The Gambler’s Fallacy

The gambler’s fallacy is one of the more well-known fallacies, but people still fall victim to it in everyday analysis.  This is not to be confused with the gambler’s phallus, which, unfortunately, people still fall prey to as well.  In some sort of shell most appropriate for a nut, the gambler’s fallacy is assuming that past events influence statistically independent future events.  So, if your friend beats you five times in a row at war, you might incorrectly assume that you are more likely to win next time since winning six times in a row is very unlikely.

Ok, so what does this have to do with, y’know, interesting things?  Well, today the Pittsburgh Steelers play the Baltimore Ravens.  In the regular season, the Steelers beat the Ravens in both of their encounters.  I’ve heard many analysts use the old standby of pointing out how difficult it is to beat an NFL team three times in a single season.  By using the gambler’s fallacy, they surmise that beating a team a third time is somehow more difficult than beating a team a first or a second.  That’s like flipping a coin and saying that it’s more likely that you’ll get heads the first time than the third time.  Actually, it’s even dumber, since football games are more predictable than coin tosses.  If a team beats another team twice, wouldn’t that signal to you that one team is better than the other and would thus be more likely to win a third time?

The numbers support this, albeit in a limited sample size, with the two-game-winning team possessing a record of 11-7 since the AFL-NFL merger in 1970.  I’m not saying the Steelers will win, especially since the two regular season games were very close.  I’m just saying that I’d rather be the 2-0 team than the 0-2 team.

For some bonus statistics enjoyment, check out Jeff Atwood’s write-up of the Boy or Girl problem.  While his phrasing of the question may not be perfect, his explanation is thorough.  Check it out if you enjoy things like the Monty Hall problem.

Arbitrary song of the day: Klaxons – Atlantis to Interzone

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