Some alternative men’s doubles scoring systems

1. Some alternative men’s doubles scoring systems Tristan Barnett – Sportsbet21 Pty Ltd Alan Brown – Swinburne University of Technology Graham Pollard – University of Canberra Geoff Pollard – Tennis Australia

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

3. 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.

4. Background • In 2006 it was decided that the third of these systems would be used in all ATP men’s 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.

5. Introduction • Characteristics in scoring systems • New 50-40 game • Alternative men’s doubles scoring systems • Conclusions

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

7. 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

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

9. New 50-40 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 50-40 game, 7th Mathematics and Computers in Sport. Barnett and Pollard, Reducing injuries by substantially decreasing the likelihood of long tennis matches, Medicine and Science in Tennis.

10. Alternative Scoring Systems • The (old) system consisting of standard best-of-three tiebreak sets, using advantage games. • 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. • System 2. above, modified in two ways, namely using 50-40 games instead of no-ad games, and using ‘first-to-seven games’ sets instead of standard tiebreak sets. • System 3. above modified in one way, namely that all tiebreak games are played as ‘first-to-nine points, …’ tiebreak games.

11. Alternative Scoring Systems • System 4. above modified in two ways. The first two sets are ‘first-to-five games’ sets, and games are ‘60-50’ games. Thus, this system has ‘longer’ games, but ‘shorter’ sets. • 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. • 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.

12. 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, pa = pb = 0.65.

13. Alternative Scoring Systems Characteristics of the scoring systems when pa = 0.67 and pb = 0.63

14. Alternative Scoring Systems Characteristics of the scoring systems when pa = 0.72 and pb = 0.68

15. 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.

16. Acknowledgements • Sportsbet21 Pty Ltd (www.sportsbet21.com.au) • Strategic Games (www.strategicgames.com.au) • KAN-Soft (www.oncourt.info) Thank you!