# College Football Conference Construction

So the Big XII is pissed.  (And probably rightly so).  As I’ve said before, if the committee was trying to pick the best 4 teams in college football, they failed miserably.  TCU and Baylor, both one loss tams, are both better than Ohio State, imho.  Further, there are several multi-loss teams that are better than Ohio State or Florida State.  I’d suggest Mississippi State (2 losses) AND Ole Miss (3 losses) for starters.  But I’d also include basically any team from the SEC West including Georgia, Auburn, and LSU.  And screw it, I’m going to include Arkansas.  I think Arkansas would beat Florida State or Ohio State.  The SEC is that good.

Since the simpletons on the College Football Playoff committee can apparently only see wins, is it possible to game the system?  For instance, could a conference add or remove teams from their conference to maximize their potential for getting a team into the playoffs?  How would a conference do that?  Let’s do a simulation study.

### Motivating question

How could a college football conference construct its conference to maximize their chances of getting at least one of their teams into the playoff?

#### Simulation Description

Let’s assume a simple model for the college football world.  Let’s assume there are 5 conferences each with 10 teams.  25 of these 50 total teams are “good” and the remaining teams are “bad”.  Each team plays nine games against the other teams in their conference and three “random” non-conference games for a total of 12 games.  When a good team plays a good team or a bad team plays a bad team, each team has a 0.5 probability of winning the game.  When a good team plays a bad team, the good teams probability of a win is expit(1)=.731.  I then simulated a schedule and simulated the season.  I counted the 4 teams with the most wins as the four teams that made the playoff.  The tie-breakers for teams that were tied in wins was drawing lots (i.e. using runif in R).  I then counted how often a team from each of the conferences made it to the playoffs as related to the number of “good” teams in the conference.

### Results

Obviously, when all 5 conferences are completely balanced and have 5 good and 5 bad teams, each conference has the same chances to get a team to the playoffs.  So let’s look at some unbalanced situations.  If the good teams are split up so that the conferences have 2, 3, 5, 7, and 8 good teams, respectively, the conference with the 5 good teams is the most likely to get a team into the playoffs getting in about 71.3% of the time. In this setting, with 7 teams, a conference is just slightly less likely to get a team into the playoffs at 69.4% and it drops even more to 63.1% with 8 good teams.  While there are more good teams in the conference to have an opportunity to get into the playoff, these good teams cannibalize each other.

This trend continues throughout all of the simple simulations that I looked at where a conference with about half good and half bad teams was the most likely conference to make the playoffs.  At the extremes where there is one conference with 5 good teams and the other conferences are all or nearly all good or bad teams, the conference with 5 good teams probability is the largest.

2 3  5  7 8
57.7%  66.5%  71.3%  69.4%  63.2%
1  2  6  7  9
53.2% 63.4%  74.9%  72.6%  62.5%
0 1 5 9 10
34.9%  59.6%  80.6%  71.5%  69.9%
1  3  5  6  10
51.1%  71.3%  75.6%  74.0%  51.7%

The plot below shows graphically the results of the above table.  On the x-axis are the number of “good” teams in each conference and the y-axis is the probability that a team from that conference gets into the playoffs (i.e. Is top 4 in terms of number of wins.

### What does this mean?

From the point of view of a conference commissioner, if your goal is to build a conference with the purpose of putting teams in a position to win a national championship, your best bet is NOT to construct a power house conference.  You want to put together a conference with about half of the teams being elite and the other half of the teams being not so good.  If you construct a conference with all elite teams, the teams cannibalize each other and no team is clearly the best.  No matter how hard the schedule, this committee, I believe, absolutely will not let a 2 loss team into the playoffs even if that two loss team lost to the number 1 and number 2 best teams in the country.  So to all those conference commissioners looking to add a power house program to their conference, maybe they should reconsider and add a middling program to their conference and get their elite teams another win.  Cause after all, that’s basically all this committee cares about.

### Future Work

What I’d like to do in the future, is run this simulation on real college football teams this year to try to construct the ultimate conference for getting a team to the college football playoffs.  I’d use some sort of estimated team strength (Maybe Sagarin) to simulate games during a season and then take the top 4 teams in terms of wins.  That could be really interesting.

Cheers.

Posted on December 10, 2014, in Uncategorized. Bookmark the permalink. 4 Comments.

1. JTin

Although it may be their stated goal, does anyone actually think the point of this playoff is to pick the 4 ‘best’ teams in an absolute sense? Even if, hypothetically, all 4 of the best teams exist in the SEC, I see little reason to have them conduct a playoff amid themselves. We JUST SAW a season-long competition where SEC teams played each other every week, and produced a conference champion. Specifically BECAUSE there are so few inter-conference matchups of import each year, I’d much rather see major conference champions PROVE they are truly the best team by beating other conference champions.

All that said, your methodology and examination of how to structure a conference to maximize playoff bids was an interesting read.

• But then how do you explain the BCS national championship game between Alabama and LSU who were both from the SEC? In that year, they clearly were interested in finding the two best teams. Of course, it all depends of your definition of “best”. To the NCAA that might mean the teams that will make the most money. To me, it means the teams with the best chance of winning.

Cheers!

2. JTin

What’s the goal? In my mind, it’s not to find the best final four, but to find the champion – the SINGLE BEST team.
Your model may lead you to believe that 6 SEC West teams are all better than OSU & Florida St. But we KNOW they’re not the best team in the country, since they’re not even the best team in their own half of their own conference. Therefore, they shouldn’t take up space in the playoff. Give another conference a chance to let the SEC champ prove their superiority. Or surprise people?
Because college football scheduling is so insular, we frequently see situations where a team is perceived as elite, and turns out to be a fraud. Think Ohio St in 2006. AFAIK, your model wasn’t around back then, but that OSU team was so dominant that i’d guess they would have ranked at/near the top? People were arguing vehemently that Michigan deserved a rematch in the title game over Florida. The “best teams” is a GUESS (whether it’s the committee or a good model) – and a smart guesser leaves open the possibility that they are wrong.

• But a good way to find the single best team is to put the four best teams into the playoff.

I’d also pose the question “What do you mean by best?” Seriously think about that. It can mean many different things.

Cheers!