Monday, November 30, 2015

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
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Sunday, November 15, 2015

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
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Monday, November 2, 2015

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

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