Do Points Get Shorter as the Match Progresses?

On Friday, some interesting ideas were batted around in the comments to my post on the 61-shot rally.  One of the simpler ones boils down to the question that titles today’s post: Do points get shorter as the match progresses?

Two forces seem to work in opposite directions:

• As players get used to each other’s games (and specifically their serves), more balls get returned.  Before looking at the numbers, I would’ve bet that this was the case, meaning that aces and service winners decline as you go deeper into a match.
• The longer the match, the more tired the players.  Tired (or even slightly injured) players take more risks and probably have shorter rallies.

To answer the question, I looked at rally lengths shown in Pointstream at the last three grand slams.  That gives us close to 250 men’s matches, all best-of-five sets.

The short, unsatisfying conclusion is: The results are mixed.  At Wimbledon and Roland Garros, rally length increased later in matches–as much as 10% in London and 20% in Paris.  At the Australian Open, the result was the exact opposite, with rally length decreasing substantially.  Perhaps rally length increases in most cases, except when it is extremely hot or the players are not yet in top shape.  The blistering heat in Melbourne is certainly a plausible reason for a decrease in rally length.

As we’ll see when we move into more specific findings, the results get even more jumbled.  It seems that points generally get longer as a match progresses, but not necessarily because players read and return serves better.  While rally lengths increase, the number of one-stroke points (aces, service winners, service return errors) often increases, as well.

Follow the jump for my methodology and full results.

Methodology

As noted, we have about 250 matches to work with.  I split each match in half–one half for each server–so that I could treat, say, del Potro’s service points differently than Olivier Rochus’s service points.

For each “half-match,” I broke it down into 30-point segments.  Thus, if Delpo hit 90 serves, the first segment was his first 30, the second segment was his second 30, and so on.  (I threw out some serves when there was a “leftover” segment of 15 serves or less.)  Then I compared the rally lengths in each of those 30-point segments.  I converted the average rally lengths of each segment to a ratio, so we call the first segment “1”, then if the rally length increased, the second segment might be “1.12.”  This puts all servers on the same scale.

Once that was done, I averaged all the ratios.  There was plenty of variation, with ratios anywhere from 0.6 to 1.5, but the averages never strayed too far from 1.  I went through this process for three statistics:

• Average rally length of all points.  (Aces and service winners have a rally length of 1; double faults, 0.)
• Average rally length of points where the service return was in play.  (I thought eliminating shorter points might be valuable.)
• Percentage of “short” points.  (When the returner didn’t get the ball back in play.)

The vast majority of best-of-five matches reach at least 80 service points per player, so the data for the 2nd and 3rd segments should be meaningful.  Beyond that, the sample size shrinks quickly, so there may be some bias for the 4th, 5th, and 6th segments.

Results

As you can see below, the results aren’t very clean, especially for the percentage of short points.  As always, it’s frustrating not to have more data–it would be fascinating to see whether some of the differences between these slams was similar to results on the same surfaces, or in similar weather conditions.  As it is, we can only draw the most basic of conclusions, and we can’t have a ton of confidence in those.

WIMBLEDON
            Sample  AvgRally  AvgRally+  Short%
1st 30         124      1.00       1.00    1.00
2nd 30         124      1.03       1.01    1.04
3rd 30         114      1.05       1.02    0.98
4th 30          63      1.04       1.05    1.05
5th 30          28      1.05       1.01    0.95
6th 30           9      1.13       1.08    0.99  

FRENCH
            Sample  AvgRally  AvgRally+  Short%
1st 30         196      1.00       1.00    1.00
2nd 30         196      1.00       0.99    1.06
3rd 30         171      1.20       0.94    1.00
4th 30          92      1.20       0.95    1.08
5th 30          37      1.03       0.95    1.02
6th 30          13      1.02       1.00    1.14  

AUSTRALIAN
            Sample  AvgRally  AvgRally+  Short%
1st 30         166      1.00       1.00    1.00
2nd 30         166      0.98       0.98    1.10
3rd 30         145      0.97       0.95    1.05
4th 30          80      0.93       0.92    1.13
5th 30          28      0.94       0.94    1.09
6th 30           8      0.87       0.81    0.95