Yesterday I dove deep into tiebreak luck. I explained that while better players tend to win more tiebreaks, there’s no special tiebreak skill that causes certain players to perform better at the end of sets than they do at other stages of the match. Therefore, if a player has a long stretch of excellent or dismal tiebreak results, we should discard the tempting hypothesis that he or she possesses some special tiebreak talent and assume that he or she will post more average results in the future.

**The same is true of break points.** In any given season, you can find players who win or lose a disproportionate number of break points, and it’s tempting to point to mental strength by way of explanation. Yet more often that not, the unusual results disappear, along with any convincing case that we’ve identified a notably steely or flimsy tennis brain.

To quantify those over- and underachievements, I’ve attempted to measure the number of break points converted compared to the “expected” number, where the expectation is defined by how often the player wins return points. (It’s a bit more complicated than looking up a player’s single season return-points-won (RPW) rate. Instead, we consider their RPW for each match, and weight the matches according to how many break point opportunities occurred in the match.) For example, Gael Monfils converted 146 of his 317 break point chances last year, good for a 46.1% win rate. That far outstrips his weighted RPW of 38.7%. He claimed 23 more break points than expected, or an excess of 19%. Parallel to my approach with tiebreaks, I’ve named those stats, so the counting stat is Break Points Over Expectation (BPOE) and the rate stat is Break Points Overperformance Rate (BPOR).

(On average, returners win slightly fewer break points than non-break points. I’ve adjusted the “expected” level downward by 1.4% to account for this.)

Monfils was an outlier, the only player in 2018 to exceed +20 BPOE, and the only player with 40-plus matches to post a BPOR of more than 15%. Yet there was little in his past performance that would have told us what was coming. From 2009 to 2017, he had three negative seasons, two years indistinguishable from neutral, and four above average. Over the entire span, he won break points less than one percent more often than expected. The Frenchman’s pressure-point success in 2018 could be thanks to some newfound mental strength, but if history is any guide, he won’t continue to display whatever mix of luck and nerves led him to post his circuit-leading figures.

Here are the best and worst break point performances, by BPOE, posted by ATPers with at least 20 tour-level matches last year:

Player Chances Won BPOE BPOR Gael Monfils 317 146 23.4 1.19 Mackenzie Mcdonald 252 116 19.0 1.20 Michael Mmoh 129 63 16.9 1.37 Malek Jaziri 298 134 16.2 1.14 Pierre Hugues Herbert 297 126 16.1 1.15 Adrian Mannarino 318 136 14.1 1.12 Ricardas Berankis 235 103 13.8 1.15 Sam Querrey 290 118 13.8 1.13 Martin Klizan 313 139 13.5 1.11 Jan Lennard Struff 272 118 13.4 1.13 Marton Fucsovics 414 162 -11.5 0.93 Filip Krajinovic 238 86 -11.8 0.88 Evgeny Donskoy 239 79 -11.9 0.87 Stan Wawrinka 217 66 -11.9 0.85 Aljaz Bedene 303 108 -12.9 0.89 John Isner 308 85 -13.0 0.87 Mischa Zverev 347 123 -14.1 0.90 Marin Cilic 568 209 -18.1 0.92 Joao Sousa 484 176 -21.6 0.89 Novak Djokovic 617 246 -21.7 0.92

It’s striking to see Novak Djokovic at the bottom of the list, nearly as bad or unlucky as Monfils was good or fortunate. Yet Novak’s story is surprisingly similar to Gael’s. From 2009 to 2017, his overall BPOR was 0.997–almost precisely neutral–and he posted nearly as many positive seasons as negative ones.

**Yep, it’s random**

To give more player-specific examples would only belabor the point: A player’s performance on break points (independent of his overall return-point skill) has no relationship from one year to the next. I found 700 pairs of consecutive player-seasons between 2009 and 2018 (for example, Djokovic’s 2017 and 2018) and found that the correlation between the two seasons was effectively zero. (r^2 = 0.002)

Here’s one more illustration of the point. This table shows the ten players who recorded the highest 2017 BPOR figures of those men who played at least 20 ATP matches in both 2017 and 2018. The right-most column shows what they did the following year:

Player 2017 BPOR 2018 BPOR Damir Dzumhur 1.16 1.05 Alexander Zverev 1.15 1.02 Nicolas Kicker 1.15 1.04 Peter Gojowczyk 1.14 0.92 Dusan Lajovic 1.13 1.04 Mikhail Kukushkin 1.13 0.94 Mischa Zverev 1.13 0.90 John Isner 1.12 0.87 Andrey Rublev 1.12 0.96 Thiago Monteiro 1.12 1.17 AVERAGE 1.14 0.99

Only Thiago Monteiro continued to be successful enough to maintain a place amid the tour leaders; John Isner’s follow-up campaign was so different that he registered as one of the tour’s worst in 2018. Taken together, five of 2017’s top ten ended 2018 below average, and the ten men combined for a BPOR just a bit worse than neutral. This is all just another way of saying we’re looking at something indistinguishable from chance.

