Category: Serve speed

The Effect of Serena’s Serve Speed

Italian translation at settesei.it

Yesterday at FiveThirtyEight, Tom Perrotta highlighted the relationship between Serena Williams’s first serve performance and her chances of winning. According to the article, Serena has won only (“only”) 74% of her first serve points over the fortnight, compared to an outlandish 87.5% when she won the title in 2010. She has never won Wimbledon while winning fewer than 75% of her first-serve points, and even the three-quarters mark is no guarantee, as she topped 77% last year en route to a second-place finish.

A lot of factors go into first-serve winning percentage, including serve placement, serve tactics, and all the shots that a player hits when the return comes back. The most obvious, though, is another category in which Serena has often topped the charts: serve speed. When Williams beat Garbine Muguruza to win the Championships in 2015, her average first serve clocked in at 113 miles per hour, the third straight match in which her typical first delivery topped 111 mph. Over her last 13 matches, she has averaged only (“only”) 106.4 mph, never exceeding 109 mph in a single contest.

How much does it matter?

It seems fair to assume that, all else equal, a faster serve is more effective than a slower one. Complicating things is the fact that all else is rarely equal: wide serves are often deadly despite requiring less raw power, more conservative serves can be easier to place, andwe haven’t even scratched the surface of the effect of spin. A faster serve isn’t always better than a slower one. But on average, the basic assumption holds true.

For each of Serena’s 23 matches at Wimbledon 2014, 2015, 2018, and 2019 (she didn’t play in 2017, and I don’t have the relevant data at hand for 2016–don’t ask), I split her first serve points into quintiles, ranked from fastest serves to slowest serves. This is a crude way of controlling for the effects of different opponents and giving us an initial sense of how much Serena’s serve speed influences the outcome of first-serve points:

Quintile     1SP W%  Avg MPH  
Fastest       80.6%    116.9  
2nd fastest   73.7%    112.2  
Middle        79.5%    108.0  
2nd slowest   73.7%    103.7  
Slowest       74.9%     98.1

Clearly, serve speed doesn’t tell the whole story. At the same time, it looks like a 117 mph serve–or even a 108 mph one–is a better bet than a 98 mph offering.

Another way to isolate the effect of serve speed is to ignore the influence of specific opponents and simply sort first serves by miles per hour. From these 23 matches, we have 43 first serves recorded at exactly 100 mph, with a corresponding winning percentage of 72.1%. Serena hit 33 first serves at 101 mph, of which she won 72.7%. While the winning percentages don’t usually move so neatly in lockstep with first serve speed, there is a general trend:

The correlation is a loose one: winning percentages at 99 mph and 103 mph are better than those at 116 mph and 117 mph, for example. We could attribute that to the possibility that the slower serves are tactically savvier, or more approximate placement of the faster deliveries, or just dumb luck, because our sample size at any specific speed isn’t that great. Still, we can draw an approximate conclusion:

Each additional two miles per hour of first-serve speed is worth an additional one percentage point to Serena’s 1st serve winning percentage.

To take it one step further: Serena usually lands about 60% of her first serves, and roughly half of total points will be on her serve, so each additional two miles per hour of first-serve speed is worth an additional 0.6 percentage points of total points won. In a close match, like her 2014 loss to Alize Cornet–in which she averaged only 104 mph on her first serves and won exactly 50% of the points played–that could be the difference.

Serena in context

The same general rule cannot be applied to all women. (Several years ago, I took a similar look at ATP serve speeds, and–perhaps foolishly–I didn’t break it down by player.) I ran the same algorithm on the recent Wimbledon records of the nine other women for whom I have at least 15 matches worth of data. The effect of serve speed varies from “quite a bit” for Johanna Konta to “not at all” for Venus Williams and “I don’t understand the question” for Caroline Wozniacki.

The following table shows two numbers for each player. The “Addl MPH =” column shows the effect of one additional mile per hour on first serve winning percentage, and the “_ MPH = 1% SPW” column shows how many additional miles per hour are required to increase first serve winning percentage by one percentage point:

Player               Addl MPH =  MPH = 1% SPW  
Johanna Konta             0.89%           1.1  
Angelique Kerber          0.56%           1.8  
Serena Williams           0.48%           2.1  
Garbine Muguruza          0.47%           2.1  
Simona Halep              0.41%           2.5  
Petra Kvitova             0.29%           3.5  
Agnieszka Radwanska       0.28%           3.6  
Victoria Azarenka         0.02%          50.9  
Venus Williams            0.00%             -  
Caroline Wozniacki       -0.40%             -

Konta’s serve speed is almost twice as important to her first-serve success as Serena’s is. Her average first-serve speed in her quarter-final loss to Barbora Strycova was 99.9 mph, her lowest at Wimbledon since a first-round loss in 2014.

