Some alternative mens doubles scoring systems Tristan Barnett – Sportsbet21 Pty Ltd Alan Brown – Swinburne University of Technology Graham Pollard – University of Canberra Geoff Pollard – Tennis Australia

Background For the first time in 30 years the tennis doubles scoring system has been changed. New rules on alternative mens doubles scoring came into force after the 2005 US Open. Three alternative systems allowed.

Background Best-of-3 tiebreak sets are first to six with a standard tiebreak game at 5-5, no-ad games. Best-of-3 tiebreak sets are first to five with a standard tiebreak game at 4-4, no-ad games. The first two tiebreak sets are first to six with a standard tiebreak game at 6-6, no-ad games. The third set is simply a first-to-ten points match-deciding tiebreak game. In all three systems the receiving team can decide which side to return from if deuce is reached in a game.

Background In 2006 it was decided that the third of these systems would be used in all ATP mens doubles events with the exception of Grand Slams. The purpose of the change was to have matches of shorter and more predictable duration. Hopefully, this would attract the top singles players and also allow more doubles matches to be played on centre court.

Introduction Characteristics in scoring systems New game Alternative mens doubles scoring systems Conclusions

Graphical representation of characteristics Comparison of the distributions of points in a match for two scoring systems; (a)previous, (b) current; probability of server winning a point, p a = p b = 0.65.

Characteristics in systems Fairness Probability of winning Average number of points in the match Standard deviation (predictable duration) Coefficient of skewness (likelihood of a long match) Efficiency Markov Chain model in Excel was used to calculate these characteristics

Numerical representation of characteristics A comparison of the current and previous scoring systems

New game Server has to win the standard four points while the receiver only has to win three points. Such a game requires at most 6 points. Works very well for doubles as this game creates symmetry. The seventh point used in the no-ad game creates an unattractive lack of symmetry. Pollard and Noble, The benefits of a new game scoring system in tennis, the game, 7 th Mathematics and Computers in Sport. Barnett and Pollard, Reducing injuries by substantially decreasing the likelihood of long tennis matches, Medicine and Science in Tennis.

Alternative Scoring Systems 1. The (old) system consisting of standard best-of-three tiebreak sets, using advantage games. 2. The (current) system where the first two sets are tiebreak sets, using no-ad games. The third set is simply a match deciding first- to-ten points tiebreak game. 3. System 2. above, modified in two ways, namely using games instead of no-ad games, and using first-to-seven games sets instead of standard tiebreak sets. 4. System 3. above modified in one way, namely that all tiebreak games are played as first-to-nine points, … tiebreak games.

Alternative Scoring Systems 5 System 4. above modified in two ways. The first two sets are first- to-five games sets, and games are games. Thus, this system has longer games, but shorter sets. 6 System 3. above, modified in a way that allows the outcome of a game to be a win, loss or draw. The first pair to win 7 points wins the game and if the points score reaches 6-6, the game is a draw. 7 System 3. above, modified in a way that allows the outcome of a set to be a win, loss or draw. The first pair to win 7 games wins the set and if the games score reaches 6-6, we have a draw.

Alternative Scoring Systems Comparison of the distributions of points in a match for six scoring systems; (a) current, (b) … (f) new; probability of server winning a point, p a = p b = 0.65.

Alternative Scoring Systems Characteristics of the scoring systems when p a = 0.67 and p b = 0.63

Alternative Scoring Systems Characteristics of the scoring systems when p a = 0.72 and p b = 0.68

Conclusions The purpose of the changes in 2005 and 2006 was to have matches of shorter and more predictable duration and has succeeded. A downside of the current scoring system is that it is somewhat less efficient, with a smaller value for the probability that the better player wins. Five alternative scoring systems making use of some recent ideas in the literature are considered. Each of the five systems is more efficient than the current system, and has a higher value for the probability that the better player wins. Thus, on statistical grounds, they would appear to be legitimate alternatives to the current system.

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