86. San Jose St (1-6) [0.2317]
87. Washington St (1-7) [0.2299]
88. San Diego St (4-4) [0.2258]
89. Kent St (5-4) [0.2189]
90. Colorado (2-6) [0.2176]
91. Maryland (2-6) [0.2113]
92. Central Florida (4-3) [0.2107]
93. Tulsa (4-4) [0.2093]
94. Louisiana-Lafayette (4-4) [0.2077]
95. UNLV (3-6) [0.2069]
96. Illinois (2-6) [0.2042]
97. Alabama-Birmingham (3-5) [0.2037]
98. Toledo (4-5) [0.2018]
99. Baylor (3-5) [0.1968]
100. Western Michigan (4-5) [0.1901]
101. Buffalo (3-5) [0.1798]
102. Tulane (2-6) [0.1780]
103. Hawai`i (2-6) [0.1666]
104. Arkansas St (2-5) [0.1647]
105. Vanderbilt (2-7) [0.1580]
106. Utah St (2-6) [0.1555]
107. Louisiana Tech (3-5) [0.1539]
108. Florida Int'l (2-6) [0.1537]
109. New Mexico St (3-6) [0.1476]
110. Miami OH (1-8) [0.1444]
111. Florida Atlantic (2-5) [0.1443]
112. Army (3-5) [0.1292]
113. North Texas (2-6) [0.1264]
114. Memphis (2-6) [0.1161]
115. Akron (1-7) [0.0875]
116. Ball St (1-8) [0.0440]
117. Rice (0-8) [0.0391]
118. New Mexico (0-8) [0.0277]
119. Eastern Michigan (0-8) [0.0183]
120. Western Kentucky (0-8) [0.0063]
Conference Rankings (Average Per Team):
SEC 0.6522
Pac10 0.6154
Big10 0.5271
BigEast 0.5147
ACC 0.5009
Big12 0.4309
FBSInd 0.4098
MWC 0.3946
WAC 0.3582
CUSA 0.2694
MAC 0.2097
SunBelt 0.2033
Non-FBS -0.0854

Concise Definition of RWFL Rankings

2009-11-01T08:18:00.003-05:00

The general mathematical description of the random walker (RW) ranking methodology is presented as a sidebar on p.889 of ''The Bowl Championship Series: A Mathematical Review,'' T. Callaghan, P. J. Mucha and M. A. Porter, Notices of the American Mathematical Society 51, 887-893 (2004). These RW rankings, which amount to an amalgamation of first-place votes, depend on a bias value p setting the extent to which random walkers respect each individual game outcome.

The RWFL rankings at bias value p are calculated by the difference between first-place votes (following game winners) and last-place votes (following game losers). This is equivalent to subtracting RW at bias value (1-p) from RW at bias value p.

Starting in November 2009, all of our rankings are calculated on the full connected network of teams connected by games played, of which the FBS teams are a relatively small subset (even when we only report the FBS results). Prior to November 2009, our weekly rankings treated all non-FBS teams as a single catch-all "team" (who played a lot of games). However, our bowl predictions have used the full connected network in previous seasons. See this post for more discussion about this switch and its consequences.

Got Math? Part Two: The Consequences

2009-10-31T17:10:00.003-04:00

In an earlier post, we explored the remarkable similarities between our RWFL rankings posted on Kenneth Massey's comparisons page, using our selected p=0.75 bias value, and Eugene Potemkin's E-Ratings. Through completely independent rationalizations, we ended up at equivalent linear algebra problems that we each solved to reach our rankings.

Well, this didn't seem to be adding much value to the comparisons, so Kenneth nicely asked me if we would do something to make sure ours were unique. So we're going to tweak our algorithm used to bring you weekly rankings, though we're going to do so in a logically consistent way. From now on, we're going to bring you the RWFL rankings as obtained by running the algorithm on the full set of 716 connected college football teams that include the FBS (that is, including all the FCS and DivII schools that play against the FBS, and all the schools who play them, etc.), and we'll report the ordered results from the FBS. This isn't actually "new" per se for us, as these are the rankings we've been using for our bowl predictions the past two years, because we think in principle they should be better. We just didn't want to spring a change without a compelling reason; needing to do something distinct from the E-Ratings is certainly a good enough reason.

If you decide you liked the old RWFL run on the FBS plus a single made-up catch-all non-FBS team, don't worry: you can still see those as the E-Ratings in Massey's comparisons. Indeed, comparing and contrasting the two should be interesting, in that the difference is all because of the treatment of the non-FBS teams, emphasizing the follow-on indirect effects present in the rankings.

An interesting part about this switch has to do with the only other change we've ever made in our rankings. Back in the original days of the Random Walker rankings, when all of us involved were all still at Georgia Tech, our "RW" rankings were just the linear algebra problem described in our manuscripts (which you can reach quickly from the sidebar), describing walkers with first-place votes. As noted at the end of our American Mathematical Monthly paper, there were a lot of reasons to expect improvement using this along with a second set of walkers, with last-place votes. For years, we've simply subtracted these second vote counts from the first to give the RWFL rankings ("Random Walkers First-Last").

But on the whole connected network of 716 teams, very little total weight of those last-place votes ends up in the FBS at all, so the rankings of the FBS teams are only very slightly modified by the last-place piece. One might argue that it would be more interesting to look at ratios instead of differences between the first-place and last-place votes, but that's not something we're going to do without some mathematical and computational investigation first.

Without further ado, as a means of comparison, let's back up to the beginning of the week (not just so we can relive the Carolina victory over Virginia Tech). The rankings listed below with the full connected set of teams definitely differs in some places from the old, simpler setting.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 24th:
1. Iowa (8-0) [1.5817]
2. Florida (7-0) [1.5259]
3. Alabama (8-0) [1.5150]
4. Boise St (7-0) [1.1477]
5. TCU (7-0) [1.1042]
6. Southern Cal (6-1) [1.0839]
7. Oregon (6-1) [1.0780]
8. Texas (7-0) [1.0615]
9. LSU (6-1) [1.0351]
10. Georgia Tech (7-1) [1.0196]
11. Cincinnati (7-0) [0.9606]
12. Virginia Tech (5-2) [0.8658]
13. Arizona (5-2) [0.8354]
14. Penn State (7-1) [0.7979]
15. Miami FL (5-2) [0.7636]
16. Notre Dame (5-2) [0.7396]
17. South Carolina (6-2) [0.7216]
18. Pittsburgh (7-1) [0.7082]
19. Houston (6-1) [0.7080]
20. Oklahoma St (6-1) [0.6849]
21. Ohio State (6-2) [0.6686]
22. West Virginia (6-1) [0.6671]
23. Wisconsin (5-2) [0.6599]
24. California (5-2) [0.6102]
25. Utah (6-1) [0.5987]
26. Clemson (4-3) [0.5983]
27. Washington (3-5) [0.5971]
28. Georgia (4-3) [0.5816]
29. Kentucky (4-3) [0.5785]
30. Central Michigan (7-1) [0.5483]
31. Stanford (5-3) [0.5317]
32. Auburn (5-3) [0.5246]
33. Mississippi (5-2) [0.5227]
34. Michigan (5-3) [0.5090]
35. Oregon St (4-3) [0.5085]
36. Brigham Young (6-2) [0.4973]
37. Arkansas (3-4) [0.4728]
38. Kansas (5-2) [0.4617]
39. Navy (6-2) [0.4476]
40. Tennessee (3-4) [0.4473]
41. Boston College (5-3) [0.4472]
42. Troy (5-2) [0.4423]
43. Idaho (6-2) [0.4359]
44. Michigan St (4-4) [0.4309]
45. South Florida (5-2) [0.4255]
46. Oklahoma (4-3) [0.4157]
47. UCLA (3-4) [0.4119]
48. Arizona St (4-3) [0.4097]
49. Fresno St (4-3) [0.4068]
50. Iowa St (5-3) [0.3971]
51. Minnesota (4-4) [0.3863]
52. Nebraska (4-3) [0.3834]
53. Florida St (3-4) [0.3770]
54. Texas Tech (5-3) [0.3711]
55. Kansas St (5-3) [0.3708]
56. Marshall (5-3) [0.3688]
57. Missouri (4-3) [0.3631]
58. Virginia (3-4) [0.3422]
59. Wake Forest (4-4) [0.3391]
60. Rutgers (5-2) [0.3358]
61. Temple (5-2) [0.3357]
62. Mississippi St (3-5) [0.3356]
63. UTEP (3-4) [0.3356]
64. Nevada (4-3) [0.3286]
65. North Carolina (4-3) [0.3278]
66. Connecticut (4-3) [0.3232]
67. Purdue (3-5) [0.3231]
68. Louisiana-Monroe (4-3) [0.3146]
69. Duke (4-3) [0.3062]
70. SMU (3-4) [0.2991]
71. Texas A&M (4-3) [0.2976]
72. East Carolina (4-3) [0.2973]
73. North Carolina St (3-4) [0.2907]
74. Louisiana-Lafayette (4-3) [0.2842]
75. Colorado St (3-5) [0.2837]
76. Northern Illinois (4-3) [0.2814]
77. Southern Miss (5-3) [0.2748]
78. Wyoming (4-3) [0.2716]
79. Ohio U. (5-3) [0.2709]
80. Colorado (2-5) [0.2703]
81. Northwestern (5-3) [0.2684]
82. Air Force (4-4) [0.2677]
83. Bowling Green (3-5) [0.2592]
84. Syracuse (3-4) [0.2571]
85. Middle Tennessee St (4-3) [0.2457]
86. Toledo (4-4) [0.2452]
87. Western Michigan (4-4) [0.2379]
88. Indiana (4-4) [0.2353]
89. Tulsa (4-3) [0.2344]
90. Washington St (1-6) [0.2296]
91. Baylor (3-4) [0.2288]
92. Louisville (2-5) [0.2238]
93. Central Florida (4-3) [0.2203]
94. San Jose St (1-5) [0.2175]
95. San Diego St (3-4) [0.2165]
96. Arkansas St (2-4) [0.2080]
97. Buffalo (3-5) [0.2024]
98. Florida Atlantic (2-4) [0.2010]
99. Maryland (2-6) [0.1958]
100. Hawai`i (2-5) [0.1819]
101. Kent St (4-4) [0.1814]
102. UNLV (3-5) [0.1725]
103. Louisiana Tech (3-4) [0.1615]
104. Alabama-Birmingham (2-5) [0.1571]
105. Tulane (2-5) [0.1545]
106. Vanderbilt (2-6) [0.1516]
107. Utah St (2-5) [0.1453]
108. New Mexico St (3-5) [0.1423]
109. Memphis (2-5) [0.1413]
110. Illinois (1-6) [0.1366]
111. North Texas (1-6) [0.1264]
112. Florida Int'l (1-6) [0.1256]
113. Army (3-5) [0.1185]
114. Miami OH (0-8) [0.1078]
115. Akron (1-6) [0.1038]
116. Ball St (1-7) [0.0379]
117. Rice (0-8) [0.0368]
118. New Mexico (0-7) [0.0185]
119. Western Kentucky (0-7) [0.0139]
120. Eastern Michigan (0-7) [0.0083]
Conference Rankings (Average Per Team):
SEC 0.7010
Pac10 0.6296
Big10 0.5452
ACC 0.4894
BigEast 0.4877
Big12 0.4422
FBSInd 0.4353
MWC 0.3812
WAC 0.3519
CUSA 0.2690
SunBelt 0.2180
MAC 0.2169
Non-FBS -0.0867

Rankings through October 24th

2009-10-25T08:49:00.003-04:00

Many of the top teams won easily yesterday, while both Iowa and Alabama maintained their undefeated records through end-of-game heroics. But to these rankings, a win is a win, period.

