# 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%```