At the opposite extreme, we have Victoria Azarenka and Venus, for whom serve speed doesn’t seem to matter. (Venus, for one, excels at the deadly wide serve, which she converts into aces regardless of speed.) Wozniacki apparently lulls her opponents into confusion and illogic, giving her better results on slower first serves.

Serena vs Simona

These are small effects, so even the range between Serena’s slowest serving performance this fortnight (105 mph first serves against Carla Suarez Navarro) and the 2015 final against Muguruza would only have effect Serena’s total points won by about 2.5 percentage points. Nine out of ten times Williams and Halep have gone head to head, Serena has come out on top, always with more than 52.5% of total points, usually with more than 55%. That’s an ample margin of error–or, more precisely, margin of slow serving.

On the other hand, the most recent Serena-Simona contest, the only time they’ve played since 2016, was the closest of the lot. Halep is a great returner, but she is not immune to powerful serving: her rate of return points won is affected by serve speed just as much as Williams’s serve stats are. The gap between the finalists could be narrow, and Serena’s serve speed is one of the few tools completely in her own power that she could deploy to tilt the scales in her favor.

The Oddity of Naomi Osaka’s Soft Second Serves

Italian translation at settesei.it

Naomi Osaka has quickly risen to the top of the women’s game on the back of some big hitting, especially a first serve that is one of the fastest in the game. Through Thursday’s semi-final, Osaka’s average first-serve speed in Melbourne was 105 mph, faster than all but two of the other women who reached the third round. Even those two–Aryna Sabalenka and Camila Giorgi–barely edged her out, each with average speeds of 106.

Shift the view to second serves, and Osaka’s place on the list is reversed. While Sabalenka’s typical second offering last week was 90 mph and Giorgi’s was 94, Osaka’s has been a mere 78 mph, the fourth-slowest of the final 32. That mark puts her just ahead of the likes of Angelique Kerber and Sloane Stephens, both whose average first serves are nearly 10 mph slower.

Osaka’s 27 mph gap is the biggest of anyone in this group. The next closest is Caroline Wozniacki’s 23 mph gap, between her 102 mph first serve and 79 mph second serve–both of which are less extreme than the Japanese player’s. Expressed as a ratio, Osaka’s average second serve is only 74% the speed of her typical first. That’s also the widest gap of any third-rounder in Melbourne; Wozniacki is again second-most extreme at 77%.

The following table shows first and second serve speeds, along with the gap and ratio between those two numbers, for a slightly smaller group: women for whom the Australian Open published at least four matches worth of serve-speed data:

Player          Avg 1st  Avg 2nd   Gap  Ratio  
Osaka             105.5     78.5  27.0   0.74  
Keys              105.2     85.4  19.7   0.81  
SWilliams         103.8     88.6  15.2   0.85  
Barty             102.0     88.2  13.7   0.87  
KaPliskova        101.9     80.5  21.4   0.79  
Collins           101.2     82.2  19.1   0.81  
Kvitova            99.6     91.6   8.0   0.92  
Muguruza           98.1     82.5  15.6   0.84  
Pavlyuchenkova     97.9     84.5  13.4   0.86  
Sharapova          97.9     89.6   8.2   0.92  
Svitolina          97.6     78.2  19.4   0.80  
Stephens           96.1     75.1  21.0   0.78  
Halep              95.3     80.9  14.4   0.85  
Kerber             94.0     78.4  15.7   0.83

Oddly enough, having such a slow second serve doesn’t seem to be causing any problems. In today’s semi-final against Karolina Pliskova, Osaka won 81% of first serve points and only 41% of second serve points, but her typical performance behind her second serve is better than that. And in this match, both women feasted on the other’s weaker serves: Pliskova won only 32% of her own second serves. (Though to be fair, Pliskova had the second-largest gap of the players listed above. She tends to rely more on spin than speed when her first serve misses.)

Across her six matches, Osaka has won 73.3% of her first serve points and 49.7% of her second serve points–a bit better than the average quarter-finalist in the former category, a very small amount worse than her peers in the latter. The ratio of those two numbers–68%–is almost identical to those of Danielle Collins, Petra Kvitova, Anastasia Pavlyuchenkova, and Serena Williams, all of whom have smaller gaps between their first and second serve speeds. Of the eight quarter-finalists, Kvitova has the smallest speed gap of all, yet the end result is the same as Osaka’s, she’s just a few percentage points better on both offerings.