Comparing with last week's RWFL ranking, there has been significant shakeup in the ordering of the teams immediately following the top 4. GT and VT both fall a few spots because of Miami's loss to Clemson (the intertwined nature of these three teams was discussed last week). In contrast, USC jumped a number of spots, presumably due to similar secondary effects from victories obtained by teams they previously beat (e.g., Ohio State and Notre Dame). We note the very close net vote percentages in square brackets, from #5 USC [1.6882] down to #9 Boise State [1.6228], with the difference between #5 and #7 in the fourth digit after the decimal point (under rounding). That's really close, so future secondary effects could continue to shake up these rankings, while we await more losses among the top 10 to hopefully decide things.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 24th:
1. Florida (7-0) [2.5831]
2. Iowa (8-0) [2.5206]
3. Alabama (8-0) [2.4836]
4. Texas (7-0) [1.8001]
5. Southern Cal (6-1) [1.6882]
6. TCU (7-0) [1.6881]
7. Oregon (6-1) [1.6879]
8. LSU (6-1) [1.6597]
9. Boise St (7-0) [1.6228]
10. Cincinnati (7-0) [1.5428]
11. Georgia Tech (7-1) [1.5167]
12. Virginia Tech (5-2) [1.2926]
13. Arizona (5-2) [1.0958]
14. Notre Dame (5-2) [1.0319]
15. Miami FL (5-2) [0.9884]
16. Penn State (7-1) [0.9727]
17. Pittsburgh (7-1) [0.9532]
18. Houston (6-1) [0.9350]
19. South Carolina (6-2) [0.8567]
20. Oklahoma St (6-1) [0.8559]
21. Wisconsin (5-2) [0.8480]
22. Ohio State (6-2) [0.8447]
23. Utah (6-1) [0.8052]
24. West Virginia (6-1) [0.7966]
25. California (5-2) [0.6695]
26. Kentucky (4-3) [0.6415]
27. Washington (3-5) [0.6179]
28. Georgia (4-3) [0.6150]
29. Clemson (4-3) [0.5506]
30. Brigham Young (6-2) [0.5400]
31. Oregon St (4-3) [0.5221]
32. Stanford (5-3) [0.5134]
33. Mississippi (5-2) [0.4995]
34. Central Michigan (7-1) [0.4918]
35. Auburn (5-3) [0.4483]
36. Kansas (5-2) [0.3811]
37. Idaho (6-2) [0.3730]
38. Boston College (5-3) [0.3716]
39. Oklahoma (4-3) [0.3697]
40. Michigan (5-3) [0.3167]
41. Arkansas (3-4) [0.2987]
42. Navy (6-2) [0.2916]
43. Troy (5-2) [0.2619]
44. Arizona St (4-3) [0.2591]
45. UCLA (3-4) [0.2513]
46. Minnesota (4-4) [0.2418]
47. Iowa St (5-3) [0.2333]
48. Nebraska (4-3) [0.2251]
49. Michigan St (4-4) [0.2172]
50. South Florida (5-2) [0.2126]
51. Missouri (4-3) [0.1572]
52. Tennessee (3-4) [0.1469]
53. Fresno St (4-3) [0.1418]
54. Rutgers (5-2) [0.1200]
55. Nevada (4-3) [0.0854]
56. Connecticut (4-3) [0.0675]
57. Texas Tech (5-3) [0.0539]
58. Florida St (3-4) [0.0486]
59. Louisiana-Monroe (4-3) [0.0448]
60. Marshall (5-3) [0.0350]
61. Mississippi St (3-5) [0.0117]
62. Kansas St (5-3) [0.0113]
63. North Carolina (4-3) [-0.0818]
64. Wake Forest (4-4) [-0.0973]
65. Texas A&M (4-3) [-0.1199]
66. Air Force (4-4) [-0.1264]
67. Purdue (3-5) [-0.1306]
68. Northern Illinois (4-3) [-0.1443]
69. Colorado St (3-5) [-0.1773]
70. Southern Miss (5-3) [-0.1884]
71. East Carolina (4-3) [-0.2288]
72. UTEP (3-4) [-0.2325]
73. Baylor (3-4) [-0.2581]
74. Wyoming (4-3) [-0.2635]
75. Louisiana-Lafayette (4-3) [-0.2675]
76. Northwestern (5-3) [-0.2768]
77. Syracuse (3-4) [-0.2855]
78. North Carolina St (3-4) [-0.3074]
79. Louisville (2-5) [-0.3100]
80. SMU (3-4) [-0.3102]
81. San Diego St (3-4) [-0.3315]
82. Duke (4-3) [-0.3404]
83. Central Florida (4-3) [-0.3514]
84. Middle Tennessee St (4-3) [-0.3598]
85. Ohio U. (5-3) [-0.3613]
86. Virginia (3-4) [-0.3724]
87. Colorado (2-5) [-0.3881]
88. Tulsa (4-3) [-0.3909]
89. Temple (5-2) [-0.4241]
90. Western Michigan (4-4) [-0.4333]
91. Indiana (4-4) [-0.4431]
92. Bowling Green (3-5) [-0.4488]
93. Arkansas St (2-4) [-0.4608]
94. Toledo (4-4) [-0.4756]
95. Florida Atlantic (2-4) [-0.5493]
96. UNLV (3-5) [-0.5680]
97. Louisiana Tech (3-4) [-0.5888]
98. San Jose St (1-5) [-0.6078]
99. Kent St (4-4) [-0.6440]
100. Washington St (1-6) [-0.6731]
101. Buffalo (3-5) [-0.6979]
102. Hawai`i (2-5) [-0.7916]
103. Utah St (2-5) [-0.7968]
104. Tulane (2-5) [-0.8196]
105. Alabama-Birmingham (2-5) [-0.8352]
106. Memphis (2-5) [-0.8717]
107. New Mexico St (3-5) [-0.8827]
108. Maryland (2-6) [-0.9288]
109. Vanderbilt (2-6) [-0.9366]
110. Illinois (1-6) [-1.0920]
111. Army (3-5) [-1.1913]
112. Florida Int'l (1-6) [-1.3427]
113. North Texas (1-6) [-1.4819]
114. Akron (1-6) [-1.4836]
115. FCS teams (XXX-XXX) [-1.6343]
116. Miami OH (0-8) [-1.7733]
117. Rice (0-8) [-2.3124]
118. New Mexico (0-7) [-2.3608]
119. Ball St (1-7) [-2.7930]
120. Western Kentucky (0-7) [-2.8963]
121. Eastern Michigan (0-7) [-3.4677]
Conference Rankings (Average Per Team):
SEC 0.7757
Pac10 0.6632
BigEast 0.3871
Big10 0.3654
Big12 0.2768
ACC 0.2200
FBSInd 0.0441
MWC -0.0882
WAC -0.1605
CUSA -0.4643
SunBelt -0.7835
MAC -0.9735
Non-FBS -1.6343

Got Math?

2009-10-24T20:12:00.006-04:00

On a day full of exciting action, including a last-second blocked FG attempt that may turn out to have serious BCS implications, it may seem rather pedestrian to ask a math question. Then again, that's essentially what we do here. So while we're watching the rest of the games, I have a question, brought to my attention by another football ranking fan, Martien Maas.

Martien Maas' Rating System also appears on Kenneth Massey's College Football Ranking Comparison page. Perhaps in part because we ended up very close to each other in the comparisons this week, Martien noted that the RWFL rank order this week is precisely the same as that from Eugene Potemkin's E-Rating System (see also his more detailed discussion). Indeed, the two are nearly the same every week (except for some examples from last year, including here, here, and here). And there are clearly some philosophical similarities between the two rankings. But I haven't sat down to try to work out whether we're mathematically equivalent, so I'd be happy if someone could tell me if they have an expert opinion here. My gut instinct is that our p=0.75 bias value choice happens to set our rankings to the same linear algebra problem, with perhaps the small differences in the past due to details about how non-FBS teams are handled. But, like I said, I haven't looked at it sufficiently yet. Nevertheless, I thought it was worth mentioning...

----

Addition (October 25): Of course, while I tried to leave this puzzle for others, I couldn't let it go myself. I can never resist a good puzzle. It's probably a good thing that I get to solve puzzles for a living. Plus I received an email from Eugene Potemkin responding to a query I sent him directly.

Eugene and I had a wonderfully pleasant exchange of emails back and forth today, wherein he shared some of the details of his E-Rating implementation for college football, adding further mathematical details, including: (1) Where he uses ratios of "ratings" and "anti-ratings" to obtain scores in other sports, he uses a difference for American college football (this is the same as the "First-minus-Last" part in RWFL). (2) Like us, he usually treats the collection of all non-FBS teams as effectively one team. (3) To get around the singular nature of random walks on the fully directed graph---sorry for the lingo here but be thankful I'm not using it to launch into an entire discussion of how this relates to the original PageRank algorithm!---he doesn't treat a win as a full win; rather he equates a win as effectively 3 wins and 1 loss. This is perfectly identical to the "bias value" p=0.75 choice that we've espoused here, which is nice for a variety of reasons. So it appears that the minor differences must be small round-off or tie-breaking differences, and the RWFL(p=0.75) and E-Ratings are completely identical.

Again, a huge thanks to both Martien and Eugene. It's been nice emailing with both of them.

Going forward, we still have value to add, don't worry. For instance, we should spend a lot more time in future posts looking at the plots I post every week that show the top rankings across different choices of this infamous "bias value" p, because those plots hold a lot of utility in being a proxy for various kinds of ranking choices.

Rankings through October 17th

2009-10-18T08:42:00.004-04:00

Some quick, probably insufficiently thought out comments about the new rankings... It seems fairly typical (in an unscientifically sampled way) to see algorithmic rankings start to make more sense here in the middle part of the season, as there is more information available and, in particular, as the number of undefeateds dwindles. The big end-of-season controversies usually don't start to make themselves clearer until later, because there are so many games left to play with so many different possible outcomes between now and then. Still, if you want, you can definitely start to guess at possible controversies to come, if the game outcomes align certain ways, particularly as more of the remaining undefeateds eventually lose.

Looking at the one-loss teams in the top 10 or top 12, along with two-loss Virginia Tech, one could certainly quibble over ordering; but each team's appearance there seems reasonable enough at this stage. LSU lost to Florida. Oregon's only loss was to Boise State (and helps to make the Broncos look subsequently better). But how does two-loss VT stay ranked so high? It's all about who they lost to, and who those teams lost to. Taken as a 3-team unit, ignoring their games against each other, the GT-VT-Miami triangle have only one loss: VT's loss to Alabama. The other three losses on their combined schedules are the three times one of them beat another. So in the "but my team beat your team" arguments, there are a lot of victories drawing some votes towards these teams, only the one loss to Alabama draining them away, and a lot of votes cycling around the triangle made up of these three teams.

And just in case you think there's an ACC bias here (there isn't), take a look at the conference rankings at the bottom of this post (told you).

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 17th:
1. Florida (6-0) [2.7889]
2. Alabama (7-0) [2.5812]
3. Iowa (7-0) [2.3490]
4. Texas (6-0) [1.9274]
5. Cincinnati (6-0) [1.7367]
6. Boise St (6-0) [1.7106]
7. LSU (5-1) [1.6075]
8. Georgia Tech (6-1) [1.5798]
9. Virginia Tech (5-2) [1.4777]
10. TCU (6-0) [1.4662]
11. Miami FL (5-1) [1.4501]
12. Oregon (5-1) [1.3937]
13. Southern Cal (5-1) [1.3706]
14. Arizona (4-2) [0.9424]
15. Houston (5-1) [0.8916]
16. Pittsburgh (6-1) [0.8087]
17. Wisconsin (5-2) [0.7842]
18. South Carolina (5-2) [0.7816]
19. Notre Dame (4-2) [0.7693]
20. Oklahoma St (5-1) [0.7482]
21. Penn State (6-1) [0.7235]
22. West Virginia (5-1) [0.7054]
23. Ohio State (5-2) [0.6803]
24. Georgia (4-3) [0.6789]
25. Washington (3-4) [0.6633]
26. Oregon St (4-2) [0.6617]
27. Kansas (5-1) [0.6232]
28. Utah (5-1) [0.6163]
29. Idaho (6-1) [0.6050]
30. California (4-2) [0.5798]
31. Brigham Young (6-1) [0.5688]
32. Arizona St (4-2) [0.5329]
33. Kentucky (3-3) [0.5328]
34. Auburn (5-2) [0.5222]
35. Arkansas (3-3) [0.5151]
36. Nebraska (4-2) [0.5019]
37. Boston College (5-2) [0.4647]
38. Michigan (5-2) [0.4579]
39. Central Michigan (6-1) [0.4220]
40. South Florida (5-1) [0.3967]
41. Stanford (4-3) [0.3564]
42. Texas Tech (5-2) [0.3335]
43. Troy (4-2) [0.2902]
44. UCLA (3-3) [0.2691]
45. Minnesota (4-3) [0.2675]
46. Mississippi (4-2) [0.2595]
47. Connecticut (4-2) [0.2587]
48. Clemson (3-3) [0.2447]
49. Tennessee (3-3) [0.2421]
50. Oklahoma (3-3) [0.2386]
51. Louisiana-Monroe (4-2) [0.2129]
52. North Carolina (4-2) [0.2005]
53. Michigan St (4-3) [0.1703]
54. Missouri (4-2) [0.1654]
55. Navy (5-2) [0.1533]
56. Rutgers (4-2) [0.1225]
57. Fresno St (3-3) [0.0799]
58. Louisiana-Lafayette (4-2) [0.0288]
59. Iowa St (4-3) [0.0141]
60. Wake Forest (4-3) [0.0076]
61. Colorado St (3-4) [0.0069]
62. Marshall (4-3) [-0.0084]
63. Mississippi St (3-4) [-0.0512]
64. Ohio U. (5-2) [-0.0572]
65. Florida St (2-4) [-0.0702]
66. Colorado (2-4) [-0.1013]
67. Air Force (4-3) [-0.1065]
68. Kansas St (4-3) [-0.1351]
69. Tulsa (4-2) [-0.1379]
70. Northern Illinois (3-3) [-0.1729]
71. East Carolina (4-3) [-0.1880]
72. Nevada (3-3) [-0.1923]
73. Baylor (3-3) [-0.2273]
74. Wyoming (4-3) [-0.2399]
75. Indiana (4-3) [-0.2487]
76. Southern Miss (4-3) [-0.2644]
77. SMU (3-3) [-0.2732]
78. Purdue (2-5) [-0.2974]
79. Central Florida (3-3) [-0.3155]
80. Virginia (3-3) [-0.3174]
81. Toledo (4-3) [-0.3289]
82. North Carolina St (3-4) [-0.3388]
83. Louisville (2-4) [-0.3594]
84. Middle Tennessee St (3-3) [-0.3620]
85. Louisiana Tech (3-3) [-0.3830]
86. Syracuse (2-4) [-0.3991]
87. Bowling Green (3-4) [-0.4010]
88. Texas A&M (3-3) [-0.4198]
89. UTEP (2-4) [-0.4266]
90. Northwestern (4-3) [-0.4289]
91. Duke (3-3) [-0.4764]
92. San Diego St (2-4) [-0.5287]
93. Western Michigan (3-4) [-0.5348]
94. Buffalo (3-4) [-0.5741]
95. Arkansas St (1-4) [-0.5934]
96. UNLV (2-5) [-0.6491]
97. Tulane (2-4) [-0.6502]
98. Washington St (1-5) [-0.6666]
99. San Jose St (1-5) [-0.6679]
100. Temple (4-2) [-0.6850]
101. Maryland (2-5) [-0.7816]
102. Hawai`i (2-4) [-0.8064]
103. Alabama-Birmingham (2-4) [-0.8168]
104. Kent St (3-4) [-0.8451]
105. Florida Atlantic (1-4) [-0.8665]
106. New Mexico St (3-4) [-0.8706]
107. Memphis (2-5) [-0.9384]
108. Illinois (1-5) [-0.9454]
109. Vanderbilt (2-5) [-0.9860]
110. Florida Int'l (1-5) [-1.0750]
111. Army (3-4) [-1.2312]
112. Akron (1-5) [-1.2534]
113. Utah St (1-5) [-1.2864]
114. North Texas (1-5) [-1.5233]
115. FCS teams (XXX-XXX) [-1.6214]
116. Miami OH (0-7) [-1.8190]
117. New Mexico (0-6) [-2.2315]
118. Rice (0-7) [-2.2360]
119. Eastern Michigan (0-6) [-2.7336]
120. Western Kentucky (0-6) [-2.7543]
121. Ball St (0-7) [-3.6397]
Conference Rankings (Average Per Team):
SEC 0.7894
Pac10 0.6103
BigEast 0.4088
Big10 0.3193
Big12 0.3057
ACC 0.2867
FBSInd -0.1029
MWC -0.1219
WAC -0.2012
CUSA -0.4470
SunBelt -0.7381
MAC -0.9710
Non-FBS -1.6214

