On 9/6/11, Erich Friedman <efriedma@stetson.edu> wrote:
... if we think of players' abilities as uniform random numbers from 0 to 1, then after the tournament, E(A)=1080/2295 and E(B)=1024/2295.
erich
To some extent, the algorithms used to rank players in chess, tennis etc. reflect this phenomenon. At one time, a highly-rated chess player would refuse a match with one much lower-rated, on the grounds that regardless of who won, the weak player's rating would improve at the expense of the strong. I once refereed a somewhat poorly attended tournament, at which the stronger players were finding themselves under-occupied after quickly winning their games; so in between times, I challenged them to friendly matches, which unknown to me subsequently somehow or other found their way onto the official returns. When the annual league ranking list was published, scanning down columns revealed one idle but fortunate individual who had managed to land halfway up the table on the strength of only 3 games. Scanning across rather lengthy rows eventually identified this ingenious operator as none other than --- Fred Lunnon