Some alternative men’s
doubles scoring systems
Tristan Barnett
Alan Brown
Graham Pollard
Geoff Pollard
– Sportsbet21 Pty Ltd
– Swinburne University of Technology
– University of Canberra
– Tennis Australia
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.
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 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.
Introduction

Characteristics in scoring systems

New 50-40 game

Alternative men’s doubles scoring systems

Conclusions
Graphical representation
of characteristics
2 set
3 set
match
System 1
3.00%
2.50%
2.50%
2.00%
2.00%
frequency
frequency
3.00%
2 set
3 set
match
System 2
1.50%
1.50%
1.00%
1.00%
0.50%
0.50%
0.00%
0.00%
0
25
50
75
100
125
150
points
175
200
225
250
275
300
0
25
50
75
100
125
150
175
200
225
250
275
points
Comparison of the distributions of points in a match for two scoring systems;
(a) previous, (b) current; probability of server winning a point, pa = pb = 0.65.
300
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
pa
pb
P
μ
σ
sk
pa
pb
P
μ
σ
sk
0.60
0.60
0.5000
164.0
41.2
0.27
0.60
0.60
0.5000
123.4
20.3
0.35
0.62
0.58
0.6974
160.0
41.4
0.34
0.62
0.58
0.6583
122.0
20.5
0.35
0.64
0.56
0.8491
149.6
40.8
0.55
0.65
0.65
0.5000
164.0
40.7
0.26
0.67
0.63
0.6893
160.4
40.8
0.33
0.69
0.61
0.8380
151.0
40.3
0.52
0.70
0.70
0.5000
165.5
40.4
0.22
0.64
0.56
0.7923
118.0
20.8
0.39
0.65
0.65
0.5000
125.0
20.3
0.34
0.67
0.63
0.6579
123.6
20.5
0.34
0.69
0.61
0.7916
119.8
20.7
0.39
0.70
0.70
0.5000
127.9
20.4
0.26
A comparison of the current and previous scoring systems
0.72
0.68
0.6795
162.4
40.6
0.29
0.72
0.68
0.6577
126.6
20.6
0.27
0.74
0.66
0.8243
154.1
40.4
0.47
0.74
0.66
0.7915
122.9
20.9
0.32
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 5040 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.
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 firstto-ten points tiebreak game.
3.
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.
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
6
7
System 4. above modified in two ways. The first two sets are ‘firstto-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.
Alternative Scoring Systems
2 set
3 set
match
System 2
2.50%
2.00%
2.00%
1.50%
1.00%
2.50%
2.00%
1.50%
0.50%
0.50%
0.00%
0.00%
0.00%
0
25
50
75
100
125
150
175
200
225
250
275
300
0
25
50
75
100
125
points
150
175
200
225
250
275
2 set
3 set
match
3.00%
3.00%
2.00%
1.50%
1.00%
0.50%
0.00%
0.00%
125
150
points
100
125
175
200
225
250
275
300
150
175
200
225
250
275
300
2 set
3 set
match
2.50%
2.00%
1.50%
1.00%
1.00%
100
75
System 7
1.50%
0.50%
75
50
3.00%
frequency
2.00%
frequency
2.50%
50
25
points
2 set
3 set
match
System 6
2.50%
25
0
300
points
System 5
0
1.50%
1.00%
1.00%
0.50%
2 set
3 set
match
System 4
3.00%
frequency
2.50%
frequency
2 set
3 set
match
System 3
3.00%
frequency
frequency
3.00%
0.50%
0.00%
0
25
50
75
100
125
150
points
175
200
225
250
275
300
0
25
50
75
100
125
150
175
200
225
250
275
300
points
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.
Alternative Scoring Systems
1
2
3
4
5
6
7
P
0.6893
0.6579
0.6660
0.6676
0.6605
0.6722
0.6620
μ
160.4
123.6
123.8
124.7
118.0
127.9
110.2
σ
40.8
20.5
19.8
21.5
22.7
19.8
14.5
sk
0.33
0.34
0.34
0.56
0.43
0.17
-0.05
ku
-0.74
-0.24
-0.08
0.29
-0.18
-0.10
-0.27
ρ
0.5343
0.4745
0.5259
0.5328
0.5143
0.5497
0.5617
98%
244.2
167.9
166.8
172.4
167.1
170.4
140.6
Characteristics of the scoring systems when pa = 0.67 and pb = 0.63
2%
94.5
85.6
87.4
86.8
76.7
91.0
85.4
Alternative Scoring Systems
1
2
3
4
5
6
7
P
0.6795
0.6577
0.6699
0.6719
0.6628
0.6795
0.6647
μ
162.4
126.6
126.1
127.2
122.0
128.0
111.2
σ
40.6
20.6
19.9
22.0
23.3
20.1
13.9
sk
0.29
0.27
0.37
0.58
0.37
0.17
-0.03
ku
-0.85
-0.40
-0.09
0.25
-0.34
-0.06
-0.22
ρ
0.4355
0.4268
0.5002
0.5080
0.4731
0.5524
0.5314
98%
243.8
170.8
169.6
175.7
172.2
171.1
140.7
2%
96.0
88.6
90.7
89.6
80.0
90.4
87.1
Characteristics of the scoring systems when pa = 0.72 and pb = 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.
Acknowledgements



Sportsbet21 Pty Ltd (www.sportsbet21.com.au)
Strategic Games (www.strategicgames.com.au)
KAN-Soft (www.oncourt.info)
Thank you!