Rankings through October 10th

2009-10-11T06:45:00.002-04:00

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 10th:
1. Alabama (6-0) [2.8485]
2. Florida (5-0) [2.6827]
3. Virginia Tech (5-1) [2.2702]
4. Iowa (6-0) [2.0390]
5. Boise St (5-0) [1.6920]
6. LSU (5-1) [1.6258]
7. Cincinnati (5-0) [1.5538]
8. Texas (5-0) [1.3964]
9. Miami FL (4-1) [1.3367]
10. Oregon (5-1) [1.3116]
11. Kansas (5-0) [1.2830]
12. TCU (5-0) [1.2791]
13. Southern Cal (4-1) [1.2467]
14. Nebraska (4-1) [1.1471]
15. Ohio State (5-1) [1.1221]
16. Notre Dame (4-1) [1.0609]
17. Wisconsin (5-1) [1.0124]
18. Washington (3-3) [0.9582]
19. Georgia Tech (5-1) [0.9528]
20. South Carolina (5-1) [0.8006]
21. Idaho (5-1) [0.7461]
22. Auburn (5-1) [0.7218]
23. Stanford (4-2) [0.7102]
24. Arizona (3-2) [0.6976]
25. Arkansas (3-2) [0.6553]
26. Utah (4-1) [0.6315]
27. Houston (4-1) [0.6219]
28. Georgia (3-3) [0.5921]
29. Oregon St (4-2) [0.5826]
30. Brigham Young (5-1) [0.5434]
31. Pittsburgh (5-1) [0.5422]
32. Michigan (4-2) [0.5398]
33. South Florida (5-0) [0.5376]
34. Missouri (4-1) [0.5340]
35. Oklahoma St (4-1) [0.5112]
36. UCLA (3-2) [0.5055]
37. Penn State (5-1) [0.5033]
38. Boston College (4-2) [0.4687]
39. West Virginia (4-1) [0.4296]
40. Troy (3-2) [0.3954]
41. California (3-2) [0.3941]
42. Wake Forest (4-2) [0.3808]
43. Minnesota (4-2) [0.3324]
44. Rutgers (4-1) [0.3309]
45. Oklahoma (3-2) [0.3057]
46. Central Michigan (5-1) [0.2853]
47. Marshall (4-2) [0.2571]
48. Tennessee (3-3) [0.2478]
49. Mississippi (3-2) [0.2379]
50. Louisiana-Lafayette (3-2) [0.2371]
51. Kentucky (2-3) [0.2229]
52. Michigan St (3-3) [0.1393]
53. Northern Illinois (3-2) [0.1218]
54. Connecticut (3-2) [0.1204]
55. Arizona St (3-2) [0.0818]
56. Clemson (2-3) [0.0669]
57. Baylor (3-2) [0.0500]
58. North Carolina (4-2) [0.0485]
59. Ohio U. (4-2) [-0.0222]
60. Middle Tennessee St (3-2) [-0.0295]
61. Colorado St (3-3) [-0.0413]
62. Fresno St (2-3) [-0.0631]
63. Navy (4-2) [-0.0905]
64. SMU (3-2) [-0.0962]
65. Texas Tech (4-2) [-0.0999]
66. Louisiana-Monroe (3-2) [-0.1121]
67. Iowa St (3-3) [-0.1201]
68. Florida St (2-4) [-0.1366]
69. Tulsa (4-1) [-0.1541]
70. East Carolina (3-3) [-0.1733]
71. Bowling Green (2-4) [-0.1905]
72. Texas A&M (3-2) [-0.1974]
73. Nevada (2-3) [-0.2029]
74. North Carolina St (3-3) [-0.2071]
75. Wyoming (4-2) [-0.2754]
76. Duke (3-3) [-0.2805]
77. Mississippi St (2-4) [-0.3006]
78. Kansas St (3-3) [-0.3077]
79. Louisville (2-3) [-0.3211]
80. Arkansas St (1-3) [-0.3220]
81. Air Force (3-3) [-0.3373]
82. Southern Miss (3-3) [-0.3419]
83. Indiana (3-3) [-0.3512]
84. Northwestern (4-2) [-0.3527]
85. Central Florida (3-2) [-0.3544]
86. San Jose St (1-4) [-0.4218]
87. Syracuse (2-4) [-0.4240]
88. San Diego St (2-3) [-0.4299]
89. UTEP (2-4) [-0.4442]
90. Western Michigan (3-3) [-0.4619]
91. Maryland (2-4) [-0.4661]
92. Tulane (2-3) [-0.5388]
93. Louisiana Tech (2-3) [-0.6053]
94. Purdue (1-5) [-0.6489]
95. Illinois (1-4) [-0.6538]
96. Virginia (2-3) [-0.6539]
97. Alabama-Birmingham (2-3) [-0.6564]
98. New Mexico St (3-3) [-0.6630]
99. Toledo (3-3) [-0.6763]
100. UNLV (2-4) [-0.6777]
101. Memphis (2-4) [-0.6936]
102. Washington St (1-5) [-0.7090]
103. Colorado (1-4) [-0.7794]
104. Kent St (2-4) [-0.8684]
105. Buffalo (2-4) [-0.8856]
106. Hawai`i (2-3) [-0.9227]
107. Temple (3-2) [-0.9663]
108. Army (3-3) [-0.9929]
109. Vanderbilt (2-4) [-0.9958]
110. North Texas (1-4) [-1.0296]
111. Utah St (1-4) [-1.0645]
112. Akron (1-4) [-1.0808]
113. Florida Int'l (1-4) [-1.1920]
114. Florida Atlantic (0-4) [-1.4301]
115. FCS teams (XXX-XXX) [-1.6184]
116. Miami OH (0-6) [-1.8676]
117. New Mexico (0-6) [-2.2432]
118. Rice (0-6) [-2.3721]
119. Eastern Michigan (0-5) [-2.5733]
120. Western Kentucky (0-5) [-3.0848]
121. Ball St (0-6) [-3.6768]
Conference Rankings (Average Per Team):
SEC 0.7783
Pac10 0.5779
BigEast 0.3462
Big10 0.3347
ACC 0.3150
Big12 0.3102
FBSInd -0.0075
WAC -0.1672
MWC -0.1723
CUSA -0.4122
SunBelt -0.7297
MAC -0.9894
Non-FBS -1.6184

Comparing Conferences: So much movement, so little reason

2009-10-07T08:14:00.001-04:00

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 3rd
Conference Rankings (Average Per Team):
SEC 0.7928
Pac10 0.6051
Big10 0.4282
ACC 0.3528
Big12 0.3359
BigEast 0.3310
WAC -0.1242
FBSInd -0.1543
MWC -0.2016
CUSA -0.4783
SunBelt -0.8022
MAC -1.0214
Non-FBS -1.5533

Only a week ago, the rankings made it look like the ACC was hands down the weakest of the so-called major conferences. Sure, VT and Miami were highly ranked; but on average, the squads in the ACC garnered fewer net RWFL votes per team. But here we are only a week later, and the same methodology puts the ACC very slightly ahead but in essentially a dead heat with the Big 12 and the Big East (varying the bias value p in the plot at the bottom of this post does change things, but not as vigorously as last week).

How is this big change in one week possible?

First, it would seem easy to go to my favorite rationalization: it's still early in the season. The problem with that argument in this case is that last weekend resulted in very little new information about the ACC's strength relative to the other conferences, with 10 of the 12 teams playing against each other.

Okay, so it must be those two interconference games? Sure, Georgia Tech beat Mississippi State, and of course the big win was Miami over Oklahoma. Those two ACC victories over SEC teams certainly move up the ACC rankings, especially the win over a highly rated Oklahoma team (starting QB or no). Such apparent sensitivity of rankings to a few interconference games only highlights the difficulty in ranking teams from the limited information that the BCS Standings allow.

Did anything else happen to cause this change in the rankings? Very possibly. The ACC was likely also helped this week by intraconference outcomes changing the rankings inside the conferences. For instance, Florida State's intraconference loss to Boston College further suppressed their RWFL rating, thereby decreasing the newly-assessed value of South Florida's interconference win over Florida State the week before. Reshuffled comparisons like this are happening all throughout the season, potentially changing the relative rankings of conferences even in the absence of direct matchups. The potential importance of such indirect effects make attempts to rank teams both interesting and maddening.

