Italian translation at settesei.it
Earlier this week, we looked at whether Nick Kyrgios is unusually inconsistent. That is, is he more likely to upset higher-ranked players and lose to lower-ranked players than his peers? The numbers say he isn’t.
But that isn’t all we mean when we talk about Kyrgios’s unreliability. He often undergoes dramatic shifts within matches. At times, he is visibly distracted; during his Delray Beach match against Radu Albot, he even shouted that he wanted to get off the court. Other times, he comes up with breathtaking serving and shotmaking at the most crucial moments. He seems motivated by both packed grandstands and on-court pressure. Unfortunately, both of those are missing from a lot of professional tennis.
We already have some evidence for the better-under-pressure hypothesis. In his five matches in Acapulco last week, he won a mere 50.4% of points, one of the lowest totals ever for a title-winner. In three of the five matches, he won return points at a lower rate this opponent, resulting in Dominance Ratios (DRs) below 1.0. Winning a match with a sub-1.0 DR (or fewer than 50% of total points won) isn’t unheard of, but it’s not a reliable way to rise to the top of the sport. Such contests are called “lottery matches” for a reason–there’s a lot of luck involved in winning with such fine margins, and fortune tends to even out.
Yet Kyrgios’s “luck” keeps nudging his results in the same direction. He has played 15 career tour-level matches in which his DR is between 0.9 and 0.99–close matches in which he was slightly outplayed, at least in the points column. With stats like that, players tend to win about one-third of the time. Kyrgios, however, has won eleven of those 15 matches. His good fortune doesn’t cancel out when he narrowly edges out an opponent: In 13 matches with DRs between 1.0 and 1.1, he has lost only two. The Australian is doing something right.
Big points are big
You probably already know what’s going on here, even if you haven’t listened to commentators speculate during Nick’s matches. The key to such narrow victories is converting the “big” points–break points, deuces, tiebreaks, and so on. It doesn’t matter if you throw away a point or two when serving at 40-love. Other situations have considerably more leverage, and that’s when Kyrgios brings his best tennis.
I tallied up Kyrgios’s return points won over the course of his career, based on the point score of each one. (I don’t have the point-by-point sequence of every one of his tour-level matches, but most of them are included, more than enough to constitute a reliable sample.) Here are the five games scores when he wins the most return points, starting with the most effective:
- 0-40, 40-AD, 15-30, 30-40, 40-40
And the five scores, again in order, starting with least effective:
- 30-0, 40-0, 40-15, 0-15, 0-0
In other words, when he has a chance to break, he’s great. In my sample of matches, he won 31.5% of return points; when the opposing server is facing him at 0-40, he wins the point 45.0% of the time. At 40-AD, it’s 41.9%. When his opponent serves with a 30-0 advantage, Kyrgios wins a mere 27.3% of return points.
Everybody does it (a little)
Astute readers will realize that I haven’t accounted for a key variable. In a data set of dozens of matches, scores that favor the returner will occur more often against weaker servers. Kyrgios didn’t get many 0-40 or even 40-AD chances against John Isner last week, but he can expect to get more against the likes of Albot. So to some extent, we should expect players to win more return points at these moments. In the last 52 weeks, ATPers have won 37.3% of return points, but 40.1% of break points.
Everybody does it, but Nick does it more. The following table shows the ratio of return points won at each game score to average return points won. The middle column shows Kyrgios’s ratios and the right-most column shows the 2018 ATP tour average:
Situation NK ATP 0-40 1.43 1.14 40-AD 1.33 1.09 15-30 1.27 1.05 30-40 1.26 1.06 40-40 1.16 1.02 15-40 1.13 1.06 15-15 1.11 0.99 15-0 1.11 0.98 30-15 1.09 1.00 Situation NK ATP 0-30 1.07 1.06 AD-40 1.06 1.02 40-30 1.05 1.00 30-30 1.03 1.01 0-0 1.02 0.99 0-15 1.01 1.05 40-15 0.95 0.92 40-0 0.91 0.87 30-0 0.87 0.91
Most players take advantage in 0-40 situations, and to a lesser extent at break points, but Kyrgios is on another planet. The average player wins roughly 10% more return points in break situations; Kyrgios triples the ratio.
Leverage
We’ve taken a big step toward explaining Kyrgios’s pattern-breaking results and his in-match inconsistency. But even game scores don’t tell the whole story. A deuce point at 5-0 usually matters a great deal more than a break point when the returner is already up a set and a break.
To account for those differences, we’ll turn to the leverage metric. (You’ll also see it referred to as “volatility” or “importance.”) Here’s the idea: Given what we know about two players, we can calculate the probability that one of them will win the match, based on the current situation. If the server wins, that probability shifts in his favor. If the returner wins, it shifts in the opposite direction. Leverage is the sum of those two shifts: the amount of win probability that is at stake at any given point.
For today’s purposes, there are no specific numbers; you need only to understand the concept. The higher the leverage, the more the point matters. Players might disagree with some of the details that a purely math-based approach spits out, but for the most part, the equations capture our intuition about which points matter, and how much.
I calculated the leverage for every point of the 2018 ATP season and split the points into ten categories, from least important (1) to most important (10). The following graph shows the tour average rate of return points won (RPW) for each of those ten categories:
If we ignore the leftmost and rightmost data points, there’s something of a trend here. From the second-to-least-important category to the second-to-most-important, players increase their return points won from about 36.0% to 37.5%. Some of that shift can be explained by a phenomenon I’ve already mentioned: returners find themselves in crucial situations (such as break points) more often against weaker servers.
Here’s the same graph, now with a second line showing Kyrgios’s RPW in the ten categories, from least important to most important. I’ve kept the ATP average trendline for comparison:
Remember that 36.0% to 37.5% increase I mentioned a minute ago? For Kyrgios, the same shift is 27.0% to 35.2%–eight percentage points instead of less than two. It appears that the Australian is extremely sensitive to what’s at stake throughout matches, and when the rewards are high enough, he turns into a credible returner.
Some of you are probably thinking, “of course, I knew that all along.” First of all, I hate it when people say that, because what they really mean is, “I suspected that all along,” and they didn’t really know. Some of the other things such people “know” are actually wrong.
Second, I need to underline just how unusual this is. I’ve been playing around with point-by-point data for a few years now, looking for in-match patterns, for specific players and for the sport overall. Such patterns exist: points and games aren’t entirely independent of each other. But usually they are minor–a percentage point or two, not the kind of thing you could spot even in a fortnight’s worth of matches. Kyrgios breaks the mold. When it comes to the mercurial Australian, the assumptions that are adequate to account for most of professional tennis simply fail.