Last week, I wrote an article for the Wall Street Journal noting the relatively slow speed of this year’s U.S. Open. It’s not clear whether the surface itself is the cause, or whether the main factor is the humidity from Hurricane Irene and Tropical Storm Lee. For whatever reason, aces were lower than usual, creating an environment more favorable to, say, Novak Djokovic than someone like Andy Roddick.

The limited space in the Journal prevented me from going into much detail about the methodology or showing results from tournaments other than the slams. There’s no word limit here at Heavy Topspin, so here goes…

**Aces and Server’s Winning Percentage**

Surface speed is tricky to measure–as I’ve already mentioned, “surface speed” is really a jumble of many factors, including the court surface, but also heavily influenced by the atmosphere and altitude. (And, possibly, different types of balls.) If you were able to physically move the clay courts in Madrid to the venue of the Rome Masters, you would get different results. But teasing out the different environmental influences is little more than semantics–we’re interested in how the ball bounces off the court, and how that affects the style of play.

So then, what stats best reflect surface speed? Rally length would be useful, as would winner counts–shorter rallies and more winners would imply a faster court. But we don’t have those for more than a few tournaments. Instead, I stuck with the basics: aces, and the percentage of points won by the server.

Important in any analysis of this sort is to control for the players at each tournament. The players who show up for a lower-rung clay tournament are more likely to be clay specialists, and the men who get through qualifying are more likely to be comfortable on clay. Also, the players who reach the later rounds are more likely to be better on the tournament’s surface. Thus, the number of aces at, say, the French Open is partially influenced by surface, and partially influenced by who plays, and how much each player plays.

Thus, instead of looking at raw numbers (e.g. 5% of points at Monte Carlo were aces), I took each server in each match, and compared his ace rate to his season-long ace rate. Then I aggregated those comparisons for all matches in the tournament. This allows us to measure each tournament’s ace rate against a neutral, average-speed surface.

**The Path to Blandness**

The ace rate numbers varied widely. While the Australian Open and this year’s US Open were close to a hypothetical neutral surface speed, other tourneys feature barely half the average number of aces, and still others have nearly half-again the number of aces of a neutral surface. I’ve included a long list of tournaments and their ace rates below; you won’t be surprised to see the indoor and grass tournaments on the high end and clay events at the other extreme.

But there’s a surprise waiting. I also calculated the percentage of points won by the server, and like ace rate, I controlled for the mix of players in every event. While ace rate varies from 53% of average to 145% of average, the percentage of points won by the server never falls below 90% of average, rarely drops below 95%, and never exceeds 105%. 53 of the 67 tournaments listed below fall between 97% and 103%–suggesting that *surface influences the outcome of only handful of points per match*.

That may defy intuition, but think back to the mix of players at each tournament. Big-serving Americans don’t show up at Monte Carlo, while South Americans generally skip every non-mandatory event in North America. The nominal rate at which servers win points varies quite a bit, but that’s because of the players in the mix.

Also, this finding suggests that, as a stat, aces are overrated. They may be a useful proxy for server dominance–if a players hits 15 aces in a match, he’s probably a pretty good server–but they come nowhere near telling the whole story. Aces on grass turn into service winners on hard courts, and then become weak returns and third-shot winners on clay. The end result is usually the same, but Milos Raonic is a lot scarier when the serves bounce over your head.

Finally, it would be a mistake to say that a variance of 3-5% in serve points won is meaningless. It may be less than expected, but especially between good servers, 3-5% can be the difference. Move Saturday’s Federer/Djokovic semifinal to a surface like Wimbledon’s, and we’d be looking at a different champion.

**All the Numbers**

Here is the breakdown of ace rate and serve points won, compared to season average, for nearly every current ATP event.

Since I am using each season’s average, you may wonder whether the averages themselves have changed from year to year. I’ve read that courts are getting slower, but in the five-year span I’ve studied here, the ace rate has actually crept up a tiny bit. Each tournament varies quite a bit–probably due to weather–but generally ends up at the same numbers.

Below, find the 2011 ace rate and percentage of serve points won, as well as the average back to 2007. Again, these are controlled for the mix of players (including how much each guy played), and the numbers are all relative to season average.

The little letter next to the tournament name is surface: c = clay, h = hard, g = grass, and i = indoor.

