Thursday, October 14, 2004

Elo ratings for colleges 

If you don't play chess you probably don't know what Elo ratings are. They are used in games such as chess to rank players on the basis of their results playing each other, while recognizing that game outcomes contain a degree of randomness. Developed in the 1940s by the US Chess Federation, they're the number we chess players use when we play in handicapped tournaments. The world's #1 player -- though not current championship holder -- Garry Kasparov has an Elo score around 2800; I haven't played tournament chess in over 25 years, but when I did my score was never as high as 1800, meaning I was a decent club player at best.

Today's Chronicle of Higher Education carries an article (subscribers only) about a paper by four education researchers put out by the National Bureau for Economic Research. Here's a public abstract of the paper (the link to the paper is available therein if you're a subscriber, or you can buy a copy for $5.)
We show how to construct a ranking of U.S. undergraduate programs based on students' revealed preferences. We construct examples of national and regional rankings, using hand-collected data on 3,240 high- achieving students. Our statistical model extends models used for ranking players in tournaments, such as chess or tennis. When a student makes his matriculation decision among colleges that have admitted him, he chooses which college "wins" in head-to-head competition. The model exploits the information contained in thousands of these wins and losses. Our method produces a ranking that would be difficult for a college to manipulate. In contrast, it is easy to manipulate the matriculation rate and the admission rate, which are the common measures of preference that receive substantial weight in highly publicized college rating systems. If our ranking were used in place of these measures, the pressure on colleges to practice strategic admissions would be relieved.
It takes a good deal of time explaining Elo ratings, but their point for using it is probably more important. As the Chronicle article points out, schools can manipulate the traditional measures like matriculation rates and rejection rates by using recruiting tools such as early admissions programs or heavy recruitment of applications that are rejected.

Here are the top ten schools ranked by the authors' system, along with some Minnesota schools and their near peers, with their Elo score attached:

1 Harvard 2800
2 Yale 2738
3 Stanford 2694
4 Cal Tech 2632
5 MIT 2624
6 Princeton 2608
7 Brown 2433
8 Columbia 2392
9 Amherst 2363
10 Dartmouth 2357
33 Oberlin 2027
34 Carleton 2022
35 Vanderbilt 2016
51 Claremont 1936
52 Macalester 1926
53 Colgate 1925

To put those in perspective, a 2022 player playing a 1926 player would win approximately 60% of games played, so a Minnesota high school senior admitted to both Carleton and Macalester, given the same tuition rate and grants rate, probably chooses to attend Carleton 60% of the time. The authors controlled for distance from home, financial package, and whether or not the student had a family member attend that school.