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

Who Should Make The Playoffs? (feat. SORTACUS)

It's now been over two years since I made a blog post, but the process behind the college football playoff selection was too much for me to resist.  Does Ohio State deserve a shot?  Is the SEC overrated (or underrated)?  Should we be talking about Marshall?  I brushed off an old skill set in an attempt to answer these questions and more.

College Football Playoffs

I have long had a fascination with the process used to select college football's champion.  It a sport uniquely unsuited for a large playoff bracket, the kind the selects appropriate champions in the NBA, or creates a month of excitement in college basketball.  I wrote about my philosophy on NCAA football champions extensively a few years ago during what I termed BCS Week. 

For now I'll skip the details on who deserves to be in the playoffs, and instead hit upon the main points here.

-Championships, and therefore playoffs, should reward performance, not potential.  Luck happens in sports, and sometimes Northwestern beats Notre Dame.  The only goal in a game is to win, and playoff selection should reflect that.

-Not all wins are equal.  In other sports nothing besides record determines seeding, but with the disparity in college football that is often unreasonable.

-There should be an algorithm for determining qualifiers.  This is true in most other sports, the algorithm is just wins and tie breakers.  A committee of people, all with ties to teams, has inherent biases a computer doesn't.  Coming up with an algorithm is a challenge.  Fortunately, I have a proposal.

SORTACUS

SORTACUS is a computer ranking system that I created with Andy Meisner to rate items based off head to head comparisons.  It's currently used only to rank Andy's 100 favorite movies, and occasionally help my family select where to go to dinner.  Because games are just head-to-head comparisons however, it is easily applied to college football.

If these posts continue I'll describe the algorithm in detail at some point, but a summary will have to satisfy the math nerds for now.  It uses Bayesian theory to adjust the odds that a team has any given rating.  Each game is another observation to adjust the probability that team A has rating X.  It's fun and exciting math, if you're into that sort of thing.  For now though, I'll post a few summary points.

-Only wins and losses matter.  Margin of victory is ignored.  This makes the ratings worse at predicting future results, but better determining the most deserving playoff qualifiers.  If you want predictions and projections, check out my work for TeamRankings.

-Home and away are not implemented currently.  I think it would be reasonable to adjust and include a game's locations, it would just require some additions to the code.

-Only games against FBS teams matter.  A loss to Northern Iowa would slip through the cracks (for now).

-A win never hurts a team.  Many ratings systems include average opponent strength in some way.  A win against a bad team could hurt a good team, even if it was a lopsided game.  With SORTACUS, even a win against a junior high team can't hurt.

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.

Rank	Team	Record	Rating
1	Florida St	9-0	22.62
2	Alabama	9-1	21.90
3	Mississippi St	8-1	20.39
4	Oregon	8-1	19.95
5	TCU	8-1	19.26
6	Mississippi	7-2	17.49
7	Ohio St	9-1	17.41
8	UCLA	8-2	16.68
9	Marshall	9-0	16.29
10	Baylor	7-1	16.20
11	Auburn	7-3	15.63
12	Georgia	8-2	14.38
13	Colorado St	8-1	14.36
14	Arizona	8-2	14.06
15	Michigan St	7-2	13.70
16	Kansas St	6-2	13.70
17	Boise St	8-2	13.44
18	Arizona St	7-2	12.90
19	Oklahoma	7-3	12.72
20	Georgia Tech	8-2	12.53
21	Nebraska	7-2	11.90
22	Missouri	7-2	11.23
23	Wisconsin	7-2	11.20
24	Louisiana Tech	7-2	10.53
25	LSU	6-4	10.46

Through Novermber 16 the playoffs should contain Florida State, Alabama, Mississippi State, and Oregon with TCU on the outside looking in.  The playoff rankings this week may actually agree with that, which is a good check for both SORTACUS and the committee.

What else stands out here?

The Big Ten is probably being overrated by the committee.  Ohio State is probably worthy of a fair shot at the playoffs, but Michigan State, Nebraska, and Wisconsin don't fare well with SORTACUS.

The SEC is as good as midseason polls said.  Schools in the West have beaten up on each other, potentially jeopardizing an SEC spot in the playoff.  SORTACUS puts five teams in the top twelve though, almost guaranteeing at least one deserves a final spot.

Marshall is number nine?  That seems high and probably is.  There aren't enough inter-conference data points for SORTACUS to work with.  Still, for Marshall to be undefeated but not among the 25 most deserving playoff teams is a silly mistake on the committee's part.

How is my team doing?

Schools I'm associated with don't show up in the top 25.  Here's where a few notable ones land:
Maryland:  41st, rating of 5.18
Iowa:  49, 3.51
Stanford:  55, 1.96
Northwestern:  68, -0.26
Iowa State:  85, -4.92
Purdue:  91, -6.15
New Mexico:  106, -10.68

The Game Theory of 21

On Sunday a great basketball rivalry was renewed. It was not the Kings and Timberwolves fighting to stay out of last place, it was Andy, Jimmy and I playing 21 (a basketball game). In general when we play I win probably two thirds of the time, Andy will win one third, and Jimmy will never win (Burn!*). Recently though, Jimmy has started winning, highlighted by a game Sunday when Jimmy had 19, I came back to 17, and then Andy let Jimmy get a free layup for 21! With two victories in the last nine games (and zero for Andy) it appears that my secret has been uncovered: don't guard Jimmy.

Turns out, this is a classic Prisoner's dilemma. In all situations it is better for both Andy and me to not guard Jimmy (example odds of winning in each case are illustrated in the table). As a result though, both of us have significantly lowered our odds of winning the game.

This sort of idea comes up often in life, and a fair bit in recreational sports too. The same phenomenon applies to capture the flag: Offense is fun, but defense wins, so both teams play defense and have no fun, but still each have 1/2 chance of winning.

Could this phenomenon happen in national sports leagues? Absolutely. Off the top of my head here are a couple examples.

Helmet hits in NFL: Knocking the other team's star player out helps you win, but both teams are better off if there are no helmet to helmet hits.

College Recruiting Violations: Paying to get the best players can help you win (SMU), but if everybody does it then everybody loses.

Steroids in Baseball: Again, it's an advantage for you if you're the only one on the juice, but once everyone does it then the playing field is level again and your health sucks.

How do you get out of a Prisoner's Dilemma? Put a negative incentive on the negative behavior, including fines, sanctions, and suspensions. The leagues are all actually controlling for it fairly well. That doesn't mean I'll guard Jimmy though.

*Jimmy actually played really well when we played today. Somewhere over the past couple years he has learned to shoot and take advantage of his athleticism on the boards. He should probably get better than 0% odds on winning. That wouldn't amuse me as much though.

Bowl Win Effect

In the pre-season rankings column I slyly slipped in that winning a bowl actually indicated a likely drop off in the next season. It has been however challenged by the ever astute observer Andy Meisner, and to be honest it seemed a little ridiculous to me too. Using the top 50 teams in each season over the last 5 seasons, I have now re-examined the data. Here are the rough changes in Power Rankings (technically ln(Power Rankings). To adjust, a score of .1 means that the average team was about 1.1 times as good the next season).

	Winners	Losers
2004-05	-0.0153	-0.1812
2005-06	0.1258	-0.2386
2006-07	0.0434	-0.0602
2007-08	0.1577	-0.1085
2008-09	-0.1417	0.1158
Average	0.0339	-0.0945

So it appears the 2008-09 season was just a strange aberration. While it's true that winners got worse in 08-09, it was the other way for other seasons, and on average momentum from the bowl carries over.