Rankings through October 3rd

2009-10-04T08:15:00.003-04:00

There are obviously still a lot of unknowns this early in the season (there's a reason the official BCS Standings don't come out this early), but rankings do start to make a little more sense with another week of games on the books. Obviously, all eyes are on the upcoming Florida-LSU game. Meanwhile, there are only two potential BCS busters left after Houston's loss.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 3rd:
1. Alabama (5-0) [2.5017]
2. LSU (5-0) [2.4968]
3. Iowa (5-0) [2.0009]
4. Virginia Tech (4-1) [1.8947]
5. Wisconsin (5-0) [1.5998]
6. Miami FL (3-1) [1.5444]
7. Auburn (5-0) [1.5160]
8. Texas (4-0) [1.4734]
9. Florida (4-0) [1.4694]
10. Boise St (5-0) [1.4400]
11. Cincinnati (5-0) [1.3715]
12. TCU (4-0) [1.2569]
13. Stanford (4-1) [1.2250]
14. Kansas (4-0) [1.2161]
15. Southern Cal (4-1) [1.1354]
16. Georgia Tech (4-1) [1.1309]
17. Oregon (4-1) [1.0211]
18. Notre Dame (4-1) [1.0181]
19. Arizona (3-1) [1.0069]
20. Ohio State (4-1) [0.8263]
21. Washington (2-3) [0.8211]
22. Missouri (4-0) [0.8186]
23. Georgia (3-2) [0.8182]
24. UCLA (3-1) [0.7916]
25. Boston College (4-1) [0.7564]
26. Nebraska (3-1) [0.7227]
27. Idaho (4-1) [0.6980]
28. South Florida (5-0) [0.6580]
29. Michigan (4-1) [0.6452]
30. Penn State (4-1) [0.6292]
31. Baylor (3-1) [0.6022]
32. Connecticut (3-1) [0.6013]
33. Wake Forest (3-2) [0.5748]
34. Brigham Young (4-1) [0.5423]
35. South Carolina (4-1) [0.5347]
36. West Virginia (3-1) [0.4952]
37. Central Michigan (4-1) [0.4842]
38. Houston (3-1) [0.4083]
39. California (3-2) [0.3957]
40. Utah (3-1) [0.3867]
41. Oklahoma St (3-1) [0.3446]
42. Rutgers (3-1) [0.3301]
43. Minnesota (3-2) [0.3293]
44. Louisiana-Lafayette (2-2) [0.2786]
45. Middle Tennessee St (3-1) [0.2491]
46. Clemson (2-3) [0.2491]
47. Arkansas (2-2) [0.2421]
48. Pittsburgh (4-1) [0.2379]
49. Oregon St (3-2) [0.2180]
50. Kentucky (2-2) [0.1927]
51. Northern Illinois (3-2) [0.1752]
52. Michigan St (2-3) [0.1551]
53. Mississippi (3-1) [0.1403]
54. Mississippi St (2-3) [0.1342]
55. North Carolina (3-2) [0.0998]
56. Oklahoma (2-2) [0.0922]
57. Florida St (2-3) [0.0567]
58. Colorado St (3-2) [0.0383]
59. North Carolina St (3-2) [0.0314]
60. Indiana (3-2) [0.0182]
61. Marshall (3-2) [0.0152]
62. East Carolina (3-2) [0.0144]
63. Navy (3-2) [0.0051]
64. Kansas St (3-2) [-0.0052]
65. Iowa St (3-2) [-0.0111]
66. Texas A&M (3-1) [-0.0771]
67. Tennessee (2-3) [-0.0811]
68. Arizona St (2-2) [-0.1049]
69. Ohio U. (3-2) [-0.1323]
70. Louisiana Tech (2-2) [-0.1732]
71. Southern Miss (3-2) [-0.1735]
72. Troy (2-2) [-0.1832]
73. Tulsa (4-1) [-0.1996]
74. Louisiana-Monroe (3-2) [-0.2057]
75. Fresno St (1-3) [-0.2100]
76. UTEP (2-3) [-0.2418]
77. Maryland (2-3) [-0.2482]
78. Syracuse (2-3) [-0.2810]
79. Wyoming (3-2) [-0.2888]
80. Air Force (3-2) [-0.3169]
81. San Jose St (1-3) [-0.3252]
82. Texas Tech (3-2) [-0.3597]
83. SMU (2-2) [-0.3628]
84. Nevada (1-3) [-0.3841]
85. Central Florida (3-2) [-0.3879]
86. San Diego St (2-3) [-0.3948]
87. Illinois (1-3) [-0.4138]
88. Vanderbilt (2-3) [-0.4519]
89. Washington St (1-4) [-0.4590]
90. Northwestern (3-2) [-0.4649]
91. Tulane (2-2) [-0.4788]
92. Toledo (3-2) [-0.4989]
93. Kent St (2-3) [-0.5253]
94. Arkansas St (1-3) [-0.5730]
95. Bowling Green (1-4) [-0.5739]
96. Western Michigan (2-3) [-0.5815]
97. Purdue (1-4) [-0.6155]
98. Hawai`i (2-2) [-0.6160]
99. Akron (1-3) [-0.6825]
100. UNLV (2-3) [-0.6936]
101. Utah St (1-3) [-0.6950]
102. Duke (2-3) [-0.7184]
103. Louisville (1-3) [-0.7645]
104. Alabama-Birmingham (2-3) [-0.7741]
105. Colorado (1-3) [-0.7861]
106. New Mexico St (2-3) [-0.8521]
107. North Texas (1-3) [-0.9751]
108. Temple (2-2) [-1.0962]
109. Memphis (1-4) [-1.1092]
110. Virginia (1-3) [-1.1385]
111. Buffalo (1-4) [-1.1989]
112. Army (2-3) [-1.4860]
113. FCS teams (XXX-XXX) [-1.5533]
114. Florida Atlantic (0-4) [-1.6109]
115. Florida Int'l (0-4) [-1.6260]
116. Miami OH (0-5) [-1.6788]
117. New Mexico (0-5) [-2.3440]
118. Rice (0-5) [-2.4494]
119. Western Kentucky (0-4) [-2.5740]
120. Eastern Michigan (0-4) [-3.3076]
121. Ball St (0-5) [-3.6623]

Virginia Tech, Really?

2009-10-02T07:42:00.004-04:00

The midweek games have already come and gone, and I'm still a little puzzled about our RWFL rankings previously posted. Again, it's far too early in the season to expect good performance out of a computer ranking system that, like ours, ignores margin of victory, dates of games, and the previous season. But Virginia Tech (3-1) edging Iowa (4-0) for 2nd place?!? Now, sure, from a ranking violations standpoint, that's fine, since the loss came at the hands of #1 Alabama. But with so many undefeateds (including three potential BCS busters!), I found this result surprising.

The surprise disappears when we dig just a little further into the rankings. As we've done in this space for previous years, our tabulated results are for the specific bias value p=0.75 for the random walker algorithm. What this means is that each walker, considering a game between two teams, will decide that the winner is the better team 75% of the time. Why 75%? Seriously, essentially because it's halfway between 50% (ignoring the outcome altogether) and 100% (complete certainty that the outcome represents the better team). Okay, there's very slightly more to it than that: we tested the rankings across different p values and found that the middle of the range, around 75%, typically corresponds to the low values of rankings violations and the best values to predict bowl game outcomes in historical comparisons. And if you really press me for some other mathematical reasons, it turns out that RWFL rankings of round-robin tournaments appear (in numerical exploration) to agree perfectly with the resulting standings provided p is less than a value somewhere roughly around 0.75.

So, after all that mumbo jumbo, let's vary p and see what happens. You can see in the figure below that Virginia Tech and Miami both do well on the left (p closer to 0.5), but they fall quickly from these high perches as p increases moving to the right in the figure (VT and Miami are represented by the two curves moving quickly upwards towards worse rankings as p increases from left to right). Loosely speaking, this corresponds to the algorithm assigning an on-average stronger schedule to these teams on the left, while penalizing them for their losses on the right. At this point, the balance happens to be working out one way for them; but this high ranking is clearly tenuous at best.
We close today's post by briefly noting that the upcoming conference play might drastically change the above plot against Virginia Tech and Miami, even if they win, simply because the ACC is, on average, not ranked highly by this algorithm. In the plot below, we plot the average numbers of net RWFL votes (expressed as percentages) per team for each FBS conference (grouping the independents together). The way to read this plot is to look at vertical slices (fixed p values), wherein higher values correspond to greater numbers of net votes per team. So far, the ACC appears to be the weakest of the so-called major conferences at most p values, and indeed, it ranks weaker than some of the so-called mid-majors at higher values of p! No hate mail about this please; I'm just the messenger.

Return of the Random Walkers!

2009-09-27T10:29:00.003-04:00

It's still very early in the season to expect anything accurate from the random walker rankings, so apologies up front if your team isn't highly ranked. Let's concisely review the methodological essentials, so that you can rationalize why your team might not be where you want them to be at this point.

First and foremost, we're enormously grateful to Peter Wolfe for posting scores in an easy-to-parse format, and to Kenneth Massey for his College Football Ranking Comparison page. So with data to parse and a place to post results, what happens in the steps in between? We ignore margins of victory. We ignore the dates of games. And we collapse all non-FBS teams into a single representative node in our network (which we misname "FCS teams" below, though there are probably some DivII schools in there). Each of these could be easily handled differently; indeed, the last is a simple matter of considering the whole network and we've done this in recent years to try to predict the outcomes of bowl games (once turned out reasonably well and once not so much). The first two, however, require some modeling choices to specify how to handle these pieces of information, and our entire philosophy from the beginning has been to demonstrate what one gets from simple rankings.

Working solely from "but my team beat your team" arguments, we let loose two sets of random walkers on this network of teams: the "first-place votes" are biased to switch their votes to game winners 75% of the time, the "last-place votes" are biased to switch their votes to game losers 75% of the time, and we see how many votes on average each team gets (in reality, we solve the associated linear algebra problems). The RWFL ranking of a team is the number of first-place votes obtained minus the number of last-place votes (each expressed in the square brackets below in terms of the percentages of the respective totals).

Again, it's really early in the season to be making statements from such limited information. But the results below give a starting point for discussion and debate. Later in the week, we'll try to discuss the corresponding plots of rankings and violations across the bias value p (like we've produced in previous seasons) and perhaps also look at the rankings on a conference level.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday September 26th:
1. Alabama (4-0) [3.0342]
2. Virginia Tech (3-1) [2.4080]
3. Iowa (4-0) [2.4022]
4. LSU (4-0) [2.2689]
5. Houston (3-0) [2.0676]
6. Boise St (4-0) [1.9937]
7. Michigan (4-0) [1.7490]
8. Miami FL (2-1) [1.7174]
9. Cincinnati (4-0) [1.5009]
10. Florida (4-0) [1.3036]
11. Texas (4-0) [1.2741]
12. UCLA (3-0) [1.2486]
13. Oregon (3-1) [1.2442]
14. Georgia (3-1) [1.2347]
15. Auburn (4-0) [1.1884]
16. Georgia Tech (3-1) [1.1684]
17. Wisconsin (4-0) [1.0183]
18. TCU (3-0) [0.9325]
19. Kansas (4-0) [0.9044]
20. Arizona (3-1) [0.8854]
21. Oklahoma St (3-1) [0.8371]
22. Missouri (4-0) [0.7968]
23. Washington (2-2) [0.7779]
24. Nebraska (3-1) [0.7671]
25. South Carolina (3-1) [0.7105]
26. North Carolina (3-1) [0.6915]
27. Southern Cal (3-1) [0.6472]
28. Marshall (3-1) [0.6114]
29. Stanford (3-1) [0.6099]
30. California (3-1) [0.6062]
31. South Florida (4-0) [0.5924]
32. Penn State (3-1) [0.5889]
33. Brigham Young (3-1) [0.5620]
34. Minnesota (3-1) [0.5481]
35. Clemson (2-2) [0.5175]
36. Iowa St (3-1) [0.5102]
37. Connecticut (3-1) [0.5074]
38. Notre Dame (3-1) [0.5049]
39. Indiana (3-1) [0.4978]
40. Ohio State (3-1) [0.4843]
41. Idaho (3-1) [0.4233]
42. Utah (3-1) [0.4232]
43. Boston College (3-1) [0.3997]
44. Rutgers (3-1) [0.3321]
45. Arizona St (2-1) [0.2678]
46. Middle Tennessee St (3-1) [0.2601]
47. Florida St (2-2) [0.2566]
48. Mississippi St (2-2) [0.2308]
49. Texas A&M (3-0) [0.2218]
50. Central Michigan (3-1) [0.2208]
51. Baylor (2-1) [0.2136]
52. Kentucky (2-1) [0.2053]
53. North Carolina St (3-1) [0.2032]
54. Louisiana-Lafayette (2-2) [0.1960]
55. West Virginia (2-1) [0.1828]
56. Oklahoma (2-1) [0.1231]
57. Colorado St (3-1) [0.1121]
58. Oregon St (2-2) [0.0465]
59. Arkansas (1-2) [0.0341]
60. Wake Forest (2-2) [0.0169]
61. Mississippi (2-1) [-0.0033]
62. Pittsburgh (3-1) [-0.0462]
63. Tennessee (2-2) [-0.0467]
64. Air Force (3-1) [-0.0543]
65. Northern Illinois (2-2) [-0.0562]
66. Bowling Green (1-3) [-0.0636]
67. Southern Miss (3-1) [-0.0797]
68. Syracuse (2-2) [-0.1489]
69. Fresno St (1-3) [-0.1589]
70. Texas Tech (2-2) [-0.1620]
71. Western Michigan (2-2) [-0.1630]
72. Tulsa (3-1) [-0.1804]
73. Troy (2-2) [-0.1837]
74. Toledo (2-2) [-0.2178]
75. Louisiana-Monroe (2-2) [-0.2211]
76. East Carolina (2-2) [-0.2783]
77. Kansas St (2-2) [-0.2809]
78. Hawai`i (2-1) [-0.2944]
79. Wyoming (2-2) [-0.2952]
80. Vanderbilt (2-2) [-0.2972]
81. Purdue (1-3) [-0.2979]
82. Ohio U. (2-2) [-0.3529]
83. Kent St (2-2) [-0.3612]
84. Illinois (1-2) [-0.3999]
85. UNLV (2-2) [-0.4330]
86. San Jose St (1-3) [-0.4694]
87. SMU (2-1) [-0.4772]
88. Navy (2-2) [-0.4865]
89. Washington St (1-3) [-0.5129]
90. Colorado (1-2) [-0.5247]
91. Utah St (1-2) [-0.5517]
92. Louisville (1-2) [-0.5529]
93. Michigan St (1-3) [-0.5556]
94. Northwestern (2-2) [-0.5637]
95. San Diego St (1-3) [-0.5662]
96. Arkansas St (1-2) [-0.6476]
97. Akron (1-3) [-0.6534]
98. Tulane (1-2) [-0.6841]
99. Maryland (1-3) [-0.6868]
100. Central Florida (2-2) [-0.7041]
101. Memphis (1-3) [-0.7420]
102. Louisiana Tech (1-2) [-0.8184]
103. Duke (2-2) [-0.8396]
104. New Mexico St (2-2) [-0.9394]
105. North Texas (1-3) [-1.0065]
106. Nevada (0-3) [-1.0218]
107. Florida Int'l (0-3) [-1.0773]
108. Army (2-2) [-1.1548]
109. Florida Atlantic (0-3) [-1.1604]
110. UTEP (1-3) [-1.1829]
111. Alabama-Birmingham (1-3) [-1.2814]
112. Miami OH (0-4) [-1.4748]
113. Temple (1-2) [-1.4759]
114. FCS teams (XXX-XXX) [-1.5860]
115. Buffalo (1-3) [-1.7419]
116. New Mexico (0-4) [-2.1243]
117. Eastern Michigan (0-3) [-2.5679]
118. Rice (0-4) [-2.6886]
119. Western Kentucky (0-4) [-2.8495]
120. Virginia (0-3) [-2.9512]
121. Ball St (0-4) [-3.8851]

Trent McCotter talks about the monkeys

2009-09-13T10:20:00.005-04:00

A quick but big thank you to Trent McCotter for mentioning our random walker "monkey" rankings in his latest column! See "Time to monkey around with the BCS?"