Here are the first- and second-serve points won in Melbourne for the eight quarter-finalists, along with the ratio of those two figures and each player’s serve-speed ratio from the previous table:

QFist           1SPW%  2SPW%  W% Ratio  Speed Ratio  
Kvitova         77.9%  52.8%      0.68         0.92  
Williams        74.7%  50.0%      0.67         0.85  
Osaka           73.3%  49.7%      0.68         0.74  
Collins         72.5%  50.0%      0.69         0.81  
Barty           70.8%  55.7%      0.79         0.87  
Pliskova        70.5%  50.0%      0.71         0.79  
Pavlyuchenkova  67.0%  44.9%      0.67         0.86  
Svitolina       66.5%  48.1%      0.72         0.80

Clearly, there’s more than one way to crack the final eight. With Kvitova, we have a server who racks up cheap points with angles instead of speed, rendering the miles-per-hour comparison a bit irrelevant. Serena’s results are close to Osaka’s, though she gets there with bit more bite on her second serves. And then there’s Svitolina, who doesn’t serve very hard or that effectively but can beat you in other ways.

Knowing all this, should Osaka hit harder second serves? In extreme cases, like today’s 81%/41% performance against Pliskova, the answer is yes–had she simply hit nothing but first serves and succeeded at the same rate, she would’ve piled up a lot of double faults but won more total points. But the margins are usually slimmer, and as we’ve seen, her second-serve performance isn’t bad, it just might offer room for improvement. Every player is different, but faster is usually better.

A thorough analysis of that question may be possible with the available data, but it will have to wait for another day. In the meantime, Saturday’s final will offer us a glimpse of contrasting styles: Osaka’s powerful first offering and soft second ball, against Kvitova’s angles and placement on both serves. Both my forecast and the betting market see the title match as a close one–perhaps Osaka’s second serve will be the shot that makes the difference.

How Servers Respond To Double Faults

Italian translation at settesei.it

In the professional game, double faults are quite rare. They sometimes reflect a momentary lapse in concentration, and can negatively impact a server’s confidence. Players are sometimes particularly careful after losing a point to a double fault, taking some speed off their next delivery, or aiming closer to the middle of the box.

Let’s dig into some data from last year’s grand slams to see what players do–and how it affects their results–immediately after double faults. IBM’s Slamtracker provided point-by-point data for most 2017 grand slam singles matches, including serve speed and direction, and the available matches give us about 5,000 double faults to work with. (I’ve organized the data and made it freely available here.)

For each server in each match, I’ve tallied their results on points immediately following double faults. (That means that we exclude after-double-fault points when the double fault ended the game.) Then, for each player, I compared those results with match-long averages. Because double faults are so unusual, and because we only have this data for the majors, the sample isn’t adequate to tell us much about individual players. But for tour-wide analyses, it’s more than enough.

Serve points won: As we’ll see in a moment, men and women have different overall tendencies on the point following a double fault. But by the most important measure of simply winning the next point, gender plays little part. Men, who in this sample win 65.1% of service points, fall just over one percentage point to 64.0% on the point following a double fault. Women, who average 57.8% of service points won, drop even more, to 56.1% after a double.

First serve percentage: I expected that servers become more conservative immediately after a double fault. For women, that hypothesis is correct: In these matches, they land 63.3% of their first serves, while after a double fault, that number jumps to 65.4%. On the other hand, men don’t seem to change their approach very much. On average, they make 62.3% of their first offerings, a number that barely changes, to 62.5%, after double faults.

First serve points won: Here is additional evidence that women become more conservative after double faults, while men do not. In general, women win 63.7% of their first serve points, but just after a double fault, that number drops to 62.9%. For men, there is a decrease in first serve points won, but it is almost as small as their difference in first serve percentage: 72.7% overall, 72.4% after a double fault.

First serve speed: With serve speed, we run into a limitation of the Slamtracker data, which gives us speed only for those serves that go in. So when we look at the average speed of first serves, we’re excluding attempts that miss the box. Even with that caveat, the data keeps pointing in the same direction. Contrary to my “conservative” hypothesis, men serve a bit faster than usual after a double fault–183.3 km/h following doubles, versus 182.8 km/h in general. Women do seem to change their tactics, dropping from an average speed of 155.5 km/h to a post-double-fault pace of 152.2 km/h.

First serve direction: Slamtracker divides serve direction into five categories: wide, body-wide, body, body-center, and center. After a double fault, men are less likely than usual to hit a wide serve (24.1% to 25.8%), and those serves get split roughly evenly between the body and center categories. The difference in body serves is most striking: They account for only 3.5% of first serves overall, but 4.4% of post-double first serves. This may be the one way in which men opt for the conservative path, by maintaining speed but giving themselves a wider margin of error.

