So I’m working on my own computer poll for the College Football season. I’ve developed a simulated annealing algorithm that works well from a simple premise: maximize the correlation between the rank distance of teams and the relative margin of the game.
- Let
be the rank of team t.
- Let
be a game in which team i beat team j.
- Let
be the rank distance of game .
- Let
be the margin of victory for , where 
and 
are the scores of teams i and j from the game.
- Find the rankings that maximize the correlation between
and 
.
I am using a simple simulated annealing algorithm to maximize the correlation. Even with a very simple algorithm, it shows a lot of promise in sorting out teams with harder schedules from teams with weaker schedules. The dataset I am using includes teams from Div I-A to Div III, and the simple algorithm does a good job at sorting them as we’d expect. I am looking to improve the algorithm using adaptive simulated annealing which should provide me with a better search.
I’ll probably publish my results for this season, towards the middle of October after enough games have been played.
Reed, what is the purpose behind this mathematical technique, and how will you know if you are successful? If it is for gambling, then I think you are wasting your time – people have tried to figure out how to predict football for a long time and no one gets rich using math to predict football. If it is some academic exercise, great, good for you, but how will you determine if you have a good method?
I will determine if I have a good method, based on intuition. For example, does the algorithm sort Div-IA from Div-IAA schools. So far it does.
How do you account for the weekly rank changings?
Maybe you should change the margin of victory equation. Are TDs really twice as hard to get as field goals? Are safeties 2/3 as difficult as field goals?
Josh,
My plan is to simply rerun the algorithm every week. The algorithm looks at every game played upto that point in time and tries to find the ranking that maximizes the correlation between rank difference and relative margin of victory.
Your other comment is interesting. Got any suggestions?
Update