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From time to time we have these discussions about whose serve is better. So I pulled the following stats on hard courts over the last 5 years for the following players (comparing overall stats is unfair because, let's say Soderling played more matches on clay than Tsonga; also hard courts are playing more even from year to year than natural surfaces and there are more matches on them allowing for a lot of observations).

1srv effect = 1srv won * 1srv perc

Name__________________1srv won___1srv perc___1srv effect___srv games won

Andy Roddick__________78.8%______67.0%_______52.8%________89.6%

Roger Federer_________78.4%______62.8%_______49.2%________89.8%

Jo-Wilfried Tsonga____77.4%______62.8%_______48.6%_________86.2%

Robin Soderling_______77.6%______62.0%_______48.1%________86.6%

Juan Martin Del Potro_73.3%______61.8%_______45.2%_________83.0%

Tomas Berdych_________77.4%______57.4%_______44.4%________84.4%

Mardy Fish____________78.0%______54.0%_______42.1%________83.6%

These statistics are not very informative about the effectiveness of the serve per se but about the effectiveness of the serve + ground game. For example, Federer is good on these stats because he backs up his serve so well.

To evaluate the effect of the serve alone, I net out the percentage of points won in rallies. ATP doesnt publish this one explicitly, so I estimate it as (perc of points won on 2nd serve + perc of points won returning 2nd serve) / 2. This is reasonable since 2nd serves are mostly rally-starters. From here I calculate the percentage of unreturned first serves.

*Here is the example that shows how it is estimated: let’s assume Karlovic has x% of his first serves unreturned and (1-x%) goes to the rally. Of these rallies, Karlovic wins 46.8%. So on the whole, he wins x% + 0.468(1-x%) of his first serves. This must be equal to 82.8% (first column), so x = (0.828-0.468)/(1-0.468) = 67.7%. I thank*

**romismak**for making me think about the right method to correctly estimate unreturnablesColumn "service winner probability" is the product of "1st serve unreturned" and "1st serve percentage". This is the key column because it shows the probability of winning the point directly off the serve. So, basically once the player steps up to serve, this is the chance that the serve will win the point immediately.

Name__________________rallies won___1srv unret_____service winner probability

Andy Roddick__________52.8%_________55.1%__________36.9%

Jo-Wilfried Tsonga____49.8%_________55.0%__________34.5%

Robin Soderling_______52.2%_________53.2%__________32.9%

Roger Federer_________54.7%_________52.2%__________32.8%

Tomas Berdych_________52.4%_________52.5%__________30.1%

Mardy Fish____________51.3%_________54.8%__________29.5%

Juan Martin Del Potro_52.6%_________43.6%__________26.9%

Conclusions:

1) Andy Roddick, as expected, is by far the best server of the pack. His official stats are great but his rally-adjusted stats are also good. His dominance comes largely from high first-serve percentage.

2) Federer is better than anybody else but Roddick on official stats. But much of it comes from his ground game. Once you adjust for that, he falls behind Tsonga and Soderling but is still ahead of Fish and Berdych.

3) JMDP's serve is really not that great. He is a steady rallier but his serve by itself is subpar relative to the oter guys. I though he would rank better, that's why I included him in the mix.

4) Berdych's serve also ranked lower than I expected. Possibly, too predictable for returners.

5) Tsonga's serve by itself is excellent and is close to Roddick's by its adjusted effectivenss. However, he is the weakest rallier of the group. So he loses to Soderling when it comes to holding.