Quarterback ratings

2009-08-23T09:43:00.006-04:00

Trent McCotter is back again as one of the targets of links in today's post, courtesy of his first column in the The News & Observer, which he will write in his copious spare time as a UNC law student. Yesterday, I sang the praises of Steve Strogatz, so now it's Trent's turn. One of the outwardly most mellow people I know, Trent's outward calm conceals a strong passion for sports statistics. A four time winner of the Jack Kavanagh Memorial Youth Baseball Research Award from SABR (three times in the college division, once in the high school division), Trent distinguishes himself by frequently taking a different tack in his work while also delving into the detailed numbers when needed.

In "How to fix the 'perfect game'," Trent avoids the details of the quarterback ratings definition and gets right to the interesting issue of the recent prevalence of perfect passer rating performances, wondering along the way quite how perfect they are.

While we're talking about quarterback ratings and looking forward to the upcoming season, check out "Vick as a Quarterback? He’s Underrated" by Brian Burke of Advanced NFL Stats in The Fifth Down (both sites are full of interesting items). Without getting into recalculations of possible quarterback ratings, Burke's discussion about more conventional statistics makes clear that neither they nor quarterback ratings tell the whole story.

The Mathematics of Hitting Streaks

2009-08-22T16:39:00.007-04:00

With the hope that there's actually someone other than my coauthors reading these posts once the college football season arrives (when the hits to the old page understandably ramped up in past years), one of the upsides to transitioning to a blog is to provide easy pointers to other interesting work in the mathematics and statistics of sports.

There are a pair of papers about hitting streaks that have appeared on arXiv.org in the past year. Making things particularly interesting, these two papers take completely different methodological approaches. Sam Arbesman and Steve Strogatz "examine Joe DiMaggio’s 56-game hitting streak and look at its likelihood, using a number of simple models. And it turns out that, contrary to many people’s expectations, an extreme streak, while unlikely in any given year, is not unlikely to have occurred about once within the history of baseball." Meanwhile, Trent McCotter uses permutation tests to find that there appear to have been a significantly larger number of 20-25 game streaks in real life than one would obtain in an independent-games model. You can hear Steve talk more about both studies in a Radiolab podcast from earlier this summer.

Finally, for perhaps the only timely element of this post, Steve has a new book just out this past week, The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math. If it's like everything else Steve does, it will be amazing.

----
Addition (29Aug): For more discussion about hitting streaks, other streaks, and the way that people tend to overinterpret streaks, check out Leonard Mlodinow's interesting WSJ essay, "The Triumph of the Random."

----
Another addition (31Aug): Trent McCotter's second N&O column is about hitting streaks, with a decidedly local-to-NC flavor ("Zimmerman best in state at hitting streaks").

Random walking through baseball

2009-08-11T09:30:00.000-04:00

Now that the new site format appears to be largely up and working, it's time to start digging into a backlog of math-in-sports topics I've wanted to briefly write about. That said, if anyone has a general solution for the seemingly infamous "Publishing your blog is taking longer than expected" problem occasionally afflicting those of us who ftp-publish to other servers, I would love to hear about it, please!

Today's links are all about baseball. No, not the recent Yankees 4-game sweeping of the Red Sox (just typing that hurts). Instead, consistent with the title of this site, today is all about random walker rankings applied to baseball players. Well, sort of. Specifically, some of my collaborators and I recently wrote a paper (submitted for publication) studying the network of baseball players defined by the collection of pitcher-batter matchups across 1954-2008. Our focus so far is the study of this large network, and one of the (many) ways to try to understand a network is to study some process occurring on that network: enter the biased random walkers that can be used to define a ranking. Of course, the result is a very crude ranking. If one wanted to turn this into a more serious ranking of baseball players, numerous effects could and indeed should be included.

Brandon Keim picked up the story about our work for Wired Science, nicely including some thoughts (both ours and his) about the limitations of using this as a ranking. From there it got some nice attention and further helpful comments, some of which we'll use to clarify and acknowledge in an eventual revision. My coauthor, Mason Porter, has already collected most of the resulting links, including an interview he did with 27pitches.com.

A big thanks to Brandon for writing such a nice story about our work.

Don't worry, we'll start discussing and adding links to less narcissistic topics soon. Maybe.

Rebuilding the old site into a blog

2009-08-09T20:40:00.000-04:00

With the new college football season almost upon us, I wanted to finally start to clean this site up and see if we can't give it a more uniform look and feel, now that we've switched to a blog format. The blog will have its benefits, including automatically archiving everything and allowing for comments. But converting the old, existing pages is a pain; in particular, there are already figures and tables in those pages that would have to be reformatted for the blog. I would rather use that time to start adding some new content here. So we're going to keep most of the old site as is, at http://rankings.amath.unc.edu/old.

Apologies to those who click through and find themselves on the old site. The old sidebar now includes a link back to the "RWR Blog" on most pages. If you end up somewhere without this link, please make use of your friendly browser's back button.

Press coverage (college football edition)

2009-08-09T20:35:00.000-04:00

We're grateful for the positive attention about the random walker rankings as a means of ranking college football teams. We have particularly enjoyed the diversity of outlets interested in this project, including

ESPN the Magazine (issue dated Nov. 10, 2003),
Nature Science Update (Nov. 14, 2003),
Georgia Tech news releases [long and short] (Nov. 18, 2003),
The Chronicle of Higher Education (issue dated Nov. 28, 2003; subscription required),
CNN Headline News (Dec. 30, 2003),
La Recherche (Jan. 2004, subscription required),
Atlanta Business Chronicle (Jan. 16, 2004),
WGST AM640 (May 20, 2004),
The Atlanta Journal-Constitution (May 24, 2004; registration required),
WKY AM930 (May 28, 2004),
American Mathematical Society press release (Aug. 11, 2004),
Science News (week of Sept. 4, 2004),
The Washington Post (Sports columnist Sally Jenkins, Dec. 10, 2005), and
The Mathematical Tourist at MAA Online (Nov. 15, 2007).

Our manuscripts about college football

2009-08-09T20:32:00.001-04:00

In addition to the rants on this collection of web pages, we have written a pair of scholarly, academic articles about ranking with random walkers. The now somewhat amusingly misnamed "Division I-A Football" article (it was properly named when it was submitted; and the Michigan Wolverines hadn't famously lost to Appalachian State Mountaineers, an FCS née I-AA program) discusses a number of issues in greater depth than covered on this website, including the community structure of the football matchups network and its influence on rankings, ideas about choosing a good p value, and the improved properties of the RWFL ranking system.

''Random Walker Ranking for NCAA Division I-A Football,''
T. Callaghan, P. J. Mucha and M. A. Porter,
American Mathematical Monthly, 114, 761-777 (2007)
[originally made available as arxiv.org/physics/0310148].
Abstract: Each December, college football fans and pundits across America debate which two teams should meet in the NCAA Division I-A National Championship game. The Bowl Championship Series (BCS) standings employed to select the teams invited to this game are intended to provide an unequivocal #1 v. #2 game for the championship; however, this selection process has itself been highly controversial in four of the past six years. The computer algorithms that constitute one part of the BCS standings often act as lightning rods for the controversy, in part because they are inadequately explained to the public. We present an alternative algorithm that is simply explained yet remains effective at ranking the best teams. We define a ranking in terms of biased random walkers on the graph formed by the schedule of games played, with two teams (vertices) connected by an edge if they played each other. Each random walker moves from team to team by selecting a game and "voting" for its winner with probability p, tracing out a never-ending path motivated by the "my team beat your team" argument. We study the statistical properties of a collection of such walkers, relate the rankings to the community structure of the underlying network, and compare these rankings for recent NCAA Division I-A seasons. We also discuss the algorithm's asymptotic behavior, illustrated with some analytically tractable cases for round-robin tournaments, and discuss possible generalizations.

''The Bowl Championship Series: A Mathematical Review,''
T. Callaghan, P. J. Mucha and M. A. Porter,
Notices of the American Mathematical Society 51, 887-893 (2004).
Abstract: We discuss individual components of the college football Bowl Championship Series. Comparing with a simple algorithm defined by random walks on a biased graph, we attempt to predict whether the proposed changes will truly lead to increased BCS bowl access for non-BCS schools. We conclude by arguing that the true problem with the BCS Standings lies not in the computer rankings, but rather in misguided addition.

2008 Random Walker Rankings [link]

2009-08-09T20:31:00.001-04:00

http://rankings.amath.unc.edu/old/2008.htm

2007 Random Walker Rankings [link]

2009-08-09T20:30:00.001-04:00

http://rankings.amath.unc.edu/old/2007.htm

2006 Random Walker Rankings [link]

2009-08-09T20:29:00.000-04:00

http://rankings.amath.unc.edu/old/2006.htm

2005 Random Walker Rankings [link]

2009-08-09T20:28:00.002-04:00

http://rankings.amath.unc.edu/old/2005.htm

2004 Random Walker Rankings [link]

2009-08-09T20:28:00.001-04:00

http://rankings.amath.unc.edu/old/2004.htm

How well did the monkeys do in 2003? [link]

2009-08-09T20:27:00.000-04:00

http://rankings.amath.unc.edu/old/2003.htm

Trying to predict the bowl games

2008-12-19T15:20:00.001-05:00

Last year, we tried our hand at picking the bowl games, with entries in the ESPN.com College Bowl Mania where you pick the outcomes along with rank ordering your confidence in the outcomes. We actually did fairly well for a fully automated system, placing just above the 75th percentile of all entries. So we are trying the same methodology again this year, with all the same caveats about how fabulously wrong some of the reasoning behind these picks are, only some of the errors of which are described along with the methodology in last year's bowl predictions. We definitely do not endorse using these "predictions" for anything other than fun.

The predictions are sorted in decreasing confidence, as quantified by the middle of the stated range of probabilities (one comes from the first-place-only votes and the other comes from the last-place-only votes, with the predicted winner always picked to be the higher-ranked team in the RWFL rankings). Note in particular as you get near the bottom of the list (least confident), the range of probabilities indicate the highly tossup nature of these games.

----
MAGICJACK ST. PETERSBURG BOWL
South Florida (7-5) over Memphis (6-6)
78-81%
----
COTTON BOWL
Texas Tech (11-1) over Mississippi (8-4)
78-80%
----
PIONEER LAS VEGAS BOWL
Brigham Young (10-2) over Arizona (7-5)
75-77%
----
CHICK-FIL-A BOWL
Georgia Tech (9-3) over LSU (7-5)
66-80%
----
TOSTITOS FIESTA BOWL
Texas (11-1) over Ohio State (10-2)
72-74%
----
GAYLORD HOTELS MUSIC CITY BOWL
Boston College (9-4) over Vanderbilt (6-6)
70-75%
----
MOTOR CITY BOWL
Central Michigan (8-4) over Florida Atlantic (6-6)
65-71%
----
BELL HELICOPTER ARMED FORCES BOWL
Air Force (8-4) over Houston (7-5)
64-70%
----
AUTOZONE LIBERTY BOWL
East Carolina (9-4) over Kentucky (6-6)
65-68%
----
CHAMPS SPORTS BOWL
Florida St (8-4) over Wisconsin (7-5)
53-80%
----
INDEPENDENCE BOWL
Louisiana Tech (7-5) over Northern Illinois (6-6)
66-67%
----
ROADY'S HUMANITARIAN BOWL
Maryland (7-5) over Nevada (7-5)
57-72%
----
INTERNATIONAL BOWL
Connecticut (7-5) over Buffalo (8-5)
63-67%
----
INSIGHT BOWL
Kansas (7-5) over Minnesota (7-5)
62-66%
----
GMAC BOWL
Ball St (12-1) over Tulsa (10-3)
57-69%
----
EAGLEBANK BOWL
Wake Forest (7-5) over Navy (8-4)
60-65%
----
ALLSTATE SUGAR BOWL
Utah (12-0) over Alabama (12-1)
56-60%
----
MEINEKE CAR CARE BOWL
North Carolina (8-4) over West Virginia (8-4)
50-66%
----
CAPITAL ONE BOWL
Georgia (9-3) over Michigan St (9-3)
57-58%
----
SAN DIEGO COUNTY CREDIT UNION POINSETTIA BOWL
Boise St (12-0) over TCU (10-2)
51-62%
----
PAPAJOHNS.COM BOWL
North Carolina St (6-6) over Rutgers (7-5)
54-58%
----
THE ROSE BOWL GAME PRESENTED BY CITI
Southern Cal (11-1) over Penn State (11-1)
54-57%
----
TEXAS BOWL
Rice (9-3) over Western Michigan (9-3)
54-56%
----
SUN BOWL
Pittsburgh (9-3) over Oregon St (8-4)
53-56%
----
R+L CARRIERS NEW ORLEANS BOWL
Troy (8-4) over Southern Miss (6-6)
50-55%
----
VALERO ALAMO BOWL
Missouri (9-4) over Northwestern (9-3)
52-52%
----
PACIFIC LIFE HOLIDAY BOWL
Oklahoma St (9-3) over Oregon (9-3)
50-54%
----
OUTBACK BOWL
South Carolina (7-5) over Iowa (8-4)
49-51%
----
EMERALD BOWL
Miami FL (7-5) over California (8-4)
45-54%
----
SHERATON HAWAII BOWL
Hawai`i (7-6) over Notre Dame (6-6)
48-51%
----
NEW MEXICO BOWL
Fresno St (7-5) over Colorado St (6-6)
44-51%
----
FEDEX ORANGE BOWL
Virginia Tech (9-4) over Cincinnati (11-2)
43-52%
----
FEDEX BCS NATIONAL CHAMPIONSHIP GAME
Oklahoma (12-1) over Florida (12-1)
43-52%
----
GATOR BOWL
Clemson (7-5) over Nebraska (8-4)
38-53%
----

