I was watching a curling match night before last. At some point they put up a graphic showing that team A was ahead of team B on both draws and hits but they were tied on overall percentage. This seemed paradoxical at first, but it actually makes prefect sense.
Now for some explanations. Shots are either to land in a particular place or to hit a particular stone, usually but not always, the opponent’s. The former is called a draw, the latter a hit. Informally, someone gives each shot a rating of from 0 to 4 points. It is not part of the scoring, just a rating system. So if you throw 128 stones in a game, your max score would be 512 of these rating points. Your actual score divided by 512 would be your percentage. So the graphic went up on the screen that team A had a draw percentage of 88% to team B’s 87% and a hit percentage of 80% to 77%, but both teams had an overall average of 83%. So although team A beat B in both draws and hits then were the same overall. That didn’t seem possible, but I quickly realized it was if a majority of A’s shots were hits, while a majority of B’s were draws. In fact, if we supposed that those percentages were exact (of course, in practice they are rounded) we could prove that for A, 3/8 if their shots were draws, while for B,it was 3/5. Even worse, had 1/4 of A’s shots were draws while 7/10 of B’s were draws, then the overall percentages for A and B would be 82 and 84, even more striking.