1. REDUCING INJURIES BY SUBSTANTIALLY DECREASING THE LIKELIHOOD OF LONG TENNIS MATCHES Tristan Barnett and Graham Pollard “Mathematicians can play a role in tennis medicine”
Long matches can lead to injuries Long matches can cause problems for television scheduling A tiebreaker fifth set reduces the match length
Extended training for the possibility of long matches can lead to injuries
Long matches can be seen as unfair in the tournament setting
The game reduces the match length
Clement versus Santoro
2004 French Open
6 ½ hours in duration
Santoro won in fifth set
Roddick versus El Aynaoui
2003 Australian Open
5 hours in duration
Roddick won in fifth set
Australian Financial Review, 01/02/03
Table: Statistics for each set obtained from the Clement-Santoro match played at the 2004 French Open
Table: Predicted parameters for the Roddick-El Aynaoui match played at the 2003 Australian Open
Notice from the above table that the average time for a tiebreaker set was 55 mins, due to the long rallies played on the clay courts. One way to reduce the length of the tiebreaker set, and ultimately reduce the time duration of the match, is to replace the standard game with a game [2].
For the new game, the server must win the standard 4 points, while the receiver only has to win 3 points. This type of game requires at most 6 points. It can be shown that not only does a match using the game have reduced mean, but it also has increased efficiency, and reduced standard deviation and skewness. It can also be shown that the chances of the better player winning the match from the outset is only marginally reduced. For example, for two players winning 60% and 58% of points on their respective serves, the better player has a 62.9% of winning the match using standard games compared to 61.2% using games.
Interestingly, in the Clement versus Santoro match, both players recorded their highest wins on serve in the advantage fifth set, leading to the 173 mins to play the deciding set.
[2] G. Pollard and K. Noble, The benefits of a new game scoring system in tennis, the 50-40
game, In Proceedings of the 7M&CS, R.H. Morton and S. Ganesalingam eds. (2004), 262–265.
Given the means and standard deviations from the above table [1], it is clear that the advantage set can be substantially longer than the tiebreaker set, particularly when both players have ‘big’ serves. Yet the chances of the better player winning the match from the outset remain virtually unaffected.
For this reason, and to reduce the likelihood of injuries, and to increase fairness in the tournament setting, consideration be given to using the tiebreaker fifth set in all four grand slams.
From all the matches played at the 2003 Australian Open, the Roddick-El Aynaoui match had the highest predicted mean number of points, standard deviation, and coefficients of skewness and kurtosis for an advantage set.
For these reasons we conclude that out of all the matches played at the 2003 Australian Open, the
Roddick-El Aynaoui match had the foundations to go on for the longest if a fifth set was obtained.
[1] T. Barnett and S.R. Clarke, Combining player statistics to predict outcomes of tennis matches, IMA Journal of Management Mathematics 16(2) (2005), 113–120.
Australian Financial Review, 21/05/05