Boise State got robbed

2008-12-08T06:36:00.000-05:00

I know this isn't the first time that a BCS at-large bid went differently from the rankings. And since I've been predicting for weeks that this would happen, you'd think I'd be stoic about it. But I love cheering for the proverbial little guy. And I not-so-secretly hoped I was wrong all these weeks predicting that Boise State would be left out of the BCS bowl picture. But the Poinsettia Bowl?!? The team that ended 9th in the final Standings (8th in the computers, 9th in both polls), and who, just as a by the way, gave us perhaps the greatest ending to a bowl game in recent history (some people say ever; so don't tell me or OU that Boise State can't play with the big boys), has to go to the Poinsettia Bowl? Meanwhile, Ohio State (11th in the computers, 10th in the polls, and 10th overall) plays in the Fiesta Bowl. This is fair? I don't think so. Maybe enough people will complain about this that it will force (yet another) change to the rules about BCS at-large bids.

The bowl bids will be settled tonight

2008-12-07T08:38:00.001-05:00

We'll keep the predictions short: Oklahoma will face Florida for the title, and I'm afraid that Ohio State will probably get picked for the last at-large BCS bowl bid over Boise State.

Hopefully the bowl game officials will prove me wrong on the latter, because there are only two undefeated teams left in the FBS (Utah and Boise State), and it would be nice to see them both in BCS bowls. But I'd be really surprised if Florida doesn't jump Texas in the Standings to take a spot in the title game.

Yes, the computers are still going to rate Texas favorably---last week, 5 of the 6 official systems had Texas ahead of Florida, and 4 of those systems had both Oklahoma and Texas ahead of both Florida and Alabama. Florida will improve with the computers, but they might still be behind Texas there. Again, we're in no way part of the official system, but the family of random walker rankings across varying p values (see this week's random walker rankings) are sometimes a decent proxy for what the official computer systems will do, and the random walkers keep Oklahoma and Texas in the top two throughout. Don't blame the computers on this one: I don't believe any of them explicitly put value on conference championships, and the OU-Texas-TTech trio is collectively and formidably undefeated as a unit.

So Florida will probably need the pollsters to vote them in with sufficient numbers to make up a difference in the computers. But Florida did, after all, just knock off a #1 that got the overwhelming majority (165!) of the first place votes across the two polls last week, so I'm confident that it will happen.

Random Walker Rankings through December 6th

2008-12-07T08:30:00.000-05:00

We remain grateful to both Kenneth Massey for maintaining his comparisons page and to Peter R. Wolfe for making game results available online.

Below we list rankings according to the Random Walker (RW) system of first-place votes and the Random Walker First-Last (RWFL) system at our selected p=0.75. We use the random walkers to rank all 120 Football Bowl Subdivision teams, plus the extra made-up "team" representing their collective Football Championship Subdivision opponents. The "votes" in the Random Walker (RW) system are all essentially first-place votes, teams with more votes ranked more highly. The Random Walker with First & Last (RWFL) system is a combination of "first-place" and "last-place" votes. We have determined that our bias parameter p=0.75 has nice properties for RWFL (near the minimum crossing probability when compared against round-robin standings), so we use p=0.75 for both RW and RWFL and are happy that this is coincidentally the same primary value we have used in the past for the RW rankings.

The breakdown of the top teams across different p values for both RW and RWFL can be seen in the figures below. Additionally, we plot the fraction of ranking violations---that is, the fraction of game outcomes that have been contrary to the rankings---for each system across the p values. Ranking violations like these are also included on Kenneth Massey's site, and can be used as one measure of the efficacy of a rank ordering; indeed, one could instead choose p to minimize such errors, but we are more comfortable at the selected fixed values for ease of explanation.

[See http://rankings.amath.unc.edu/old/2008.htm for these pre-bowl rankings. Post-bowl rankings are also available.]

Breakin' the tie...

2008-11-30T09:08:00.000-05:00

We don't have much to add to what we said last week. All eyes will be watching how this week's BCS Standings break the Big 12 South division tie. Using our own random walker rankings as an imperfect stand-in for what the group of computer systems will do, it appears that Oklahoma should pick up ground on Texas in the computers this week. Importantly, Oklahoma led Texas in both polls last week, but ended up far enough behind Texas in the computers to be behind Texas in the Standings (an average of the three). We'd guess that Oklahoma will gain enough ground in the computers, between their win over highly-ranked Oklahoma State and the follow-on effects of Kansas beating Missouri, that they will close the gap with Texas in the computers. So, quite simply, it might end up to the selections of the pollsters; if they stay consistent from last week, Oklahoma will go to the Big 12 Championship, but if they change their collective minds, it could still be Texas. We'll find out soon enough, and then we'll argue about it for at least a week (if not longer)... Boise State's slimmest of hopes for a BCS bowl remain alive, but still slim. As discussed last week, it first hinges on the last at-large bid, which might still be up for grabs if USC wins the Pac-10 by beating UCLA next week. If that happens, it should come down to a bowl game selection between Boise State and Ohio State...

Random Walker Rankings through November 29th

2008-11-30T09:00:00.000-05:00

2008 Random Walker Rankings (p=0.75)
Games Through Saturday November 29th
	RW		RWFL
Rank	Team (Wins-Losses)	% of Total Votes	Team (Wins-Losses)	%(First)-%(Last)
1	Oklahoma (11-1)	2.4099	Oklahoma (11-1)	2.1205
2	Texas (11-1)	2.3095	Texas (11-1)	2.0672
3	Alabama (12-0)	2.1853	Alabama (12-0)	1.8886
4	Florida (11-1)	2.1021	Florida (11-1)	1.8138
5	Texas Tech (11-1)	2.0875	Texas Tech (11-1)	1.7311
6	Utah (12-0)	2.0415	Utah (12-0)	1.7200
7	Southern Cal (10-1)	1.9146	Southern Cal (10-1)	1.6069
8	Penn State (11-1)	1.7845	Penn State (11-1)	1.4542
9	Boise St (12-0)	1.7435	Boise St (12-0)	1.3941
10	Georgia Tech (9-3)	1.5604	Ohio State (10-2)	1.1365
11	Boston College (9-3)	1.5059	Georgia Tech (9-3)	1.1092
12	Ball St (12-0)	1.4819	Boston College (9-3)	1.0862
13	Ohio State (10-2)	1.4742	Ball St (12-0)	1.0593
14	Cincinnati (10-2)	1.4207	Cincinnati (10-2)	1.0225
15	North Carolina (8-4)	1.3617	Georgia (9-3)	0.9924
16	Georgia (9-3)	1.3532	TCU (10-2)	0.9175
17	Florida St (8-4)	1.3379	North Carolina (8-4)	0.8800
18	Virginia Tech (8-4)	1.3349	Florida St (8-4)	0.8793
19	TCU (10-2)	1.3303	Michigan St (9-3)	0.8527
20	Oklahoma St (9-3)	1.2467	Oklahoma St (9-3)	0.8479
21	Pittsburgh (8-3)	1.2451	Virginia Tech (8-4)	0.8474
22	Michigan St (9-3)	1.2219	Pittsburgh (8-3)	0.8159
23	Oregon St (8-4)	1.2017	Missouri (9-3)	0.7589
24	Missouri (9-3)	1.1565	Oregon St (8-4)	0.7492
25	Wake Forest (7-5)	1.1481	Oregon (9-3)	0.7319
26	Oregon (9-3)	1.1393	Brigham Young (10-2)	0.6765
27	Mississippi (8-4)	1.1306	Wake Forest (7-5)	0.6576
28	Brigham Young (10-2)	1.1200	Nebraska (8-4)	0.6532
29	Maryland (7-5)	1.1137	Mississippi (8-4)	0.6258
30	Clemson (7-5)	1.0949	California (7-4)	0.5957
31	Nebraska (8-4)	1.0698	Northwestern (9-3)	0.5499
32	Miami FL (7-5)	1.0589	Clemson (7-5)	0.5402
33	California (7-4)	1.0578	Miami FL (7-5)	0.5340
34	Northwestern (9-3)	1.0317	Maryland (7-5)	0.5020
35	Iowa (8-4)	0.9905	Iowa (8-4)	0.4786
36	Connecticut (7-4)	0.9656	Kansas (7-5)	0.4360
37	North Carolina St (6-6)	0.9596	Connecticut (7-4)	0.4255
38	Kansas (7-5)	0.9425	South Carolina (7-5)	0.3900
39	South Carolina (7-5)	0.9371	South Florida (7-4)	0.3525
40	South Florida (7-4)	0.9140	North Carolina St (6-6)	0.3518
41	Virginia (5-7)	0.9127	West Virginia (7-4)	0.3434
42	Navy (7-4)	0.9072	Navy (7-4)	0.3145
43	West Virginia (7-4)	0.8844	Western Michigan (9-3)	0.2932
44	Rutgers (6-5)	0.8548	Air Force (8-4)	0.2858
45	East Carolina (8-4)	0.8457	Rice (9-3)	0.2653
46	Tulsa (10-2)	0.8442	Tulsa (10-2)	0.2537
47	Rice (9-3)	0.8324	East Carolina (8-4)	0.2333
48	Vanderbilt (6-6)	0.8287	Rutgers (6-5)	0.2287
49	Air Force (8-4)	0.8269	Virginia (5-7)	0.2067
50	Western Michigan (9-3)	0.8235	LSU (7-5)	0.2004
51	LSU (7-5)	0.8144	Wisconsin (7-5)	0.1687
52	Central Michigan (8-4)	0.7642	Vanderbilt (6-6)	0.1540
53	Wisconsin (7-5)	0.7612	Central Michigan (8-4)	0.1065
54	Nevada (7-5)	0.7422	Notre Dame (6-6)	0.0633
55	Hawai`i (7-5)	0.7319	Minnesota (7-5)	0.0495
56	Notre Dame (6-6)	0.7305	Nevada (7-5)	0.0456
57	Arkansas (5-7)	0.7115	Hawai`i (7-5)	0.0343
58	Kentucky (6-6)	0.7061	Kentucky (6-6)	0.0147
59	Minnesota (7-5)	0.6905	Fresno St (7-5)	-0.0105
60	Arizona (6-5)	0.6647	Arkansas (5-7)	-0.0318
61	Fresno St (7-5)	0.6631	Colorado St (6-6)	-0.0410
62	Duke (4-8)	0.6574	Arizona (6-5)	-0.0573
63	Tennessee (5-7)	0.6493	Colorado (5-7)	-0.0653
64	Colorado (5-7)	0.6435	Houston (7-5)	-0.1004
65	Houston (7-5)	0.6432	Illinois (5-7)	-0.1229
66	Stanford (5-7)	0.6363	Tennessee (5-7)	-0.1315
67	Colorado St (6-6)	0.6362	Buffalo (7-5)	-0.1363
68	Louisiana Tech (7-5)	0.6345	Stanford (5-7)	-0.1375
69	Baylor (4-8)	0.6090	Louisiana Tech (7-5)	-0.1548
70	Troy (7-4)	0.6067	Baylor (4-8)	-0.1564
71	Illinois (5-7)	0.6008	Duke (4-8)	-0.1631
72	Louisville (5-6)	0.6001	Arizona St (5-6)	-0.1647
73	Buffalo (7-5)	0.5972	Troy (7-4)	-0.1684
74	Arizona St (5-6)	0.5903	Louisville (5-6)	-0.1894
75	Bowling Green (6-6)	0.5765	Auburn (5-7)	-0.2229
76	Auburn (5-7)	0.5758	Purdue (4-8)	-0.2730
77	Texas A&M (4-8)	0.5755	Kansas St (5-7)	-0.2828
78	Kansas St (5-7)	0.5495	San Jose St (6-6)	-0.2955
79	Mississippi St (4-8)	0.5427	Texas A&M (4-8)	-0.3155
80	Purdue (4-8)	0.5412	Northern Illinois (6-6)	-0.3458
81	San Jose St (6-6)	0.5395	UNLV (5-7)	-0.3609
82	Southern Miss (6-6)	0.5347	Southern Miss (6-6)	-0.3637
83	UNLV (5-7)	0.5344	UCLA (4-7)	-0.3818
84	Arkansas St (6-5)	0.5260	Florida Atlantic (6-6)	-0.4150
85	Northern Illinois (6-6)	0.5051	Mississippi St (4-8)	-0.4333
86	Michigan (3-9)	0.5000	Arkansas St (6-5)	-0.4496
87	UCLA (4-7)	0.4946	Bowling Green (6-6)	-0.4537
88	Florida Atlantic (6-6)	0.4883	New Mexico (4-8)	-0.4871
89	Syracuse (3-9)	0.4814	Memphis (6-6)	-0.5138
90	New Mexico (4-8)	0.4781	UTEP (5-7)	-0.5326
91	Middle Tennessee St (5-6)	0.4685	Temple (5-7)	-0.5366
92	UTEP (5-7)	0.4658	Syracuse (3-9)	-0.5480
93	Memphis (6-6)	0.4635	Michigan (3-9)	-0.5914
94	Indiana (3-9)	0.4618	Akron (5-7)	-0.6132
95	Temple (5-7)	0.4492	Indiana (3-9)	-0.6374
96	Wyoming (4-8)	0.4480	Wyoming (4-8)	-0.6389
97	Utah St (3-9)	0.4448	Middle Tennessee St (5-6)	-0.6552
98	Akron (5-7)	0.4369	Marshall (4-8)	-0.6637
99	Marshall (4-8)	0.4344	Utah St (3-9)	-0.6755
100	Central Florida (4-8)	0.3921	Louisiana-Lafayette (5-6)	-0.7116
101	Eastern Michigan (3-9)	0.3874	Central Florida (4-8)	-0.8008
102	Louisiana-Lafayette (5-6)	0.3768	Ohio U. (4-8)	-0.8346
103	Kent St (4-8)	0.3757	Florida Int'l (4-7)	-0.8643
104	Ohio U. (4-8)	0.3716	Alabama-Birmingham (4-8)	-0.8743
105	New Mexico St (3-9)	0.3711	Kent St (4-8)	-1.0386
106	Florida Int'l (4-7)	0.3698	Washington St (2-11)	-1.0620
107	Washington St (2-11)	0.3492	Iowa St (2-10)	-1.0879
108	Alabama-Birmingham (4-8)	0.3463	New Mexico St (3-9)	-1.1113
109	San Diego St (2-10)	0.3417	Toledo (3-9)	-1.1199
110	Washington (0-11)	0.3409	Eastern Michigan (3-9)	-1.1364
111	Western Kentucky (2-9)	0.3369	Louisiana-Monroe (4-8)	-1.1884
112	Toledo (3-9)	0.3279	Army (3-8)	-1.2521
113	Army (3-8)	0.3275	San Diego St (2-10)	-1.3513
114	Iowa St (2-10)	0.3237	Idaho (2-10)	-1.4577
115	Louisiana-Monroe (4-8)	0.3234	Tulane (2-10)	-1.4638
116	FCS teams (XXX-XXX)	0.3040	Western Kentucky (2-9)	-1.5812
117	Tulane (2-10)	0.2999	Washington (0-11)	-1.5971
118	Miami OH (2-10)	0.2969	Miami OH (2-10)	-1.6346
119	Idaho (2-10)	0.2923	SMU (1-11)	-1.8200
120	SMU (1-11)	0.2857	FCS teams (XXX-XXX)	-1.8933
121	North Texas (1-11)	0.2121	North Texas (1-11)	-2.1141

