The More I Think About Ben Bernanke: Terry Is Smarter Than You 10/29
Back to the Bernanke/baseball article:
[Bernanke] also mentioned that the Washington Nationals, his new favorite team, had lost 13 one-run games in a row. The odds of that happening, Bernanke wrote, were roughly 8,000 to 1.
I will credit the Starbucks mint chocolate frappucino for the insight here, because as I was walking down Broadway this afternoon I realized that ain't that big a deal. Actually, it's the easiest probability problem there is.
I know what you're thinking: no, the easiest probability problem is the coin flip. Fortunately, that's exactly what we have. I first read the quote above as the Nationals having lost 13 consecutive games by one run each time, but if a streak that long and that heartbreaking had happened, I would know about it. It didn't happen. What Bernanke notes, I assume, is that in the subset of Nationals games that were decided by one run, at one point they lost 13 of them in a row. So what are the odds of that?
There are reasons for a team losing a bunch of one-run games that extend beyond mere chance - like a mediocre bullpen, or a team of rookies choking when it counts - but I figured I'd start by looking at your typical coin flip. In other words, what are the odds that a coin would turn up heads 13 times in a row? The answer is 2^13, which can be easily calculated by remembering 2^10 is 1024 (it's a kilo in computer terms, and the first two digits in the result are the same as the exponent, and ten's not a complicated number). So we continue:
2^11 = 2048
2^12 = 4096
2^13 = 8192
If you didn't spend your childhood memorizing these numbers, I can forgive you, but there's your "roughly 8000 to 1." So unfortunately Ben Bernanke's baseball probability-making is not as exciting as his proposed changes to ERA. He's right, I guess, about the chances of the Nationals losing 13 one-run games in a row, but those are the same odds of the Red Sox winning 13 games in a row, the Yankees losing 13 two-run games in a row, heads coming up 13 times in a row or a judge making the same ruling off the same precedent 13 times in a row. It's just multiplying by two a lot.
Next week: Imagine the infinite decimal 0.999999.... Is it equal to 1 or not?