Some thoughts on the Rockies' streak

Are the Rockies Really That Good, or Just Lucky?, from The Numbers Guy at the Wall Street Journal.

There's no real conclusion, though. The Rockies probably think it's because they're good. But if you wait long enough, this sort of streak will happen to somebody. What one really wants to know is the number of such streaks that should have happened, historically; this should then be compared to the number of such streaks that actually did happen.

The problem with this is that all the quick and dirty analyses will assume that all teams win exactly half their games, so the probability of winning at least 21 out of 22 games is (22+1)/2²², or about five in a million. But this isn't true. I suspect that the actual distribution of how good teams are is roughly symmetrical around .500, perhaps skewed a little bit to the left (there are more ways to be a bad team than to be a good team), so for every .300 team there should be a .700 team. The .300 team has probability (.3)²¹ (22(.7) + .3), or about one in six billion, of winning 21 out of 22; the .700 team has probability (.7)²¹ (22(.3) + .7), or about four in a thousand. (This is the figure the WSJ reports as "1 in 245".) So to really know how many long streaks are expected, we need to know the historic distribution of team abilities. If there are teams that are "really" .700 teams fairly often, we should expect that these streaks happen fairly regularly; if the best teams are usually only around, say, .600, probably not. And to know how likely the Rockies were to have this streak, we have to know how good they "really" are; are they the 76-72 team they were before the streak started, the 21-1 team they've been since, or somewhere in between? And would anybody have noticed if they had won 21 out of 22, say, starting in the middle of June?

And let's not even go into the fact that games aren't really independent; even if one doesn't believe that teams "get hot", they play in different parks, with different starting pitchers each day, and so on. As at least one commenter at the WSJ pointed out, streaks like this are more likely to happen in September than any other time, because in September you have teams (like the Rockies) that need to win games and teams that have just given up. The Rockies needed to win 14 out of 15 to end the regular season. (There was a point in late September when I thought I had the National League playoff situation all figured out... then I looked at the standings and thought "when the ^)%$!*)#$)^ did Colorado win ten in a row?")

My point is that I don't know the answer, either. I just am not happy that their streak happened to knock the Phillies out of the playoffs for the first time in fourteen years, and I hope that the Red Sox (who I started following in college) don't also become victims of it.

(By the way, my argument for not having more interleague play than there is is that right now, it's possible to be a fan of one National League team and one American League team and not have too many conflicts of interest. With more interleague play that would become less likely. Also, since I like the Phillies and the Red Sox, I essentially automatically dislike the Mets and the Yankees, which means I can never move to New York.)