Women move many of their after-double-fault serves toward the middle of the box. On average, over 44% of serves are classified as either “wide” or “center,” but immediately after a double fault, that number drops below 41%. It’s not a huge difference, but like all of the other tendencies we’ve seen in the women’s game, it suggests that for many players, caution creeps in immediately after missing a second serve.

Tactics

As usual, it’s difficult to move from these sorts of findings to any sort of tactical advice. Even the first data point, that both men and women win fewer service points than usual right after they’ve double faulted, can be interpreted in multiple ways. By one reading, players may be serving too conservatively, missing out of the benefits of big first serves. On the other hand, if confidence is an issue, perhaps serving more aggressively would just result in more misses.

When in doubt, we have to trust that the players and coaches know what they’re doing–they’ve honed these tradeoffs through decades of experience and thousands of hours of match play. For fans, these numbers add to our understanding of the conclusions that players have reached. For the pros, perhaps a more detailed look at what happens after a double fault would help tweak their own strategies, both bouncing back from their own double faults and taking advantage of the lapses in concentration of their opponents.

The Effect of One More MPH

Italian translation at settesei.it

All else equal, increasing your first serve speed is a good thing … so how useful is it?  Earlier this week, I published some generic numbers, but those are far too crude to answer this question.

To get a better answer, we need to see what happens when specific players serve a little faster or slower.  Sometimes, players dramatically mix up serve speed (as with slice serves wide), but most of the time, each player stays within a fairly limited range defined by his own power and skill.

The algorithm I’ve employed is  fairly complicated, so I’ll give you the results first.

It appears that most players, if they increased their average serve speed by one mile per hour, would win 0.2% more first service points.  That’s not many–it’s not even one point in every match.  But every little bit helps, and according to my win probability models, winning 0.2% more first serve points can increase your chance of winning an even match from 50% to just short of 51%.  Except possibly at the extremes, that continues to be the case for 2 MPH, 3 MPH, and greater increases–so a 5 MPH increase takes that 50/50 match and turns it into a 54/46 contest.

(One assumption here is that all players respond to increases in serve speed the same way.  I’m sure that’s not true, but at this stage it’s a necessary assumption.)

The effect of a speed increase is even greater on ace and service winner rates.  Each additional MPH on a player’s serve increases his ace rate by about 0.4%, and his service winner rate by about 0.5%.

Now for the algorithm and some caveats.

Process

The algorithm was designed to control (to the extent possible) for different types of serving and playing styles, as well as the different average speeds to the deuce and ad court, as well as to different directions (wide, body, and T).

I used only US Open data, to avoid differences between surfaces and between the speed guns used at different events.  I used data only from the 18 players who had more than 150 first-serve points tracked by Pointstream.  For each of those players, I found their average first-serve speed for each of six directions: wide, body, and T to the deuce and ad courts.  Then, I randomly selected 150 of their first-serve points, and for each point, noted the difference between the point’s serve speed and the player’s average in the relevant court/direction.

Thus, every one of 2700 points was labeled 0 (average for that player/court/direction), or +1 (one mph above average), or -4, and so on.  That results in large pools of points with each label.  Many of the pools were too small for useful analysis, so I grouped them in sets of five: (-2, -1, 0, +1, +2), (-1, 0, +1, +2, +3), and so on.  The pools, then, were useful from about -15 to +15.

From there, I looked at  each of several stats (points won, aces, service winners) for each pool, and compared the rates from one pool to the next.  The results were somewhat erratic–in some instances, an additional mph results in aces or points won going down, but over the set of 31 pools, they generally went up.  The numbers presented above are the averages of each one-mph change.

Caveats

It’s not a very big sample, especially when separating serves into pools of 0, +1, +2, and so on.

One issue with the dataset is that the 18 servers were usually winning–that’s how they got enough first serves to merit inclusion.  Thus, the average returner in the dataset is below average.  That isn’t necessarily a bad thing–perhaps below-average returners respond to changes in serve speed the way above-average returners do–but without more data, it’s tough to know.

Another concern is what the numbers really tell us below about 5 mph slower than average.  The algorithm operates on the assumption that a 120 mph serve is the same as a 121 mph serve, only slower.  Comparing 120 and 121, that’s probably true.   But comparing 120 and 108–for the same player, serving in the same direction–it probably isn’t.  The 108 mph isn’t a simulation of what would happen if the player wasn’t as good; it’s probably a strategic choice, likely accompanied by some spin.

That said, the algorithm doesn’t directly compare 120 and 108, it compares 108 and 109, and perhaps in the aggregate, there is something useful to be gleaned from comparing a strategic spin first serve to an identical serve one mph faster.  In any event, limiting the range to between -10 and 10, or even -7 and 7, doesn’t change the results much.

