I turned on the TV this weekend in the middle of the Wimbledon coverage. The second set of a match had just finished, and they were displaying a page full of statistics for the two players’ performances. I can’t remember the exact details, but the “points won” figures were something like this.
Points won on first serve: Player A, 75%; Player B, 70%.
Points won on second serve: Player A, 50%; Player B, 40%.
So Player A was clearly better than Player B at winning points both on his own first serve and on his own second serve; we can also deduce that Player A was better than Player B at winning points on his opponent’s first and second serves. Yet at that point in the match, Player B was winning by two sets to none and had won significantly more points than Player A… surely something was wrong here!
It took me a moment to work out what was going on — which was a moment longer than it should, because this is an example of a very well-known “paradox”. Solutions in the comments thread, please!