Sep 29, 2016
Sep 29, 2016

What is the most important point in tennis?

What is the most important point in tennis?
In tennis there are a total of 18 possible scorelines from the start of a game (0-0) to the end of it. With much speculation about the most important point to win in an individual game and with major tennis stars insisting on the 15-30 scoreline, which is the statistically most important point to win? Read on to find out.

Many experts have asserted that 15-30 is the key point to win in an individual game of tennis. The legendary American tennis player, Pancho Gonzales, who played arguably the greatest match of all time (22-24 1-6 16-14 6-3 11-9) against Charlie Pasarell, asserted that this was the most important point in a game, whilst the professor of statistics at Harvard University, Carl Morris, also studied the subject and devised a tactic that players can then apply to maximise their chances of winning.

The 15-30 scoreline

The respected website, tennisabstract.com, called 15-30 a ‘Pivotal Point’ and stated that ‘According to nearly every tennis commentator Ive ever heard, 15-30 is a crucial point, especially in mens tennis, where breaks of serve are particularly rare. One reasonable explanation is that, from 15-30, if the server loses either of the next two points, hell face break point.

Logically, it’s quite reasonable that these experts are all correct. The scoreline following the conclusion of the 15-30 point will either be 30-30 (zero points difference) or 15-40 (two points difference, in favour of the returner), but it’s also worth mentioning that 0-15 also has the same dynamic as 15-30, with there being either zero or two points difference after the point is played. 

It’s also subjectively logical, however, to assume that the writer at Tennis Abstract was correct in thinking that the 15-30 point was more important considering that break points will be faced if the point is lost.

The role of the expected service points won percentage

However, as always, it is best to use data to establish facts, as opposed to relying on subjective judgement, and a study by Princeton University determined the win game percentages for winning each individual point in a game, with reference to expected service points won percentage, and these are condensed into the tables below:

Table 1 - Expected Service Points Won Percentage = 50%

Scoreline

Server wins
point %
at scoreline

Increase in server
game win %
when server
wins point

Decrease in server
game win % when
returner wins point

Difference
sum

0-0

50

17

17

34

15-15

50

19

19

38

30-30

50

25

25

50

40-40

50

25

25

50

15-0

67

14

17

31

0-15

33

17

14

31

30-0

81

13

12

25

0-30

19

12

13

25

40-0

94

6

6

12

0-40

6

7

6

13

30-15

69

19

19

38

15-30

31

19

18

37

40-15

88

12

13

25

15-40

13

12

13

25

40-30

75

25

25

50

30-40

25

25

25

50

A-40

75

25

25

50

40-A

25

25

25

50

Looking at the sum of the differences between the various points, we can see that when expected service points won percentage is 50%, 15-30 is not the most important point.  If the server wins the point at 15-30, they boost their game win chances from 31% to 50%, whilst if they lose the point they drop from 31% to 13%.  The overall difference in the two outcomes is 37% (50%-13%), and there were various other scorelines which were more critical, with 30-30, 40-40, 40-30, 30-40, A-40 and 40-A all showing a 50% difference in the game win percentage chances from the server winning the point to the returner winning the point. 

On the evidence so far, the subjective judgement shown by the experts is somewhat flawed.

Table 2 - Expected Service Points Won Percentage = 65%

Scoreline

Server wins
point %
at scoreline

Increase in server
game win % when
server wins point

Decrease in server
game win % when
returner wins point

Difference
sum

0-0

83

8

14

22

15-15

80

10

18

28

30-30

78

14

28

42

40-40

78

14

28

42

15-0

91

5

11

16

0-15

69

11

21

32

30-0

96

3

6

9

0-30

48

14

27

41

40-0

99

1

2

3

0-40

21

12

21

33

30-15

90

7

12

19

15-30

62

16

29

45

40-15

97

3

5

8

15-40

33

17

33

50

40-30

92

8

14

22

30-40

50

28

50

78

A-40

92

8

14

22

40-A

50

28

50

78

With a higher service points won expectation, things are different. We can see that for every point, the returner winning the point has a bigger negative impact on the server winning the game than the positive impact of the server winning that point. This is entirely reasonable given that there is a higher expectation that the server wins the point than in table 1, so the effect of the returner winning the point is more profound.

Also evidenced is the greater importance of the 15-30 point, which rises from 37% deviation when service points won expectation is 50%, to 45% deviation when service points won expectation is 65%. Points at 15-40, 30-40 and 40-A have a bigger impact on the game win percentages than 15-30, but all those points in the game conclude the game if the returner wins the point. 

Therefore it is reasonable to state that when service points won expectation is 65%, 15-30 is indeed the key point in the game, if we assume that we are only looking at points where the game will still be in progress regardless of who wins the point.

ATP vs. WTA

Considering that the importance of 15-30 rises when service points won expectation also rises, it is quite reasonable to assert that 15-30 is a more important point in the ATP, which had an all-surface service points won percentage of 64.1% in 2015, than it is in the WTA, which was lower at 56.2%. 

It’s also quite logical to assume that it has extra importance on various surfaces, as the mean service points won percentage differs on each surface. For example, last year on grass, ATP servers won 66.8% of points compared to just 62.4% on clay, whilst in the WTA, those figures stood at 58.6% and 55.3% respectively. 

Therefore on grass, the 15-30 point is likely to be even more crucial than it is on clay, and at ATP level in particular, the 15-30 point on grass is likely to be the most important non-game ending point scenario in the sport.

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