Playoffs

Earlier today the college football playoff committee released their final rankings.  These rankings determined the teams that qualify for the second ever playoffs: Clemson, Alabama, Michigan State, Oklahoma.  The rankings also have other implications, sending Iowa to the Rose Bowl and qualifying Houston for a major bowl game.

In a not quite equally anticipated revealing, I'm now displaying the final SORTACUS rankings of the year.  I've just posted the top 25, since very few of the teams lower ranked played games last weekend.  If you have complaints, bottle them in.

For the new readers who aren't familiar, SORTACUS is a computer rankings system developed by me in association with Andy Meisner.  It's based entirely off of wins and losses, ignoring margin of victory.  That makes it particularly effective at determining the most deserving teams.  In previous posts I've covered more on the math behind SORTACUS, and my thoughts on a college football playoff.

Top 25

Rank	Team	Record	Rating
1	Clemson	12-0	25.28
2	Alabama	11-1	23.85
3	Michigan St	12-1	22.29
4	Iowa	11-1	21.25
5	Ohio St	11-1	20.45
6	Oklahoma	11-1	20.40
7	Stanford	11-2	20.07
8	Notre Dame	10-2	18.75
9	Northwestern	9-2	17.94
10	Houston	11-1	17.69
11	TCU	9-2	16.13
12	Oklahoma St	9-2	15.84
13	Mississippi	8-3	15.11
14	Florida	10-3	15.07
15	Michigan	9-3	14.96
16	Navy	8-2	14.89
17	LSU	8-3	14.85
18	Oregon	8-3	14.57
19	Florida St	9-2	13.52
20	North Carolina	9-2	13.18
21	Memphis	8-3	13.00
22	Utah	9-3	12.11
23	Temple	10-3	11.81
24	Wisconsin	9-3	11.32
25	Baylor	8-3	11.28

The Playoffs

SORTACUS follows the national trend and picks the top four teams as Clemson, Alabama, Michigan State and ... IOWA?!?!?!

That's right, even with a loss to the Spartans last night the Hawkeyes still stack up favorably against other one loss options like Ohio State and Oklahoma.  Despite early gripes about the Iowa schedule, the rise of Northwestern and Wisconsin plus the addition of Michigan State in the championship game have eliminated that issue in SORTACUS's eyes.

One potential issue with the SORTACUS philosophy is that it values all games equally.  In general I feel that's true.  Conference championship games may be a reasonable exception though.  The Hawkeyes had a fair shot last night, and despite a hard fought battle they couldn't pull it out.  Instead of Michigan State having to potentially face Iowa again, it might be more interesting to see the Sooners have a shot.

Of course, it's also possible that the Hawks faced an uphill battle ever since being unranked in the pre-season, something they couldn't quite overcome.  There is definitely a case for Kirk Ferentz and company to feel bitter.  Still, I won't lose many tears over the upcoming once in a lifetime Iowa-Stanford Rose Bowl matchup.  See you all there!

SORTACUS Full Rankings

This past Thanksgiving weekend signaled the end (largely) of the college football regular season.  There are a few championship games that will cause significant shuffling at the top, but for many teams all the remains is a bowl game, or even nothing.

Because many teams have completed their journeys, and because of an ever increasing number of requests for "How Is My Team Doing" this week I'll take the chance to list all 128 FBS teams by their SORTACUS ranking.

For those who are new to the game, SORTACUS is a mathematical ratings system that I designed to rank college football teams solely by wins and losses.  Because of this it is not as good at predicting future results, but does an excellent job measuring which teams have been the most successful so far.  Details on the behind the scenes Bayesian statistics based ratings were covered last post.

Kobe Bryant

Before launching into the ratings results I should also acknowledge the impending retirement of the inspiration for this blog's name: Kobe Bryant.  In many ways he represented evaluation based of reputation, "clutch" performance, and "the eye-test", all things this blog has campaigned against.  I memorably declared that Kobe was never the NBA's best player.  He was still an all-time player though.  In my heyday I would've ranked him among the best of all-time, but for now I'll just estimate he'd be ~15.  An incredible feat.

Full College Football Rankings

Enough about Kobe.  The full SORTACUS rankings are below.  There are a few interesting things to note.  Iowa, Clemson, and Alabama have established themselves as a clear top tier.  Oklahoma, Michigan State, and Ohio State are clear second tier.  North Carolina's weak schedule means that even with only one loss they don't deserve consideration for a playoff spot.  Finally, the University of Louisiana at Monroe is further away from average (above or below) than any other FBS team.

