### By: Albert Carreno

In the world of sports, it feels like it really is better to be lucky than good sometimes. But is there an underlying reason a player in a certain sport seems to be “luckier” than another? Or is it just a matter of skill? Professional tennis, like most sports, tends to have an element of both. This is most aptly showcased in the tiebreaker. In a standard tennis match, the winner is the athlete that wins the best three out of five sets(where each set is usually decided by the first player to win six games). However, there are times where the players end up tied at 5-5 in a set. Contrary to what non-tennis watchers may think, the next game doesn’t decide the set. The set will then become first to seven wins, but the winner must win the next two games to avoid a tiebreaker(they need to win 7-5 i.e.). But if the players end up tying at 6-6, then a tiebreaker is needed to determine the winner of the set, and if the players each previously won two sets, then the tiebreaker will actually determine the match itself. This part of tennis is much like extra innings in baseball, extra time in soccer, or even 3 on 3 overtime in hockey. It’s exciting to watch and every second is filled with high pressure and intensity, since every point really can and does make the difference. Whichever player wins ten points first wins the tiebreaker, and the player must win by two or else it keeps going. According to Ultimate Tennis Statistics, the average tournament player wins 51% of tiebreakers. Essentially then, it seems like a tiebreaker is something of a coin flip if we’re going off this average, but could there possibly be something more to it? Is there a certain aspect of a player’s game that might help them win more tiebreakers than they otherwise would? I aim to dissect that question in detail with this article using statistical analysis.

As aforementioned, the average tournament player wins 51% of the time in tiebreakers. The frequency histogram below models the distribution of tiebreaker win percentages of hundreds of tournament players across the world.

As we can see, there is a large peak at around 50% in the tiebreaker win rate, and most of the data falls within the 45 to 60% range. Additionally, the distribution of tiebreaker win rates seems to nearly follow a normal distribution. Nevertheless, we can still come up with a few leads for what, if anything, might contribute to a player having a greater winning percentage than another in tiebreakers. Firstly, there is a player’s serve; the serve is among the most important skills for a player to master as if they have a lethal serve, they can rely on it to start points from a position of strength and even outright win points right from the get go through aces. Additionally, other factors that might come to mind for a tennis fan reading this could include unforced error percentage(how many of a player’s points end because of an unforced error). This metric being low would indicate a player is consistent and doesn’t make costly mistakes they could have avoided. These are useful attributes to have in a tiebreaker. But now that we have some idea of what factors might be at play in tiebreaker win percentage, let’s put them to the test through regression analysis.

First, we’ll take a look at ace percentage and double fault percentage, which are both pretty self-explanatory. The scatterplots below demonstrate how correlated these statistics are with tiebreaker win percentage.

From looking at these graphs, it doesn’t really appear that ace percentage or double fault percentage has any bearing on a player’s tiebreaker win rate. Both graphs very much show a lack of correlative strength. There are several players in the ace percentage graph that have low ace percentages of around 5%, but still boast impressive tie break win percentages of over 60%. Likewise, in the double fault scatterplot, we see many players that only double fault at around a 3% rate, but still manage to win 45% or fewer of their tiebreakers. In particular, the p-value obtained from the ANOVA testing for the double fault percentage model is not valid at a .05 significance level(.44), so we cannot even be sure double fault percentage has any effect on tiebreaker win rates at all. The p-value for the ace percentage is valid at a .05 significance level(.001) and shows a tiny bit of correlation with an R^2 of .03, but that is still not much correlation to speak of and leaves nearly all the variance observed in tiebreaker win percentage unexplained. Frankly, these results are surprising considering how important serving is during a tiebreaker since having a good serve can win players points without even needing to get into a rally.

That said, when analyzing it further, we can make sense of these results. The very best servers only ace their opponents at a 20% clip, or one out of every five points they serve. In a tiebreaker, players rotate serving every two points(except at the start where the first player to serve only serves the first point) and most tiebreakers are usually decided within 18 points. This means a player with a high ace percentage will only reap the benefits, on average, for one or two points in a tiebreaker. While every point matters as I mentioned earlier, one or two points and even no points sometimes is not enough to give a player a clear advantage over another in a tiebreaker from the get go, which is likely why we observe these results. This same logic can be applied to the results for the double fault percentage model. The most consistent server only double faults once for every 33 points they serve, while the least consistent server double faults once for every 14 points they serve. This might seem like a large discrepancy when laid out like that, but when we again consider how short tiebreakers are compared to an entire set, this difference in serving consistency will only maybe score the more consistent server one extra point in a tiebreaker, but it’s just as likely it awards them no extra points.

