For those of you who’ve not worked it out, here’s the explanation of that apparent paradox in the tennis match statistics. Although Player A won a higher percentage of points on both his first serve and his second serve than Player B did, what made the difference was that Player B had a much more accurate serve — far more of his first serves went in than did Player A’s, and this was more than enough to give Player B a decisive advantage.
This is an example of Simpson’s Paradox, a phenomenon that’s most commonly associated with clinical trials of medicines. Medicine A may be more effective than Medicine B both for men and for women, but if both medicines are significantly more effective for one gender than the other and there is a significant difference in which medicine is prescribed for patients of which gender, then it is possible that when the results for men and for women are combined then Medicine B may appear more effective. (See here for a lengthier discussion of the paradox and its implications.)
I suspect that, with an unusually sport-crammed summer coming up, there will be plenty of opportunities to spot other oddities — not to mention downright abuses of statistics — among the numbers that the commentators give us when they can’t think of anything sensible to say. Let us know of any especially ripe specimens you come across!