Department Seminars

General Information

When: Thursdays from 4:00–4:50 p.m.
Where: 1170 TMCB

Bruce J. Collings
Brigham Young University
Department of Statistics

2007-09-27

Tennis Anyone? A Probabilistic Analysis of Generalized "Deuce" Games

Many two person (or team) contests require the winner to be one point (or game) ahead at the end of the competition. Examples are "best of seven" playoffs in baseball, golf tournaments, etc. Some sports, notably tennis and volleyball, require the winner to have at least a two-point advantage. Under the usual iid assumptions for individual points, the probability of winning for each player in these two scenarios is relatively easy to obtain, and in fact, gets rediscovered every decade or so. It is also possible to compute the expected length, in serves, for the contest under both these scoring requirements.

In tennis games between closely matched players, the "win by two" requirement means that the final winning score may be much higher than the nominal winning score. These are referred to (in tennis, at least) as "deuce" games. An obvious question is: "What happens if you must win by more than two points?" This seminar will consider this question for tennis games where the same player/team begins each point, and for volleyball games where the each point is begun by the player/team who won the previous point. Both the probability of winning and the expected length, in serves, will be considered. Some surprisingly elegant results are obtained.