Now the fun really starts?

2008-11-23T16:10:00.000-05:00

Volumes could be (and are being) written about the possible mess on the way to the national championship game selection. I can only hope that the near-playoff we're going to be treated to in the SEC and Big 12 will build some future interest in a true playoff system. From all accounts, it still appears that an Alabama-Florida SEC Championship game will be an unofficial national semifinal, assuming of course they both win out until then. In an amusing twist, the Big 12 conference championship matchup will be determined by the BCS standings if OU, Texas, and Texas Tech all win next weekend, the highest ranked among those three playing Missouri for the conference championship. If that team then beats Mizzou, they're all but assured a spot in the national title game; but if the conference championship goes to Missouri, it's going to be chaos...

Meanwhile, in the "BCS Busters" department, I don't want to say it, but I have to acknowledge the facts, and those facts say it is now more unlikely that Boise State is going to get a BCS bowl bid. Don't send me hate mail over this; I wish it weren't so. But their chances under the governing BCS rules are becoming thinner after this past weekend. Utah has all but officially wrapped up an automatic BCS bowl bid, barring lots of pollsters changing their minds from previous weeks and moving Boise State ahead of the Utes. The special rules that force inclusion of high ranking conference champions outside the big 6 conferences only applies to a single school, which will be Utah, assuming again they stay ahead of Boise State in the BCS Standings. The second such school has to get a bid through the normal at-large selection process, of which there will only be 3 openings left. For Boise State's purposes, a hopeful key phrase in the rules is "No more than two teams from a conference may be selected, regardless of whether they are automatic qualifiers or at-large selections." Importantly, the top of the BCS Standings is packed full of teams from the SEC and Big 12, so it's safe to say that two from each will get BCS bowl bids. That is, two of the remaining three at-large bids will go to these two conferences. So does Boise State have a shot at that last spot if they win out? After yesterday, I'm not confident. Specifically, Oregon State is now one win away from a trip to the Rose Bowl, in which case you have to think that USC is going to get an at-large BCS bid. Indeed, if USC somehow climbs to #4 in the Standings before the end of the season, that at-large bid becomes automatic under the rules. So Boise State fans have to be cheering for Oregon to beat Oregon State next weekend, and for USC to win the conference to take the Rose Bowl bid. Alternatively, USC could drop out of the picture altogether with losses to both ND and UCLA; but that's not something I'd be counting on happening! So, Boise State fans need USC to win the Pac-10. Otherwise, there is no realistic route to a BCS bowl for Boise State. If USC does win the Pac-10, then the last at-large BCS bid appears to come down to a choice, made by the bowl games themselves, between Boise State and Ohio State (ignoring other teams that might become technically eligible but that I think are even less likely to be chosen).

Random Walker Rankings through November 22nd

2008-11-23T16:00:00.000-05:00

The random walker rankings are back again for 2008! We remain grateful to both Kenneth Massey for maintaining his comparisons page and to Peter R. Wolfe for making game results available online.

Below we list rankings according to the Random Walker (RW) system of first-place votes and the Random Walker First-Last (RWFL) system at our selected p=0.75. The breakdown of the top teams across different p values for both RW and RWFL can be seen in the figures below. Additionally, we plot the fraction of ranking violations---that is, the fraction of game outcomes that have been contrary to the rankings---for each system across the p values. Ranking violations like these are also included on Kenneth Massey's site, and can be used as one measure of the efficacy of a rank ordering; indeed, one could instead choose p to minimize such errors, but we are more comfortable at the selected fixed values for ease of explanation.

We use the Random Walkers to rank all 120 Football Bowl Subdivision teams, plus the extra made-up "team" representing their collective Football Championship Subdivision opponents. The "votes" in the Random Walker (RW) system are all essentially first-place votes, teams with more votes ranked more highly. The Random Walker with First & Last (RWFL) system is a combination of "first-place" and "last-place" votes. We have determined that our bias parameter p=0.75 has nice properties for RWFL (near the minimum crossing probability when compared against round-robin standings), so we use p=0.75 for both RW and RWFL and are happy that this is coincidentally the same primary value we have used in the past for the RW rankings.

2008 Random Walker Rankings (p=0.75)
Games Through Saturday November 22nd
	RW		RWFL
Rank	Team (Wins-Losses)	% of Total Votes	Team (Wins-Losses)	%(First)-%(Last)
1	Texas (10-1)	2.3680	Texas (10-1)	2.1289
2	Alabama (11-0)	2.3317	Alabama (11-0)	2.0357
3	Oklahoma (10-1)	2.2593	Oklahoma (10-1)	1.9523
4	Florida (10-1)	2.1220	Florida (10-1)	1.8241
5	Texas Tech (10-1)	2.0932	Utah (12-0)	1.7469
6	Utah (12-0)	2.0743	Texas Tech (10-1)	1.7235
7	Southern Cal (9-1)	1.8659	Southern Cal (9-1)	1.5516
8	Penn State (11-1)	1.8156	Penn State (11-1)	1.4866
9	Boise St (11-0)	1.6526	Georgia (9-2)	1.3229
10	Georgia (9-2)	1.6402	Boise St (11-0)	1.2815
11	Ohio State (10-2)	1.4787	Ohio State (10-2)	1.1402
12	Oklahoma St (9-2)	1.4079	Oklahoma St (9-2)	1.0301
13	Ball St (11-0)	1.3948	Missouri (9-2)	0.9975
14	Florida St (8-3)	1.3799	Cincinnati (9-2)	0.9851
15	Cincinnati (9-2)	1.3796	Ball St (11-0)	0.9535
16	Georgia Tech (8-3)	1.3728	Oregon St (8-3)	0.9187
17	Missouri (9-2)	1.3498	Florida St (8-3)	0.9140
18	Oregon St (8-3)	1.3426	TCU (10-2)	0.9134
19	TCU (10-2)	1.3296	Georgia Tech (8-3)	0.8761
20	Boston College (8-3)	1.3090	Boston College (8-3)	0.8371
21	North Carolina (7-4)	1.2789	Michigan St (9-3)	0.8355
22	Michigan St (9-3)	1.2113	North Carolina (7-4)	0.7594
23	Virginia Tech (7-4)	1.2067	Virginia Tech (7-4)	0.6781
24	Miami FL (7-4)	1.1360	Brigham Young (10-2)	0.6749
25	Mississippi (7-4)	1.1321	Miami FL (7-4)	0.6520
26	Brigham Young (10-2)	1.1250	Pittsburgh (7-3)	0.6514
27	Maryland (7-4)	1.1248	Mississippi (7-4)	0.6096
28	Pittsburgh (7-3)	1.1176	California (7-4)	0.5878
29	Connecticut (7-3)	1.0744	Connecticut (7-3)	0.5803
30	Wake Forest (6-5)	1.0609	Nebraska (7-4)	0.5760
31	California (7-4)	1.0447	Northwestern (9-3)	0.5545
32	South Carolina (7-4)	1.0347	Oregon (8-3)	0.5461
33	Northwestern (9-3)	1.0346	South Carolina (7-4)	0.5386
34	Nebraska (7-4)	1.0150	Maryland (7-4)	0.5209
35	Iowa (8-4)	0.9956	Wake Forest (6-5)	0.5143
36	Oregon (8-3)	0.9875	Iowa (8-4)	0.4846
37	West Virginia (7-3)	0.9865	West Virginia (7-3)	0.4800
38	Clemson (6-5)	0.9655	LSU (7-4)	0.4221
39	LSU (7-4)	0.9587	Central Michigan (8-3)	0.4151
40	Virginia (5-6)	0.9320	Western Michigan (9-2)	0.4057
41	Vanderbilt (6-5)	0.9316	Clemson (6-5)	0.3429
42	Central Michigan (8-3)	0.9146	Vanderbilt (6-5)	0.3040
43	Western Michigan (9-2)	0.8979	Air Force (8-4)	0.2855
44	Navy (6-4)	0.8395	Kansas (6-5)	0.2638
45	Air Force (8-4)	0.8357	Virginia (5-6)	0.2488
46	Kansas (6-5)	0.8274	Tulsa (9-2)	0.2112
47	Rutgers (6-5)	0.8252	Kentucky (6-5)	0.2027
48	North Carolina St (5-6)	0.8227	Rice (8-3)	0.1945
49	Tulsa (9-2)	0.8186	Rutgers (6-5)	0.1927
50	East Carolina (7-4)	0.8100	Navy (6-4)	0.1916
51	Kentucky (6-5)	0.8029	Wisconsin (7-5)	0.1885
52	Rice (8-3)	0.7830	East Carolina (7-4)	0.1581
53	Wisconsin (7-5)	0.7715	South Florida (6-4)	0.1424
54	South Florida (6-4)	0.7555	North Carolina St (5-6)	0.1287
55	Hawai`i (6-5)	0.7231	Buffalo (7-4)	0.1171
56	Notre Dame (6-5)	0.7169	Minnesota (7-5)	0.0495
57	Colorado (5-6)	0.7095	Notre Dame (6-5)	0.0448
58	Houston (7-4)	0.7084	Colorado (5-6)	0.0268
59	Louisiana Tech (7-4)	0.6892	Fresno St (7-4)	0.0156
60	Nevada (6-5)	0.6880	Houston (7-4)	0.0077
61	Minnesota (7-5)	0.6875	Hawai`i (6-5)	-0.0255
62	Buffalo (7-4)	0.6827	Colorado St (6-6)	-0.0312
63	Fresno St (7-4)	0.6774	Arizona (6-5)	-0.0435
64	Arizona (6-5)	0.6697	Louisiana Tech (7-4)	-0.0650
65	Duke (4-7)	0.6647	Nevada (6-5)	-0.0687
66	Arkansas (4-7)	0.6582	Illinois (5-7)	-0.0941
67	Colorado St (6-6)	0.6474	Stanford (5-7)	-0.1306
68	Stanford (5-7)	0.6448	Troy (7-4)	-0.1358
69	Tennessee (4-7)	0.6293	Baylor (4-7)	-0.1373
70	Troy (7-4)	0.6231	Arkansas (4-7)	-0.1444
71	Illinois (5-7)	0.6139	Duke (4-7)	-0.1629
72	Baylor (4-7)	0.6079	Louisville (5-6)	-0.1888
73	Louisville (5-6)	0.5817	Auburn (5-6)	-0.1988
74	Auburn (5-6)	0.5803	Tennessee (4-7)	-0.2157
75	Mississippi St (4-7)	0.5786	Purdue (4-8)	-0.2561
76	Texas A&M (4-7)	0.5640	UCLA (4-6)	-0.2629
77	Arizona St (4-6)	0.5611	Arizona St (4-6)	-0.2670
78	Purdue (4-8)	0.5534	Kansas St (5-7)	-0.2879
79	Kansas St (5-7)	0.5454	Northern Illinois (6-5)	-0.2879
80	UCLA (4-6)	0.5346	San Jose St (6-6)	-0.3183
81	San Jose St (6-6)	0.5318	Texas A&M (4-7)	-0.3321
82	Bowling Green (5-6)	0.5309	Mississippi St (4-7)	-0.3505
83	UNLV (5-7)	0.5276	UNLV (5-7)	-0.3954
84	Arkansas St (5-5)	0.5211	UTEP (5-6)	-0.4084
85	Northern Illinois (6-5)	0.5176	Southern Miss (5-6)	-0.4176
86	Southern Miss (5-6)	0.5091	Arkansas St (5-5)	-0.4875
87	Michigan (3-9)	0.5050	New Mexico (4-8)	-0.4933
88	UTEP (5-6)	0.4995	Florida Atlantic (5-6)	-0.5143
89	New Mexico (4-8)	0.4808	Akron (5-6)	-0.5158
90	Syracuse (3-8)	0.4766	Syracuse (3-8)	-0.5307
91	Middle Tennessee St (5-6)	0.4740	Michigan (3-9)	-0.5500
92	Indiana (3-9)	0.4662	Bowling Green (5-6)	-0.5758
93	Florida Atlantic (5-6)	0.4612	Memphis (5-6)	-0.5924
94	Akron (5-6)	0.4541	Indiana (3-9)	-0.6045
95	Marshall (4-7)	0.4533	Middle Tennessee St (5-6)	-0.6172
96	Wyoming (4-8)	0.4444	Marshall (4-7)	-0.6215
97	Memphis (5-6)	0.4357	Temple (4-7)	-0.6548
98	Temple (4-7)	0.4187	Central Florida (4-7)	-0.6575
99	Utah St (2-9)	0.4138	Wyoming (4-8)	-0.6722
100	Central Florida (4-7)	0.4120	Louisiana-Lafayette (5-6)	-0.7191
101	New Mexico St (3-8)	0.3902	Florida Int'l (4-6)	-0.7652
102	Florida Int'l (4-6)	0.3897	Utah St (2-9)	-0.8625
103	Louisiana-Lafayette (5-6)	0.3715	Ohio U. (3-8)	-0.9288
104	Washington St (2-10)	0.3620	Toledo (3-8)	-0.9382
105	Ohio U. (3-8)	0.3557	Washington St (2-10)	-0.9981
106	Toledo (3-8)	0.3449	New Mexico St (3-8)	-1.0001
107	San Diego St (2-10)	0.3422	Alabama-Birmingham (3-8)	-1.0715
108	Western Kentucky (2-9)	0.3379	Iowa St (2-10)	-1.1016
109	Washington (0-11)	0.3354	Louisiana-Monroe (4-8)	-1.1863
110	Army (3-8)	0.3281	Army (3-8)	-1.2387
111	Louisiana-Monroe (4-8)	0.3259	Kent St (3-8)	-1.3300
112	Tulane (2-9)	0.3249	Tulane (2-9)	-1.3602
113	Iowa St (2-10)	0.3246	San Diego St (2-10)	-1.3729
114	Alabama-Birmingham (3-8)	0.3204	Eastern Michigan (2-9)	-1.4263
115	Eastern Michigan (2-9)	0.3171	Miami OH (2-9)	-1.4882
116	Miami OH (2-9)	0.3099	Idaho (2-10)	-1.4959
117	Kent St (3-8)	0.3094	Western Kentucky (2-9)	-1.5605
118	FCS teams (XXX-XXX)	0.3033	Washington (0-11)	-1.5963
119	SMU (1-10)	0.2953	SMU (1-10)	-1.7256
120	Idaho (2-10)	0.2927	FCS teams (XXX-XXX)	-1.9049
121	North Texas (1-10)	0.2182	North Texas (1-10)	-2.0391

