The data on first vs. second serve win frequency cannot be taken at face value because of selection problems that bias against second serves.  The general idea is that first serves always happen but second serves happen only when first serves miss.  The fact that the first serve missed is information that at this moment serving is harder than usual.  In practice this can be true for a number of reasons:  windy conditions, it is late in the match, or the server is just having a bad streak.  In light of this, we can’t conclude from the raw data that professional tennis players are using sub-optimal strategy on second serves.

To get a better comparison we need an identification strategy:  some random condition that determines whether the next serve will be a first or second serve.  We would restrict our data set to those random selections.  Sounds hopeless?

When a first serve hits the net and goes in it is a “let” and the next serve is again a first serve.  But if it goes out then it is a fault.  The impact with the net introduces the desired randomness, especially when the ball hits the tape and bounces up.  Conditional on hitting the tape, whether it lands in or out can be considered statistically independent of the server’s current mental state, the wind conditions, and the stage of the game.  These are the ingredients for a “natural experiment.”