A bit surprising but not a paradox

Miscellaneous and Personal Stuff I Must Share
1

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.

2

One of the easiest ways to lie to someone with statistics.

3

It is surprising that anyone would watch a curling match. But no, not a paradox.

4

This sort of thing is very common with financial reporting. Every single thing we sell has had gross profit go up, that’s awesome. Overall gross profit went down, that sucks.

It’s all because of mix, we lost volume on our most profitable items, and gained volume on our least profitable. Or the other way around.

5

The textbook example of Simpson’s Paradox was a company that was sued for paying women less than men, even though the average woman at the company was paid more than the average man. The reason was that the company had both blue-collar and white-collar jobs, and the women at the company were mostly white-collar, but white-collar women were paid less than white-collar men, and blue-collar women were also paid less than blue-collar men.