I’d like to second that. Probability is rather complicated, and it’s easy to think you’ve got it when you don’t.. The article is good without that extra bit.

]]>Assuming about 13 games a night on average have some point where one team has about a 5% chance of winning, that means that you would expect that at least one comeback will occur 50% of the time (.95^13). At least 2 comebacks will occur about 15 percent of the time. That’s about once a week. The chances mentioned above are the chances that those two particular games would feature comebacks.

But as Jack said, he wouldn’t be writing about it if it didn’t happen.

]]>Gratuitous mathery: Say there are 13 games a day that reach 97% chance of victory for one side before the end. (Games that are close late may jump straight from something below 97% to 100% — ironically, Royals-Tigers did that in the ninth inning — and teams don’t always play on the same day, so let’s use that as a guesstimate.) That gives 78 ways for exactly two of those games to involve comebacks — for each of those pairs there’s a (.03)^2 x (.97)^11 = 0.064% chance that those two games will end in a comeback and none of the other eleven will. Times 78, that’s a 5% chance that exactly two games will end in a comeback from a 3% WPA. So we should expect that to happen about eight times a season.

]]>Let’s say every game gets to the point where one team has a 97% chance of winning. It goes from 50% at the start to 100% in one teams favor at the end, so at some point it has to pass 97%, right? This is not exact, because baseball happens in discrete steps (plate appearances, outs, steals, etc.), making the changes in win probability not continuous, but perhaps it’s close enough.

There are 2,430 games in a season, so that means that 2,430 * 0.03 = 73 comebacks of the type you describe will happen on average. I can’t recall off the top of my head the next step here, but assuming these are randomly distributed, two will occur on the same night several times a season.

I know this is nit-picking, but I feel like I’ve seen several claims like this thrown in at the end of FanGraphs articles recently.

]]>