Rank	Team	Record	Rating
1	Clemson	11-0	24.12
2	Iowa	11-0	23.67
3	Alabama	10-1	22.69
4	Oklahoma	11-1	20.70
5	Michigan St	11-1	20.40
6	Ohio St	11-1	20.31
7	Stanford	10-2	18.90
8	Notre Dame	10-2	18.61
9	Northwestern	9-2	18.04
10	TCU	9-2	16.59
11	Oklahoma St	9-2	16.43
12	Florida	10-2	16.40
13	Houston	10-1	15.95
14	Baylor	8-2	15.34
15	Mississippi	8-3	15.11
16	Navy	8-2	14.81
17	Michigan	9-3	14.78
18	LSU	8-3	14.76
19	North Carolina	9-1	14.44
20	Oregon	8-3	14.18
21	Florida St	9-2	13.64
22	Temple	10-2	13.41
23	Memphis	8-3	12.94
24	Utah	9-3	12.08
25	USC	8-4	11.75
26	Wisconsin	9-3	11.42
27	Georgia	8-3	10.90
28	Washington St	8-3	10.50
29	Tennessee	7-4	10.33
30	Toledo	9-2	10.16
31	Mississippi St	7-4	9.96
32	W Kentucky	10-2	9.55
33	Texas A&M	7-4	9.43
34	UCLA	8-4	9.27
35	Arkansas	6-5	9.04
36	Pittsburgh	7-4	8.61
37	BYU	8-3	8.45
38	West Virginia	6-4	8.44
39	Bowling Green	9-3	8.44
40	Miami FL	7-4	8.27
41	Appalachian St	8-2	7.73
42	California	6-5	7.57
43	Penn St	7-5	7.30
44	South Florida	7-4	6.65
45	Texas Tech	6-5	5.95
46	Cincinnati	6-5	4.16
47	Arkansas St	7-3	4.16
48	Ga Southern	7-3	3.89
49	Auburn	5-6	3.70
50	Arizona St	5-6	3.69
51	Washington	5-6	3.51
52	W Michigan	6-5	3.38
53	Louisville	6-5	3.32
54	Southern Miss	8-3	2.41
55	San Diego St	8-3	2.36
56	Marshall	8-3	2.19
57	Minnesota	5-7	1.79
58	Nebraska	5-7	1.58
59	Indiana	5-6	1.38
60	Ohio	7-4	1.07
61	N Illinois	7-4	0.99
62	Air Force	7-4	0.91
63	Louisiana Tech	7-4	0.48
64	Arizona	5-6	0.45
65	Boise St	7-4	0.31
66	C Michigan	6-5	0.26
67	NC State	6-5	0.08
68	Illinois	4-7	-0.48
69	Duke	6-5	-0.54
70	Missouri	4-7	-0.58
71	Texas	4-7	-0.65
72	Connecticut	5-6	-0.79
73	Virginia Tech	5-6	-1.47
74	Kansas St	4-6	-1.52
75	Tulsa	6-6	-2.01
76	MTSU	6-5	-2.23
77	Akron	6-5	-2.40
78	Utah St	5-6	-3.15
79	Vanderbilt	3-8	-3.17
80	East Carolina	4-7	-3.30
81	South Carolina	3-8	-3.65
82	New Mexico	6-5	-3.76
83	Colorado St	6-5	-3.92
84	Kentucky	4-7	-4.28
85	Maryland	2-9	-4.58
86	Virginia	3-8	-5.60
87	Rutgers	3-8	-6.72
88	Syracuse	3-8	-6.86
89	Iowa St	2-9	-7.20
90	Georgia St	5-5	-7.54
91	Georgia Tech	2-9	-7.69
92	South Alabama	4-6	-8.27
93	Nevada	5-6	-8.35
94	Buffalo	4-7	-9.34
95	Colorado	3-9	-9.37
96	San Jose St	4-7	-9.94
97	SMU	2-9	-10.86
98	Purdue	1-10	-11.58
99	Old Dominion	4-7	-11.70
100	UTEP	4-7	-11.93
101	Rice	4-7	-12.16
102	Florida Intl	4-7	-12.24
103	Wake Forest	2-9	-12.82
104	ULL	3-7	-13.26
105	New Mexico St	3-8	-13.49
106	Oregon St	1-10	-13.50
107	Idaho	3-8	-13.52
108	Ball St	2-9	-13.75
109	FL Atlantic	3-9	-14.18
110	Boston College	1-9	-14.31
111	Kent	2-9	-14.71
112	UT San Antonio	3-9	-15.07
113	Massachusetts	3-9	-15.16
114	Fresno St	2-9	-15.70
115	Tulane	2-9	-15.77
116	Troy	2-8	-15.88
117	Wyoming	2-9	-16.17
118	Miami OH	2-9	-16.43
119	Texas St	2-8	-16.89
120	UNLV	2-9	-16.92
121	Hawaii	2-10	-18.91
122	North Texas	1-10	-19.22
123	Kansas	0-11	-19.53
124	Army	1-8	-21.39
125	Charlotte	1-10	-21.47
126	UCF	0-11	-22.82
127	E Michigan	1-11	-23.59
128	ULM	0-11	-26.17