Finally, the sample is completely inadequate to tell us what happens at the extremes.  The average player appears to improve his chances by adding another bit of speed, but does John Isner?  There may be a ‘sweet spot’ where a player can get maximum gains from an additional 1, 5, or 10 mph on his first serves, but beyond which, the gain is more limited.

US Open Serve Speed by Player

It’s time for more serve-speed research notes. Most of the matches at the 2011 U.S. Open were tracked by Pointstream, and serve speed was recorded for the vast majority of those points. The Open website published some serve speed numbers, but not as conveniently as I would like.

Below, find the average first and second serve speeds for every man who played three or more Pointstream-tracked matches. Oddly enough, the top and bottom of the list are held by Americans; John Isner is where you’d expect him, while Donald Young barely kept his first-serve average in the triple digits.

I didn’t expect to see nearly so much variation in the difference between first and second serve averages. Sure, Isner and Young are the endpoints in both lists, but David Nalbandian–below average on firsts–is third of 22 on seconds. To take another angle, both Marin Cilic and Jo-Wilfried Tsonga each have more than double the difference in averages than does either Alex Bogomolov or Fernando Verdasco.

(“M” is the number of matches tracked by Pointstream for each player.)

Player                 M  1sts  1stAvg  2nds  2ndAvg  
John Isner             4   313   124.5   125   106.2  
Andy Roddick           5   249   122.1   118   100.5  
Tomas Berdych          3    85   120.3    71    95.0  
Jo-Wilfried Tsonga     5   289   119.7   206    90.6  
Marin Cilic            3   125   118.7   121    86.3  
Janko Tipsarevic       3   148   116.5    84    90.5  
Roger Federer          6   355   115.6   186    94.6  
Juan Martin Del Potro  3   180   114.5    96    88.2  
Julien Benneteau       3   177   114.0    86    89.9  
Tommy Haas             3   211   113.9   124    94.1  
Novak Djokovic         7   421   113.7   226    91.4  

Player                 M  1sts  1stAvg  2nds  2ndAvg
Andy Murray            6   338   112.6   204    85.2  
Mardy Fish             4   231   112.4   165    88.0  
David Nalbandian       3   165   112.3   125    96.1  
David Ferrer           3   128   112.2    74    88.9  
Rafael Nadal           7   435   110.5   176    84.5  
Juan Monaco            3   167   109.4    70    90.4  
Gilles Simon           3   235   108.3   179    81.6  
Fernando Verdasco      3   175   107.3    72    92.6  
Alex Bogomolov Jr.     3   264   103.1    96    89.1  
Donald Young           4   213   101.9   111    80.6

The Effect of Serve Speed

Italian translation at settesei.it

All else equal, you want to serve harder. But how much does it really matter?

That’s a more difficult question than it sounds, and I don’t yet claim to have an answer. In the meantime, I can share the results of some data crunching.

In 2011 U.S. Open matches covered by Pointstream, there were more than 9,000 first serve points. The server won almost exactly 70% of those points. About 11% of points were aces, and another 24% were service winners.

To see the effect of serve speed, I looked at four outcomes: aces, service winners, short points (three or fewer shots), and points won. It’s no surprise that each type of results happens more on faster serves.

Below, find the full numbers for serves of various speeds. The finding that sticks out to me is the small change in service points won from the 95-99 MPH group to the 115-119 MPH group. It may be that the modest increase–put another way, the surprising success rate at 95-104 MPH–is a result of strategic wide serves, or the better ground games of the players who hit slower serves.

So as I said, there’s much more work to be done, identifying the effects of faster serves for individual players, looking at deuce/ad court differences (for righties and lefties), and the results on different serve directions.

MPH      SrvPts   Ace%  SvcW%  Short%  PtsWon%  
85-89       140   2.1%  17.9%   47.1%    55.0%  
90-94       275   0.7%  21.5%   47.6%    63.6%  
95-99       546   2.2%  18.5%   48.4%    66.1%  
100-104     885   4.2%  24.6%   51.0%    66.0%  
105-109    1400   6.4%  29.3%   56.6%    68.7%  
110-114    1524   8.7%  34.0%   57.3%    69.1%  
115-119    1487  12.2%  35.9%   60.8%    69.4%  
120-124    1553  16.1%  40.1%   65.2%    73.2%  
125-129     941  21.5%  48.1%   72.4%    76.3%  
130-134     353  29.7%  58.4%   77.3%    84.4%  
135-139      66  27.3%  65.2%   80.3%    89.4%