I have often wondered about how to rank sports teams. This goes way back to when I was 10 years old, when I ran across a magazine at summer camp that purported to do this for NFL football. And so I wondered for many years, looking at similar problems and wondering how a ranking of teams could be generated from a win-loss history. I finally came to a conclusion when I played the Mogul Game.
The Mogul Game has 148 rich people, and they vary from the super-rich (Gates, Buffett, Ellison) to the not-so-rich (I think they got a kick out of putting Donald Trump at/near the bottom of the list, much as he boasts to Forbes that he is much wealthier than they calculate).
After playing the game idly for a little while, I concluded that if I wanted to win, I would have to capture and analyze data from the game in order to win it. And so I did, recording who was richer than whom. I went through four phases:
- Doing qualitative comparisons when I wasn’t certain of who was richer. Who had the two parties beaten and lost to?
- Comparing the trial ranks when the difference was greater than 10.
- Looking at the highest ranked persons that a given set of contestants had won against, and the lowest ranked that they had lost to.
- Looking at the average of the highest rank won against and the lowest rank lost to as the best proxy for a contestant’s own rank, unless it violated the results of an actual contest. In hindsight, I should have adopted that rule much earlier.
It took three days of off-and-on playing to master the game. Not all that important, but as I mentioned above, the method can be applied with some modifications for ranking sports teams in an unbiased way. The same could be applied to any competitive activity where there is a win/loss result. There are two changes for other activities, though. Games are not necessarily transitive. Rich person A is richer than B. B is richer than C. A will always be richer than C. In competitions, Team A can beat team B one day, and lose the next. Also, Team A can beat team B, which can beat Team C, but C can beat A. So, if I were doing this for baseball teams, my ranks would drive probabilities of one team beating another.
Why would this be necessary when one can simply inspect the win-loss percentages? Teams with good records may have weak schedules, and this takes account of the strength of the teams played in assessing the strength of a team. I’m not sure what they do with ranking College Football or Basketball teams, but this would be a more bloodless way of making the comparison. Granted, it takes a certain number of contests before there is enough density of information to create a ranking, but given a list of wins and losses from an entire season, this method should be capable of ranking an entire league.
I know this is an odd post for me, but I found it to be an interesting project, and it does have other applications. Thoughts?
