# The ratings game for rally sports.

The ratings game for rally sports

How would you score in a match against a top professional racquetball player? That question bothered statistician David Strauss, who is both an excellent tournament chess player and a keen racquetball competitor. As a chess player, he has a rating indicating how well he plays. That rating, determined by the U.S. Chess Federation, allows him to compare his ability with that of anyone else who plays tournament chess--from world champion to club player. It goes up or down depending on his opponent's rating and whether he wins, loses or draws the match.

Racquetball has no such system, so Strauss, a professor at the University of California at Riverside, set out to develop a racquetball rating scheme. His new system, like that used in chess, is based on the idea that the wider the gap in ability, the greater the difference in rating between two players and the lower the chance of the weaker player winning. It allows players of all strengths to be rated on the same scale. Newcomers can be assigned a rating without disrupting the rank of players already listed.

"It turns out that a system for racquetball works even better than the chess system,' says Strauss, "because the actual score of a racquetball match is much more informative than the simple win/draw/loss result of a chess game.' For a given score, he uses a mathematical formula to calculate how much each player's rating changes. The formula compares the match's actual score with the theoretically expected score based on the difference in the two players' ratings. A wider margin between actual and expected scores means a greater change in rating. On Strauss's arbitrarily chosen scale, a racquetball world champion would have a rating around 2700. He estimates that his own rating is about 1600.

"The difficulty here is financial,' says Strauss. "Somebody has to be persuaded that it's worth collecting results and computing the ratings.' Strauss has tested his scheme on published scores from major championship matches and on the results from a local tournament. An account of his system appears in APPLIED STATISTICS (Vol.36, No.2). His rating scheme also fits games such as squash, volleyball, badminton and table tennis--any sport in which points can be scored only by the server.