Tournament 2011Ace 2011Sv% AvgAce AvgSv% Estoril c 57.5% 96.6% 53.3% 94.3% Monte Carlo c 52.0% 92.1% 53.9% 91.2% Umag c 58.6% 95.2% 58.7% 94.3% Serbia c 54.2% 93.5% 61.0% 94.8% Rome c 62.5% 95.9% 62.9% 94.4% Buenos Aires c 61.9% 99.0% 62.9% 98.6% Houston c 64.9% 97.2% 66.6% 96.8% Valencia i 68.0% 96.4% Barcelona c 55.7% 94.3% 68.0% 96.2% Dusseldorf c 45.7% 96.5% 72.8% 97.2% Hamburg c 78.0% 96.6% 74.3% 96.4% Bastad c 63.8% 94.5% 76.8% 97.7% Roland Garros c 78.0% 98.4% 77.1% 97.5% Santiago c 84.5% 98.5% 81.5% 99.4% Costa do Sauipe c 83.4% 101.7% 84.2% 98.9% Nice c 88.5% 97.4% 84.3% 98.1% Casablanca c 79.1% 99.0% 84.9% 98.2% Acupulco c 70.9% 95.6% 86.0% 98.7% Madrid c 77.0% 98.5% 86.1% 98.0% Munich c 87.9% 100.1% 86.5% 100.0% Beijing h 86.7% 97.3% Los Angeles h 84.7% 97.2% 87.7% 97.3% Kitzbuhel c 95.8% 97.9% 89.0% 98.6% Toronto h 89.6% 98.3% Chennai h 82.3% 98.0% 89.6% 98.7% Stuttgart c 77.0% 95.8% 89.7% 98.1% Indian Wells h 88.9% 99.0% 90.9% 98.0% Doha h 125.5% 101.9% 91.2% 97.6% Auckland h 103.1% 102.0% 93.9% 98.7% Miami h 94.5% 97.9% 94.4% 98.0% Shanghai h 94.6% 98.1% Australian Open h 97.6% 97.3% 96.5% 96.9% Kuala Lumpur h 97.1% 97.3% Sydney h 105.8% 100.0% 97.4% 99.1% St. Petersburg i 97.8% 101.7% Montreal h 91.3% 98.4% 98.1% 98.2% Delray Beach h 106.2% 99.9% 99.1% 98.6% Gstaad c 104.5% 100.1% 101.2% 101.4% Dubai h 102.7% 96.5% 103.2% 98.2% US Open h 101.3% 97.4% 104.0% 98.7% Vienna i 105.8% 101.4% Johannesburg h 110.0% 102.7% 106.0% 101.0% Washington DC h 97.5% 100.1% 106.8% 99.8% Newport g 93.3% 99.0% 107.5% 101.7% Winston-Salem h 108.1% 99.6% 108.1% 99.6% Atlanta h 110.0% 100.9% 108.4% 99.0% Bangkok h 110.5% 101.6% Cincinnati h 96.2% 98.9% 111.7% 100.5% Zagreb i 107.0% 99.2% 112.3% 102.3% Moscow i 113.0% 101.3% Brisbane h 130.6% 100.3% 113.4% 100.0% Eastbourne g 111.2% 101.8% 114.1% 102.9% Paris Indoors i 115.4% 99.6% Rotterdam i 123.8% 103.7% 115.9% 101.0% Basel i 117.7% 101.3% San Jose i 108.6% 103.0% 120.0% 102.7% Wimbledon g 119.4% 102.8% 120.7% 103.0% Queen's Club g 113.3% 101.8% 121.5% 103.2% Halle g 122.9% 104.7% 123.2% 102.5% Marseille i 127.4% 102.8% 124.2% 102.2% Stockholm i 124.4% 99.8% Metz i 124.6% 101.7% Tokyo h 124.7% 100.5% s-Hertogenbosch g 110.9% 102.1% 126.3% 104.0% Memphis i 117.1% 101.2% 129.1% 102.0% Montpellier i 145.4% 104.5%

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Just quick question. You make a lot of references to the “average” ace rate or percent service points won.

What actually is the average/are the averages?

Right around 63.2%. It’s been very consistent over the last few years.

Great, thanks for that.

sorry, a bit bleary when I posted that — 63.2% is percentage of service points won; ace rate has been between 7.6 and 7.8% for the last few years.

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Hi Jeff,

can you help me to explain, how did you got the numbers

2011Ace% and 2011Sv%?

I tried to find a way, but no chance.

Thank you very much

Peter

The individual numbers for each match are on the ATP website; I tallied those up for each tournament.