Conference bowl records mean nothing: A guide for the innumerate

A lot of stupid people who work for prominent publications are saying a lot of really stupid things these days. They are arguing that the Big Ten is a horrible terrible no-good conference because its teams went 4-6 in bowl games and that's terrible and "can't be spun." They are arguing that the SEC is the greatest conference since the Council of Nicaea in 325 CE despite being 4-2 because shut up that's why and they're the ess-eee-see.

Now we like our statistics here, and what we like better than our statistics is fundamentally sound analysis of our statistics. So we're going to do a fundamentally sound analysis of conference bowl game records, and let you all in on the secret: they're meaningless.

The topic is statistics and probability, so I'm going have to be careful and longwinded because our language is not designed to discuss these topics briefly. For our first analysis, we're going to concentrate on the Big Ten. We're going to propose a null hypothesis and that hypothesis is that each of the bowl games the Big Ten teams were played in were perfectly evenly matched. That is to say, each team had a 50% chance of winning its bowl game.

To see if the Big Ten was really bad, we're going to perform a standard statistical significance test. We would expect the conference to win half of its bowl games, and so we need to calculate the probability that they would win four games or fewer given the null hypothesis. This probability is called the p-value. For the B1G, it's the sum of the probability that they would somewhere between 0-4 games inclusive. Using basic combinatorics, we can calculate this probability as (1+10+45+120+210)/1024 = 37.7%. In order to reject the null hypothesis, we need the p-value to be no greater than 5%. So based on the 4-6 bowl record, we can conclude...nothing! Maybe the B1G is as good as everyone else, or maybe not. We can't say. We could modify the null hypothesis slightly and make each B1G team a slight favorite, and we still wouldn't be able to reject that hypothesis. So we don't know if the B1G is better, worse, or the same quality as the other conferences. There's not enough information.