Throughout the 2007 US Open, Andy Roddick's first serve percentage was 71%. When he got the first serve in, he won 82% of the points. He won 52% of his second serve points. He rarely double-faulted. I couldn't find his double fault numbers, but I'm guessing his 2nd serve percentage was around 99%.
Though these numbers are typical of Roddick, and similar for other players with big serves, they are totally bizarre. When he steps up to the line for a 1st serve, he wins the point 58.2% (71%*82%) of the time. If he misses his first serve, why would he bother hitting a conservative second serve if he has less than a 52% chance of winning the point with it? If he's trying to win points, he should just be hitting bombs for both his first and second serves. Sure, he will double fault a lot, but it's still his best chance of winning the point. If he had hit nothing but bombs when he played Federer at the US Open last year, the numbers suggest he would have won the match.
If he is trying to win points, Roddick, like many other players, is not serving rationally. It really is strange that players would continue to spin in their second serve when the numbers show this plainly that it is a bad idea. You would think that coaches would look at stats to see if there are any obvious areas of improvement like this. Sampras even demonstrated that you can have great success hitting huge 2nd serves, even with a healthy amount of double faults.
I'm sort of at a loss to explain this anomaly. Either Roddick is irrational, or he is maximizing something other than his probability of winning points. That's not to say that I don't empathize with Roddick; I too have an excessive fear of double-faulting. Nothing is more infuriating in tennis. Your opponent is just standing there waiting for you, and you lose the point before it starts because you can't even get it in the box. For some reason, it feels much worse to lose a point this way than after a nice rally.
Maybe winning isn't all Roddick cares about, and how he wins or loses is important to him. If hates double faulting a lot, he might be willing to lose some matches to avoid too many double faults. If he were consciously making that choice, it seems like unusual behavior for a professional athlete.
Maybe Roddick and I are overconfident in our groundstrokes and we think, "if I can just get the serve in, I will probably win the point anyway." Other than that, I don't really have any other idea of how to explain this. It's just so strange.
Whatever the reason for this apparent irrationality, I think it can be overcome. All Roddick needs to do to win another grand slam is serve rationally.