SORTACUS Football Rankings (And Math!)

There are only a couple weeks left in the college football season, and the race for the playoffs is heating up!  Debate and discussion abound left and right over which teams deserve to reach the playoffs.  Which conferences are the strongest?  Which wins are most impressive?  When can a one loss team pass an undefeated?  Fortunately SORTACUS is here give us an answer.

Mathematics

Back when K,TMHMST was more active it was as much about math as sports.  Probability, game theory, and variance were regularly discussed.  I've given an overview of SORTACUS:  it uses only wins and losses to rank which teams are the most deserving.  I have not discussed much of the internal workings however.  Until now.  Break out your calculators, it's math time!

SORTACUS uses Bayesian statistics to estimate the inherent ability of each team (using only wins and losses).  Each team starts of with a wide normal distribution of ratings estimates as a prior distribution.  Each game then have a likelihood function of a win or loss: it's more likely you have a higher rating if you win.  The likelihood function is the normal cumulative distribution function.  Unfortunately these are not conjugate priors, so there's no pretty mathematical solution.  Instead I have a series of ratings bins (right now 401) that each have a probability and together approximate the distribution.

Whew, that's a lot of words.  Let's try an example instead.

Say Iowa, before playing Minnesota, has three ratings probabilities:  bad, average, and good.  Let's say they have the following odds:

Odds Iowa's rating is... Bad:  10%, Average: 50%, Good:  40%

That's our prior distribution (sort of).  We also know the odds that Iowa beats Minnesota if Iowa's rating is any of those categories.  These odds depend significantly on Minnesota's ratings.

Odds Iowa beats Minnesota if its ratings is... Bad:  20%, Average: 50%, Good: 80%

Now we need the observed data.  Remembering back to an unnecessarily stressful Saturday night we know Iowa did beat Minnesota.  We can apply Bayes's formula (P(x|y) = P(y)*P(y|x)) to calculate the probabilities of Iowa's ratings given a victory over Minnesota: 

Odds after winning that Iowa's rating is... Bad:  2% [10%*20%], Average:  25%, Good:  32%

Don't forget to normalize!

Odds after winning that Iowa's rating is... Bad:  3.4%, Average:  42.4%, Good:  54.2%

That's how SORTACUS works.  It does this process for 401 bins (not 3) for 128 teams for every game they play.  It also does multiple iterations to help converge towards the true value, each iteration having more accurate calculations of opponent quality.  The program takes ~5 minutes to crunch the numbers, and then spits out the college football rankings.

Speaking of rankings, let's get to the part everybody's interested in.

Top 25

The non-mathematical readers likely just jumped straight to these ratings.  Below is the SORTACUS top 25 using games through Saturday November 14.  In theory, the top 4 teams are the most worthy of a playoff spot so far.  Note that only FBS vs FBS games are considered (I see you Washington State), and that "Rating" corresponds roughly to how many points better than the FBS average a school has been.

Rank	Team	Record	Rating
1	Clemson	9-0	23.52
2	Iowa	9-0	22.87
3	Oklahoma St	9-0	21.62
4	Alabama	9-1	21.58
5	Ohio St	10-0	21.20
6	Notre Dame	9-1	20.81
7	Houston	9-0	20.22
8	Florida	9-1	18.66
9	Navy	7-1	16.80
10	TCU	8-1	16.75
11	Oklahoma	9-1	16.41
12	Michigan St	9-1	16.35
13	LSU	7-2	15.32
14	Northwestern	7-2	15.32
15	Memphis	7-2	15.27
16	Stanford	8-2	14.73
17	Baylor	7-1	14.07
18	Michigan	8-2	14.06
19	Utah	8-2	13.33
20	North Carolina	7-1	12.72
21	Washington St	7-2	12.35
22	Toledo	8-1	12.24
23	Wisconsin	8-2	12.03
24	Mississippi	6-3	11.91
25	USC	7-3	11.16

The Playoffs

SORTACUS is making me look like a homer this year, but I promise it's just the numbers.  Iowa's victories over Northwestern and Wisconsin continue to get more impressive, and SORTACUS sees the Hawks as the nation's second most accomplished team this season.

