Wednesday, October 20, 2004

Elo ratings for colleges.

This is sure to make college admissions officers happy! Four economists have applied the Elo rating and ranking system used by chess players, and now also widely in many other fields of competition, to colleges to rate their competitive success at attracting students.

The idea is to get away from the subjective measures used by newsmagazines and books that rank colleges, and instead produce an objective numerical measure of how college applicants "vote with their feet" when they have a choice of colleges to attend.

"Elo" sounds like an acronym but it's not, the system is named after Dr. Aprad Elo who developed it for the U.S. Chess Federation, which adopted it in 1960. A few years later it was adopted by the International Chess Federation, and since then it's been picked up both by organizational bodies governing many different kinds of competition and amateurs who enjoy the fun of applying their own rating systems to ... whatever. As one example, Jeff Sagarin's Elo ranking of NCAA football teams is used by the BCS in selecting the teams to play in those year-end bowl games that are supposed to determine a national champion.

It takes four economists to make obtuse what Dr. Elo made fascinating and clear, with a fine collection of entertaining illustrative stories from chess history, in his 1978 book The Rating of Chessplayers, Past and Present -- which I see is now something of a collector's item, $140 at (Hey, what'd the kid do with my copy?) If you are interested in the statistical challenges of developing such a rating system, the history and failings of earlier systems, or the history of chess, then this book is well worth ... a trip to the library. I wouldn't pay $140 for it.

As to the college rankings the idea is simple: when a student has the choice of two schools the one the student selects "wins" and the other "loses". Each college's wins and losses against all the others are used to generate its rating, and the ratings are used for ranking.

If you are like all the college admissions officers seeing this for the first time you will download the paper (pdf) then skip all the prefatory blather and statistical gobbledygook to head straight for the rankings at the end...
1. Harvard 2800
2. Yale 2738
3. Stanford 2694
4. Cal Tech 2632
5. MIT 2624
101. Purdue 1525
102. Colorado State 1513
103. Syracuse 1506
104. Scripps 1479
105. Loyola U 1221
OK, when you do all you have to remember is the rule-of-thumb that with a 100-point difference the higher rated competitor wins a little over 60% of the time; with a 200-point difference, 75% of the time; a 300-point difference 85% of the time, and 400-point difference over 90% of the time.

That's all there is to the whole thing!

I will add this as a former tournament chess player: chess players go nuts about their Elo ratings, sometimes postal. If colleges take them half as seriously as chess players do then all the controversy to date about newsmagazine rankings of colleges will be as nothing -- the insanity is just beginning.