All told, we haven’t been able to find anything that seems to be correlated with tiebreaker win percentage, but there are still other factors to consider. Serving is only one aspect of a player’s game. Next, we’ll look at unforced error percentage and upset percentage(how many of a player’s career wins came against players seeded higher than them). Analyzing these metrics’ relationship with tiebreaker win percentage will allow us to determine how consistency and momentum factor into tiebreakers. The scatterplots below visually display the correlation for both of these metrics.

Before we dive in, it must be addressed that there are far more data points for the upset model as opposed to the unforced error rate. This is because there was more data available for a player’s upset percentage than unforced error percentage. That being said, it should not make a drastic difference as a sample size of 80 for unforced error rate is still large enough to conduct statistical analysis by most standards. Regardless, we see that unforced error percentage doesn’t seem to be correlated with tiebreaker win rates in any way, but surprisingly, upset percentage actually does seem to have some correlation. If anything, common sense would seem to indicate that unforced error percentages would have a negative correlation with tiebreaker win percentage. The more often you make errors that were in your control, the less likely you are to win the tiebreaker it would seem to follow. However, the p-value obtained from ANOVA testing for this model is not valid at a .05 significance level, so much like double fault percentage, we cannot be sure that this metric makes even an ounce of difference when it comes to whether a tennis player is more or less likely to win a tiebreaker. On the other hand though, upset percentage interestingly does have some correlation. The R^2 for the upset rate model is 0.22 and the ANOVA p-value is significant at a .05 level, so we can be sure these results are not due to chance. Nevertheless, while there is certainly a bit of negative correlation between upset percentage and tiebreaker win rates, an R^2 of 0.22 only indicates mild correlation and still leaves a lot of variability unexplained by the model.

Thinking deeper about these results, we can also somewhat make sense of them. Unforced error rates would seem to be important in winning tiebreakers, but the reality is that many errors in tennis are forced errors. Forced error is an umbrella term that includes a player being aced, their opponent hitting a winner against them(a shot that bounces twice before the player can even touch it), and a player getting a very difficult shot to return that they can only get their racket on out of pure desperation. Unforced errors only include the mistakes a player makes completely on their own which could include hitting the ball into the net or out of bounds despite the shot their opponent hit to them not being a particularly hard shot to return in bounds at least. It is highly possible that many points in tiebreakers are decided through making opponents commit forced errors, so unforced errors may not really be at play as much. As for upset percentage, the negative correlation indicates that the higher a player’s upset percentage is, the lower their tiebreaker win rate tends to be. This might be for a plethora of reasons, but the most obvious one is that higher seeded players tend to beat lower seeded players. When a lower seeded player faces off against their high seeded opponent in a tiebreaker, logic says that they will tend to lose more often than not purely because of skill, especially if the difference in seed ranking is large. This reasoning makes logical sense because a very low seeded player might only have a high upset percentage simply because there are such few players beneath them in terms of rank. Therefore, it makes sense that they would lose more than they win against higher seeded players in tiebreakers. \

In summary, we were not really able to find a smoking gun when trying to crack what attributes are most important in a tennis player’s success in tiebreakers. That being said, we were still able to debunk some common sense theories such that great servers and consistent players would have the upper hand in tiebreakers as well as discover that lower seeded players tend to be at a disadvantage. It’s also worth noting that this was a rather limited analysis that has many potential avenues to go down for greater complexity and depth. There are many other minute aspects of tennis that were not considered that could have a significant impact on tiebreaker percentage, but I’d like to think we were at least able to cover some of the major ones. It’s also completely possible that there aren’t really any factors we can chalk a player’s success in tiebreakers up to though. There’s a reason the average player only wins tiebreakers at a 51% clip: it’s often a coin flip and it’s only about being that much better than your opponent in an already incredibly contested and competitive match if it makes it to a tiebreaker.

*All data was taken from Ultimate Tennis Statistics, Tennis Abstract, and Tennis Datenbank*

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