Elsewhere in the playoffs Clemson stands out as a clear number 1.  A weak ACC is offset by an impressive victory over Notre Dame.  Number 3 Oklahoma State is the Big 12's last unbeaten, and they face a tough road in their last two games.  For the final slot Alabama jumps over defending champion Ohio State even with a loss.  Ohio State could improve that with a couple late wins, but if any undefeated team loses the Tide and Notre Dame are waiting at the door.

Further down in the standings it's interesting to notice the weakness of an ACC schedule (7-1 North Carolina at 20) compared to the surprising strength of an AAC schedule (7-2 Memphis at 15).

How Is My Team Doing

For the unlucky few who don't love the Hawkeyes (or Cardinal) here's a few notable team rankings.

Texas Tech:  44th, rating of 4.32

Auburn:  51, 3.38

Nebraska:  59, 1.22

NC State:  65, 0.17

Vanderbilt:  70, -1.32

Iowa State:  79, -3.80

Maryland:  89, -5.97

Purdue:  98, -10.32

College Football Playoffs By SORTACUS

The first college football playoff rankings will be released tomorrow.  These rankings will use an unknown combination of performance, reputation, and the infamous "eye test" to rank the top 25 FBS teams, with the top 4 in the driver's seat for one of the coveted playoff slots.

The committee actually did a very good job last year, taking the three easy choices and making a tough decision on Ohio State.  Human voters still present risks, conflicts of interest, and a lack of processing power that aren't an issue for an automated algorithm.

Fortunately SORTACUS presents a computer rankings solution to these human problems.  SORTACUS is a win-loss only Bayesian statistical program that was originally created to help my roommate rank his 100 favorite movies.  For the past couple years it's been deployed to help determine the most deserving (not best!) team in college football.  More information on SORTACUS can be found in the first rankings post of the year.

Top 25

The experienced readers likely just jumped straight to these ratings.  Below is the SORTACUS top 25 using games through Saturday October 31.  In theory, the top 4 teams are the most worthy of a playoff spot so far.  Note that only FBS vs FBS games are considered (affecting the record totals), and that "Rating" corresponds roughly to how many points better than the FBS average a school has been.

Rank	Team	Record	Rating
1	Clemson	7-0	21.82
2	LSU	7-0	21.71
3	Michigan St	8-0	21.52
4	Iowa	7-0	21.19
5	Memphis	7-0	20.29
6	Ohio St	8-0	19.95
7	Notre Dame	7-1	19.30
8	TCU	7-0	19.04
9	Oklahoma St	7-0	18.16
10	Florida	7-1	17.81
11	Alabama	7-1	17.39
12	Stanford	7-1	17.18
13	Utah	7-1	16.73
14	Baylor	6-0	16.53
15	Toledo	7-0	15.94
16	Houston	7-0	15.16
17	Mississippi	6-2	14.57
18	Temple	7-1	14.51
19	Michigan	6-2	13.69
20	Northwestern	5-2	13.01
21	Oklahoma	7-1	12.83
22	Texas A&M	6-2	12.23
23	Penn St	7-2	12.17
24	Navy	5-1	12.04
25	UCLA	6-2	10.74

The Playoffs

There's a lot of change to happen as teams play out the next few week, but for now we have four teams standing above the rest.  Clemson and LSU have the two most impressive wins of the year so far over Notre Dame and Florida.  Michigan State and Iowa have won every game so far in a surprisingly tough Big Ten.  Iowa is poised to fade however with a weak closing schedule.

That top 4 might look a little different than the committee's.  Teams with successful pasts or blowout wins like Ohio State, TCU, and Baylor may work their way towards the top at the expense of more deserving but lest renowned squads.

