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Chippewa Falls Racquetball Ladder

The Chippewa Falls Racquetball Ladder was created by Tom Arneberg ( in January, 1992. It uses an algorithm based on the one used by the USTTA (U.S. Table Tennis Association) for their national rankings:

           Difference     ----Rank Pts Exchanged----
           in Player      Expected        Unexpected
           Rankings       Result          (UPSET!)  
             0- 49 ........ 5 .............  5
            50- 99 ........ 4 .............  6
           100-149 ........ 3 .............  7
           150-199 ........ 2 .............  9
           200-249 ........ 2 ............. 12
           250-299 ........ 1 ............. 15
           300-349 ........ 1 ............. 19
           350-399 ........ 1 ............. 24
           400+    ........ 0 ............. 30

The algorithm uses negative feedback to restrain movement, like a rubber band -- the farther ahead (or behind) you move, the more difficult it is to move further.

The result of the algorithm is that a new player should quickly settle into the spot where he belongs on the ladder, no matter which players he plays.

The way the scoring works is that points are exchanged for each game played (the points are taken from the loser and given to the winner of that game).


Suppose two players are evenly matched (i.e. within 50 ranking points of each other). Then the algorithm predicts an even split, and the number of points exchanged is 5 per game, regardless of who wins.


Player C is ranked at 3600, and player D is ranked at 3525. Since C is 75 points above D, C is the player "favored" to win, and earns only 4 points from D for each win, while D will get 6 points from C for each game HE wins (since it's an upset). Thus in a typical match, if C beats D 2-1 games, he'll get a net of 2 points from D (2X4 - 1X6). But if D upsets C 2-1 games, then he'll steal 8 points from C (2X6 - 1X4).

The further apart the two players are, the less a predicted win is worth and the more an upset is worth.

The algorithm ends up being a good measure of relative racquetball abilities. If player E is 125 points above player F, then the ladder predicts that E will win 7 games to every 3 games that F wins (since the scoring is a 7-3 split). If that's the way that most of their matches turn out, they'll stay right where they are. If one of them starts to upset this balance, then they'll move up or down accordingly. Similarly, if player G is 320 points abouve player H, then the algorithm predicts that he'll win 15 times as many games (15-1 split).


One common complaint is that it's not fair that the guy at the top has a disadvantage. But the purpose of the ladder is not to reward you for winning games, it's to assign you a ranking based on your relative strength. If the Top Dog is 240 points above number two, then he'll have to continue winning about 6-1 in order to maintain his position (12-2 split).


Starting a new ladder from scratch turns out to be tough. I think I erred on the side of placing people too close together. There are large natural gaps in our 100 or so players who have taken part. I guess the thing to do is look at all the players, and try to predict manually the ratios of wins with respect to each other. In any case, it will all balance out in the end due to the negative feedback in the algorithm.

(c) 1992 by Tom Arneberg

  - Tom A.
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