Originally Posted by Bursztyn
I agree. One may say that the smaller sample should not be really small. If it is not very small then we may calculate percentages (success).
I have another match with a really small sample like you're talking about. I'm pretty sure Borg had only 8 second serves in the '79 RG final (d. Pecci). I know that he lost only one of those points, which means that he must have won 69 of 99 points on first serve (you can see his full service numbers here: http://tt.tennis-warehouse.com/showthread.php?t=187098
That's a success rate of 69.7% on first serve, and 87.5% on second serve.
So what does that mean? If you read the articles of the time, they say it was a smart strategy for Borg to spin his first serve in and deny Pecci the chance to attack second serves. But you look at the success numbers and it almost suggests the opposite: that Borg would have been no worse off, and might even have done better, if he'd missed his first serve frequently.
But that doesn't make sense. Even spinning in those first serves, they were stronger and deeper than the second balls; occasionally he went for the big one on the first serve, too, with success.
I think in a case like this something odd may be going on with the second serve points. I don't know for sure what it might be but here's a suggestion.
If a player like Pecci wants to attack second serves, he might do that with some regular success if he gets a look at second serves with some regularity. Then he can put his plan of attack, whatever that might be, into motion. He can figure out how to do it, and get into some kind of groove.
But if he sees a second serve only once or twice a set, and it comes as a complete surprise each time, he's not suddenly going to be able to switch into the attack mode that he had drawn up on paper. He's been busy playing points on first serves and doing whatever he does to win those points. He can't just switch from that and suddenly do something different. And if he tries he may find himself unsuccessful.
I'm not saying for sure that's what happened in this particular match, but in general it could explain why the returner might win so few points on second serve when you expect him to be able to take advantage of second balls.