Points are the most basic scoring unit in tennis, but they do not directly determine the outcome of a match. To win a match, you must string together combinations of points into games and games into sets, etc. Certain points can be “thrown away” while others can single-handedly determine the outcome of the match.

Tennis players understand this and change their level of play according to the situation. Some raise their game in key moments, others choke under pressure. But if we treat each point in tennis as a random event, we can establish basic notions about how points-won percentages influence a player’s probability of winning.

Let’s start by aggregating the winners’ and losers’ points won percentages for **every individual singles match** from 2005 to 2015 to give an idea of how points were distributed in ATP matches over the last decade (women’s stats are very similar). The two distributions are mirror images around the 50% line. Out of all match winners, 80% nabbed between 50 to 60% of points, meaning that a vast majority of matches are decided by a 0 to 20 % margin. The average match is decided 55 to 45%. The dark region between the two distributions shows the overlap, that is, where winners won *less* points or losers won *more* points. Judging by the small overlap, it is very uncommon to win a match with less than 50% of points. In fact, this happens in less than 5% of all matches. Even more rare are extremely one-sided matches where the victors win over 70% of points. Most often these matches involve retirements early on. Richard Gasquet, for example, has the distinction of being the only player in this entire time period to win a perfect 100% of points in a match. This occurred in the 2015 Montpellier final, when Jerzy Janowicz retired after losing 12 straight points, down 0-3.

The distributions show how often winners achieve a certain winning margin. But what about the other way around? **What does a certain points-won percentage say about a player’s probability of winning?** To do this, we looked at the number of matches won divided by the total number of matches played for each bin in the histograms. For example, if 80 matches had winners with 50-51% of points won and another 20 had losers with that same margin, then we say that winning 50-51% of points gives an 80% probability of winning (80 out 100 total matches). Here are some interesting scenarios that we considered and the resulting probabilities.

Points won |
Probability of Winning an ATP match |
Comments |

<50% |
4.5% |
That’s about 135 matches in a year. |

50-60% |
95% |
Even though this is 80% of match winners, very few players actually lose with these percentages, so the probability of winning is much higher. |

>60% |
~100% |
It’s almost impossible to win a match with 40% of points, barring a retirement. |

54-56% |
99% |
Winning right about 11 points out of every 20 virtually guarantees you a match. |

50-51% |
71% |
Even just a slight edge in points won tips the scales significantly in a player’s favor. |

In short, these observations suggest that the most suspenseful matches (that is, matches for which the outcome is highly uncertain) should see an even share of points between the two players. This is fairly obvious, but **what is surprising is how little the margins need to deviate to turn a match heavily in a player’s favor.** A 1% bump in points won is enough to make a player a good bet to win. So, even though a player only needs to win more sets, and not necessarily more points, we see that more points almost directly translate to more sets. In addition, the fact that the average winner wins with 55% of points seems to suggests that the typical ATP match is not very competitive.

A player’s probability of winning a point presumably fluctuates throughout a match, depending on whether they are serving and other factors. Still, we can use match averages to estimate overall competitiveness. In upcoming posts, we will break down point percentages by players and over time to see how their performance has improved over the years.

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