This might be a dumb question, but has anyone ever done the math on whether or not a tennis player would be better off hitting nothing but first serves, rather than hitting a lesser second serve?
Just as an example, let's take a player who hits 68% of his first serves in and wins 85% of those points. (My guess is that this is somewhere near the average.) Let's also (charitably) suppose that he hits 100% of his second serves in, winning 50% of those points. Over the course of 100 points, that player will win 73.8 of the 100 points on his serve.
If he hits nothing but first serves, sure, he'll have a lot of double faults (10.24 of them), but he'll wind up winning 76.3 points, giving him a 2.5 point advantage.
Has some Bill James of tennis already gamed this all out?
48 minutes ago