Server’s Advantage: First and Second Serves

A couple of months ago I presented some research that showed that, in the average men’s grand slam match, the server’s advantage was neutralized somewhere between the 4th and 8th shot.

That research left a major question unanswered: How do the results differ between first and second serves?  Some second serves are hardly better than rallying shots, so it stands to reason that the server’s advantage is neutralized even faster on the second serve.

Using all of the Pointstream-tracked men’s matches from this year’s grand slams, we have an enormous population of points, in which 63.2% of points were won by the server.  When the first serve went in, the percentage jumped to 71.7%.  If the first serve went out, the server’s chance of winning fell to 50.2%, then rose again to 56.1% if he landed his second serve.

On first serve points, the server’s advantage was not neutralized until at least the 8th shot of the rally, and perhaps not until the 9th or 10th.  On second serve points, however, the advantage was gone (or very nearly so) as soon as the returner got the ball back in play.

Below, find the exact percentages of service points won for rallies that reach various lengths.  In the table below, the ‘1’ row refers to points with at least one stroke (the serve) that went in.  A one-stroke rally is defined as an ace, service winner, or return error.  A two-stroke rally is defined as a point in which the return landed in but the server doesn’t get his second shot back in play.  Note that each individual percentage is biased in favor of the player (server or returner) who has the chance to put the point away; the point can be considered neutralized when the biased even out (e.g. 55, then 45, then 55, and so on).

Rally    All     1sts     2nds
0      63.2%
1      66.1%    71.7%    56.1%
2      50.3%    53.7%    45.6%
3      59.9%    63.6%    54.9%
4      46.4%    47.8%    44.6%
5      58.1%    60.3%    55.6%
6      44.9%    45.9%    43.9%
7      57.0%    58.2%    55.6%
8      44.5%    45.1%    43.9%
9      55.9%    56.4%    55.5%
10     44.1%    44.1%    44.0%
11     55.8%    55.9%    55.8%
12     43.2%    43.1%    43.3%
13     55.6%    55.6%    55.5%
14     43.5%    43.5%    43.6%
15     55.5%    55.3%    55.6%

The Effect of One More MPH

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

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%