# The playoffs, The Gambler’s fallacy, and The 50-50-90 rule

October 22, 2007 2 Comments

One of the basic rules of statistics applied to last night’s Game 7 of the ALCS last night: The 50-50-90 Rule. If there’s something that’s a 50/50 shot for the team for which you are cheering, your team will lose 90% of the time. That is, unless you’re a Red Sox fan. But I grew up in Cleveland and my first coherent memories are of watching the Cleveland Indians. (True story.) This is an iron-clad rule of statistics. You can look it up.

I work in a hospital, and in the emergency room, they have a measure called “Subjective Units of Discomfort” (SUDs), to measure people’s level of pain when they come in. It goes from 1 to 10. Being a practicing Sabermetrician and a psychologist, I felt the best way to cope with this turn of events would be to make a new statistic that would adequately capture the magnitude of what happened. I thought about calling it Pizza Cutter Depression Probability Added (this was a particularly high leverage game for that particular stat). Finally, I settled on Subjective Units for Cleveland Knockouts (I’ll let you do the acronym). The formula is Opponent wins x 2.5. The scale goes from 0 to 10.

But then again, I should have known it was coming. My wife, who’s never wrong (and the sentence should end right there, just ask her… although she did wonder out loud why Travis Hafner wasn’t trying to steal third), said this morning that she had a feeling the Indians would win. She’s had a hot hand on picking these 50/50 shots, but this morning, we found out that one of her picks for the sex of one of the 457234 babies that are being born to people we know within the next few months was wrong. (She called boy. They’re having a girl. She also picked a Cubs-Angels World Series) Looks like her hand has gone cold.

With that said, I would warn fans of the Red Sox and Rockies to watch out for a (real) property of statistics: The Gambler’s Fallacy. Consider the simplest of all games of chance: the flip of a coin. Suppose that you flip a coin ten times, and ten times in a row it comes up heads. What are the chances that the next flip will be tails? Did you say something other than “Fifty percent?” Did you mumble something about the “Law of Averages?” Sound like a baseball team about which Dane Cook has been yelling all week?

Red Sox fans will probably be saying to themselves that they are sure to win the World Series because the Rockies are “due to lose.” Rockies fans will probably be saying to themselves that they are “on a roll” and will win the World Series because of momentum. Of course, one of them will be proven “right” in the next week and a half. In fact, neither one is right. The Red Sox had a better regular season record and a better Pythagorean record, plus they have four games at home to the Rockies’ three. So, the Red Sox are the favorites. But each game starts at 0-0, so the probabilities of either team winning reset themselves after each game.

Now, the other thing that will be bandied about is that “In a short series, anything can happen.” This is a nice way of saying that a seven-game series is an inadequate sample size from which to determine the relative quality of the two teams. Which is true. If I were to submit something to a scientific journal with an N = 7, I would have the paper sent back to me with a laugh. In baseball, you get a trophy for your efforts. Still, there’s a part of me that wishes that the Indians were part of that inadequate sample size of independent events.

After the game, my wife, in an attempt to console me, said that she didn’t think of it so much as losing a series, but re-gaining a husband.

Some odds on the World Series.

Baseball Prospectus is giving the Rockies a 56.3% chance of winning the World Series. Most of this is based on the Red Sox trouble against LHP starters and the Rockies skill of beating up RHP starters.

Vegas odds gives the Red Sox a 64.91% chance of winning the World Series.

For Game #1 of the World Series.

Vegas gives the Red Sox a 66.1% chance of winning.

Log5 gives the Red Sox a 64.91% chance of winning. Based on the Red Sox home win% vs the Rockies road win pct.

The baseball simulator which plays 2500 simulated games, gives the Red Sox only a 52.1% chance of winning game #1.

vr, Xei

Nice column, albeit a late read on my part. As an Indians fan myself, I always point people to Murphy’s Law, which states as a postulate that Cleveland fans should not cheer until all replays are finished/umpires have cleared the field/no flags are seen on the field/the next day has started/there’s been a recount…and it goes on. Look it up. I don’t make these things up.