I wrote about mathematics and tennis at this time of year four years ago: specifically on the decisions about reviews and about the curious fact that, against a stronger opponent, you are more likely to break serve from 30-15 down than from love all. I had completely forgotten about that post, but was stimulated to return to the topic by a comment on the BBC web coverage of yesterday's semifinal between Raonic and Federer. Raonic was 40-love up on his service, and according to the report, rather than follow the standard tactic of playing a safe second service that is almost certain to avoid a double fault, Raonic chose to attempt to serve aces on first and second serves, backing himself to be successful in one of his six opportunities.
So is this a good strategy when you are 40-love up on your service? How much better than your second serve does your first serve have to be to make this tactic optimal?