Memphis in particular is an interesting case.  The Tigers have ridden an impressive victory over Ole Miss to 5th place in the SORTACUS polls, and their next 3 games are against Navy, Houston, and Temple (all in the SORTACUS top 25).  With all three wins they would deserve serious consideration of a playoff appearance.

How Is My Team Doing?

Not everybody gets to be a fan of the 4th and 12th most successful team in the country.  For the less fortunate, some notable team rankings are listed below.

Wisconsin:  30th, rating of 10.01

Texas Tech:  44, 3.93

Auburn:  54, 1.44

NC State:  68, -1.39

Iowa State:  71, -1.65

Nebraska:  82, -4.60

Vanderbilt:  84, -5.12

Maryland:  88, -6.60

Purdue:  98, -9.95

The Return Of SORTACUS

Last year I applied an algorithmic program named SORTACUS to rank college football teams.  SORTACUS was created in tandem by Andy Meisner and me during our grad school suffering.  Although originally written to help Andy rank his favorite movies, it applies well to college football.  With most teams seven games into the season, I thought it was time to put SORTACUS to work again.

SORTACUS and the College Football Playoffs

I've long had a fascination with the college football postseason, something I treated in detail a few years ago during BCS Week.  I believe that playoff appearances should be determined by an algorithm to calculate which team is most deserving (based solely on wins and losses).  This is done in nearly all sports, but due to the nature of college football it needs to be a more complex algorithm.  After years building and examining ranking systems, I think SORTACUS is optimal for this task.

SORTACUS is an entirely algorithmic ranking system based solely on wins and losses.  It relies on Bayesian statistics, using a prior rating and each game as an observations to calculate a posterior ratings distribution.  I haven't given a full description yet, but last year I shared a few more details of SORTACUS.

It's important to note that SORTACUS is designed to rank teams in order of performance so far.  In effect, this calculates which teams are most deserving of being in the playoffs.  If you instead want to predict which teams will win in the future, check out my work with TeamRankings.

Top 25

The experienced readers likely just jumped straight to these ratings.  Below is the SORTACUS top 25 using games through Saturday.  In theory, the top 4 teams are the most worthy of a playoff spot so far.  Note that only FBS vs FBS games are considered (affecting the record totals), and that "Rating" corresponds roughly to how many points better than the FBS average a school has been.

Rank	Team	Record	Rating
1	Utah	6-0	21.60
2	LSU	6-0	20.52
3	Iowa	6-0	20.47
4	Michigan St	7-0	19.94
5	Ohio St	7-0	19.03
6	TCU	6-0	18.63
7	Clemson	5-0	18.59
8	Memphis	5-0	17.66
9	Florida	6-1	16.57
10	Oklahoma St	5-0	16.27
11	Baylor	5-0	16.10
12	Florida St	6-0	16.10
13	Temple	6-0	15.86
14	Notre Dame	6-1	14.97
15	Alabama	6-1	14.94
16	Toledo	6-0	14.64
17	California	4-1	14.61
18	Houston	5-0	13.76
19	Michigan	5-2	12.92
20	Texas A&M	5-1	12.89
21	Stanford	5-1	12.60
22	Northwestern	4-2	11.51
23	Oklahoma	5-1	11.33
24	Washington St	4-1	10.48
25	Pittsburgh	4-1	10.12

Through October 17th the 4 teams most deserving of a playoff spot are Utah, LSU, Iowa, and Michigan State, with a gaggle of undefeateds looking on.

Wait.

What?

IOWA IN THE PLAYOFFS?!?!?!

That's right, as of now the Iowa Hawkeyes are the third most accomplished team in college football.  They have four surprisingly good wins against Northwestern, Pittsburgh, Wisconsin, and Illinois.  The Hawks have a weak schedule going forwards, and are ranked only 31st in TR's predictive rankings.  For now though, Iowans have reason to celebrate.

Outside of Iowa the rankings follow roughly as expected.  Utah has taken college football by storm so far, and is clearly deserving of it's top spot.  One loss teams like Florida, Notre Dame, and Alabama are ahead of some undefeated squads, and absolutely still have a chance to finish the year on top.  It's all setting up for a fun fall.

How Is My Team Doing?

Not everybody gets to be a fan of the 3rd most successful team in the country.  For the less fortunate, some notable team rankings are listed below.

Texas Tech:  37th, rating of 6.17

Auburn:  38, 6.12

Nebraska:  65, -0.52

NC State:  70, -2.07

Maryland:  82, -5.47

Iowa State:  83, -5.70

Purdue:  121, -15.81