**Putting a price tag on good fortune**

We’ve established that break point performance in the present has nothing to tell us about break point performance in the future. But as I pointed out in yesterday’s post about tiebreaks, that very lack of predictiveness has value.

Monfils’s BPOE of +23 helped his overall cause, helping him rack up more victories in 2018 than he otherwise would have. His break point results probably boosted his ranking and prize money tally. Reverting to neutral break point performance won’t knock him off tour, but assuming he continues to serve and return at the same level he did last year, a more pedestrian BPOE could hurt his cause. But how much?

Yesterday I suggested that two additional tiebreaks are equal to one additional win. Break points are a bit more complicated–clearly a single break point is not as valuable as an entire tiebreak, both because it is a single point and because it rarely offers the player a chance to finish off an entire set or match. On the other hand, break points are more numerous, and figures Monfils’s +23 and Djokovic’s -21 are more extreme than the most unexpected tiebreak performances.

**Measuring high-leverage points**

The key to measuring the impact of break points is the general concept of win probability, and the more specific notion of leverage. (Leverage is often referred to as volatility or importance; these are all the same basic idea.) Win probability is simply a measure of each player’s chances of winning the match at any given stage. Leverage is an index of how much a single point can affect that probability. Say two equal players embark on a new match. Before the first ball is struck, each have a 50% chance of emerging victorious. If winning the first point increases the server’s chance of winning to 51% while losing it decreases his probability to 49%, we would say that the leverage of the first point is 2%–the difference between the win probabilities that would result from winning or losing the point.

The more crucial the point, the higher the leverage. The typical point is well below 5%, but a truly high-pressure moment, like 5-6 in a third-set tiebreak, can be as high as 50%.

Win probability stats depend a great deal on the inputs you choose, so there’s no single mathematically correct leverage measurement at any given moment. If you think two players are equal, your estimate of the win probability at the start of the match is very different than if you think one of the competitors is a heavy favorite. Those judgements affect the leverage of every point as well. Still, for aggregates of large numbers of matches–say, an entire season–we can get a general idea of the value of break points.

**Necessary assumptions**

If we make the simple but clearly wrong assumption that all players are equal, the leverage of the average point on the ATP tour last year was 4.6%, and the leverage of the average *break point* on tour last year was 10.5%. Those numbers are useful as a starting point, but they are clearly too high; when we accept that most matches are not contested between players of equal skill, we realize that any given break point isn’t quite that important–if Djokovic fails to convert one against Monteiro, he’ll remain almost certain to win the match.

One alternative approach is to assume that each player’s skill level is represented exactly by their performance in a given match. So if Djokovic plays Monteiro and wins 80% of service points, while Monteiro wins only 60%, we could calculate the win probability and leverage of every point using those numbers. Using that method, we get a leverage of 2.9% on the average point and 6.5% on the average break point.

The second assumption is also not exactly right, but it probably gets closer to the truth than the first. Keeping in mind that it’s an approximation, let’s use a break point leverage of 7.5%. That figure means that, on average, changing the result of a single break point affects the win probability of a single match by 7.5%. Another of way of thinking about it–the one most relevant to the task at hand–is that winning a break point instead of losing it is equivalent to winning 7.5% (or about one-thirteenth) of a match.

**Break points are (fractions of) wins**

Returning to the concept of BPOE, we can now say that 13 additional break points is equivalent to one additional win. Monfils’s 2018 tally of +23 was good for almost two extra victories over the course of the season, and Djokovic’s count of -21 would, on average, cost him 1.5 matches. Given the multitude of other factors influencing each man’s performance, it’s unreasonable to expect either player’s won-loss record in 2019 to bounce back so predictably and precisely. (Especially since it’s impossible to win 1.5 matches.) But in the unlikely event that all else is equal, we should expect those advantages and disadvantages to disappear in the new season.

The range of minus-21 to plus-23 break points is a decent representation of how extreme break point luck can be. Since 2009, only four players have posted single-season numbers above +23, including the most extreme BPOE of +34, accumulated by Damir Dzumhur in 2017. (Dzumhur was hit hard by the ensuing reverse in fortune: His 2017 tour-level record was 37-24, but in 2018, when his BPOE fell to a still-lucky +8, his record dropped to 25-31.) At the opposite extreme, Dominic Thiem suffered from a tally of 28 break points below expectations in 2015. A year later, he bounced back to minus-5, and his ranking improved from 19th to 9th. Despite the roller-coaster descents and climbs of Dzumhur and Thiem, the range of the break-point-luck effect appears to be about five wins, from about minus-2 wins at the low end to plus-3 for the players most favored by fortune.

For most players in most seasons, however, break point luck is little more than a rouding error. And while it’s easy to get sucked into the measurements I’ve laid out, that’s the most important point of all: Just like there’s no special tiebreak factor, there’s no reason to think that certain players are somehow better at break points than others. The better a player’s return game, the more break points he’ll convert. Anything beyond that will eventually regress to the mean. And for players with extremely strong or weak break point performances, that regression is likely to have effects that extend to the overall won-loss record, ranking, and beyond.