Moving to a blog

2008-11-23T15:53:00.001-05:00

As the regular season of college football heads towards another slate of potential controversy, we've found ourselves using our rankings page for occasional commentary, both about the race for bids in the BCS National Championship game and about the race among the so-called BCS busters to see if one of them secures an "automatic" bid and if others have a shot at one of the remaining at-large bids. Unfortunately, because of the format of our old web page, it was difficult to organize an historical record of such comments. So we are finally moving to a blog...

Lots more about the current season will hopefully get posted quickly. And we will eventually move or provide links to some of the other rankings we've made over the past 5 years of running the "Random Walker Rankings" (still available at http://rankings.amath.unc.edu/old).

How well can monkeys rank football teams? [repost]

2003-12-31T19:34:00.000-05:00

We've all experienced befuddlement upon perusing the NCAA Division I-A college football
Bowl Championship Series (BCS) standings, because of the seemingly divine inspiration that must have been incorporated into their determination. The relatively small numbers of games between a large number of teams makes any ranking immediately suspect because of the dearth of head-to-head information. Perhaps you've even wondered if a bunch of monkeys could have ranked the football teams as well as the expert coaches and sportswriters polls and the complicated statistical ranking algorithms.

We had these thoughts, so we set out to test this hypothesis, although with simulated monkeys (random walkers) rather than real ones.

Each of our simulated "monkeys" gets a single vote to cast for the "best" team in the nation, making their decisions based on only one simple guideline: They periodically look up the win-loss outcome of a single game played by their favorite team, and flip a weighted coin to determine whether to change their allegiance to the other team. In order to make this process even modestly reasonable, this random decision is made so that there is higher probability that the monkey's allegiance and vote will go with the team that won the head-to-head contest. For instance, the weighting of the coin might be chosen so that 75% (say) of the time the monkey changes his vote to go with the winner of the game, meaning only a 25% chance of voting for the loser.

The monkey starts by voting for a randomly chosen team. Each monkey then meanders around a network which describes the collection of teams, randomly changing allegiance from one team to another along connections representing games played between the two teams that year. This network is graphically depicted in the figure here, with the monkeys---okay, technically one is a gorilla---not so happily lent to us by Ben Mucha (inset). It's a simple process: if the outcome of the weighted coin flip indicates that he should be casting his vote for the opposing team, the monkey stops cheerleading for the old team and moves to the site in the network representing his new favorite team. While we let the monkeys change their minds over and over again---indeed, a single monkey voter will forever be changing his vote in this scheme---the percentage of votes cast for each football team quickly stabilizes. We thereby obtain rankings each week of the season and at the end of the season, based on the games played to that point of the season, by looking at the fraction of monkeys that vote for each team.

***The Simple Rules for Each "Monkey"***
(1) Pick a game played by your "favorite" team; that is, the team you are currently casting your single vote for.
(2) Flip a weighted coin that is more likely to come up heads. [How much more likely? What percentage of the time does it come up heads? That is the one number we can modify.]
(3) Completely forgetting which team you voted for before, go with the winner of the game if heads, the loser if tails, changing your vote if necessary.
(4) Return to step 1.

Mathematically analyzing how these simulated monkeys behave, we examined the resulting rankings for the past 33 seasons of Division I-A football. The calculations involved are related to a class of so-called "direct methods" of ranking, but the interpretation in terms of random-walkers appears to be novel. Under this system, winning games is directly rewarded and strength of schedule is automatically incorporated because games played against highly-ranked opponents lead to more monkeys inquiring about and making decisions based on the outcome of such games. Armed only with the single simple rule of more often voting for the winner of a game instead of the loser, the top few teams determined by total vote counts are typically quite reasonable. For instance, it isn't any surprise that the pre-bowl-game monkey rankings at the end of the 2002 season choose Miami and Ohio State as the top two teams, nor is it surprising that they pick Miami as the top team in 2001 and Oklahoma as top in 2000 (all 4 were major, undefeated teams).

More intriguing are the differences between the #2 teams in the pre-bowl monkey rankings and the BCS standings at the ends of the controversial 2000 and 2001 seasons. The results of the monkey ranking system depend on the precise value selected to describe how strongly the flipped coin is weighted, but over a wide range of the coin's weighting, the monkeys select Tennessee to play Miami for the championship at the end of 2001 and Washington to play Oklahoma for the championship at the end of 2000. Both of these selections are mildly surprising, as neither team was commonly backed in the controversies at the ends of the respective seasons. The pre-bowl monkey rankings select these two teams in part because our simple rule includes neither information about the dates of games played (no special weight on Tennessee losing the SEC Championship game to LSU), nor margin of victory (Washington won a number of close games). We could have included date of game and margin of victory in such a system by modifying the weighting of the coin according to some formula describing these
factors, but such redefinitions would require essentially arbitrary choices about how strongly to weight such factors---in the face of such potential arbitrariness, we prefer the simpler system with just a single parameter to determine the transition probability of going with a game winner.

Also important in these controversial #2 selections is the relatively high ratings that the monkey votes accord to the top teams in the SEC in 2001 and the Pac 10 in 2000---in part because all 7 losses by the top three teams in the 2001 SEC were in conference, while 3 of the 4 losses by the top three teams in the 2000 Pac 10 were in conference.

One might very well argue over whether such selections are correct in any sense. We do not advocate that this method is superior to any other method; rather, our interest was to develop and study a very simplistic ranking system. Rather than directly rate the teams, the random walking monkeys are a simplistic behavioral model for voters who get to choose who they believe is the top team. Any arguments about who "should" have been picked for the National Championship game in controversial years remain inconclusive, underscoring the fundamental difficulty in attempting to rank college football teams based on the relatively small numbers of games played. Additionally, we should emphasize that the scheme is likely skewed towards distinguishing top teams, as opposed to separating, say, #31 from #32, since each random walking monkey has only a single vote. It may seem ironic that a group of mathematicians would prefer the easier to describe algorithm; but in the absence of more complete information---remembering that we're using only the win-loss outcome of each game---we prefer this simple ranking system of coin-flipping random-walking monkey voters with only one number (the weighting of the coin) that needs to be selected.

The virtue of this ranking system lies in its relative ease of explanation. Its performance is arguably on par with the expert polls and (typically more complicated) computer algorithms employed by the BCS. Can a bunch of monkeys rank football teams as well as the systems in use now? Perhaps they can.

[This is a partially-edited repost of material from the original, pre-blog, random walker rankings site. As such, the listed post date is approximate.]

Mathematicians examine the BCS? [repost]

2003-12-31T16:55:00.000-05:00

The figure to the right represents the expected distribution of model random-walker votes cast for each NCAA Division I-A football [known as the "Football Bowl Subdivision"] team in 2001 pre-bowl-games rankings. The organization of the teams and the lines connecting them represent the community structure hierarchy, of which the conferences are one level of organization. The colors represent the expected percentage of votes cast per team at each level in the hierarchy, from individual teams up through intra-conference organization, the conferences, and the connections between conferences. The biased probability for voting for the winners of games in the data represented in this figure is p = 0.65. Details are interspersed throughout these pages.

This work grew out of a Research Experiences for Undergraduates (REU) project in Summer 2003 by Georgia Tech undergraduate Thomas Callaghan, in collaboration with postdoctoral visiting assistant professor Mason Porter and assistant professor Peter Mucha. This work was funded (to pay Thomas' summer salary) by an NSF VIGRE "vertical integration" grant, justified by the enrichment of Thomas' educational experiences and by its true vertical integration spirit of joint work between an undergrad, postdoc, and professor. Later support for Thomas was also provided by the Georgia Tech President's Undergraduate Research Award (PURA). After graduating from GT, Thomas went on to a Ph.D. program in Computational and Mathematical Engineering at Stanford.

At the outset, we want to make three things very clear:

(1) We have NOTHING to do with the official Bowl Championship Series (BCS) standings.

(2) Volumes have been written by many mathematically- and statistically-inclined football fans who have developed a multitude of different ways of ranking college football teams (see David Wilson's excellent site).

(3) We don't claim that the system described here is "better"; rather, our approach was to ask if the most naive ranking system we could dream up would do a reasonable job. So we envisioned a collection of random walkers, which you might prefer to think of as monkeys.

[This is a partially-edited repost of material from the original, pre-blog, random walker rankings site. As such, the listed post date is approximate.]