Friday, April 27, 2012

World Series Upset Odds

Just for fun I decided to make some rough calculations about the odds of each team's winning the World Series based on assumptions about how likely they are to win each game. To simplify matters I'm ignoring the whole "clinching" thing, and just treating the Series as a seven-game series, 4 games to win. So seven-game shutouts are a possibility in my calculations. I imagine that this doesn't actually affect the odds; the entire premise of clinching is that it shouldn't. The first thing I tried was a 3-1 ratio, i.e. one team having a 75% chance of winning each game. This struck me as a decent approximation for the odds if you pitted the best team against the worst team from a given year of Major League Baseball, though it's obviously just a wild guess. The better team has a 93% chance of winning at least four of seven games. An 80% favorite game-by-game is a 96.7% favorite overall. 70%-30% gives you an 87.4% chance of a non-upset; 2-1 odds in each game give roughly 5-1 odds for the series as a whole. 60%-40% favorites have 71% chances of winning; 55%-45% gives 61%; 51%-49% gives 52%. Overall there's a genuine tendency to exaggerate the tendencies of a single game, as well there should be for a larger sample size, but for modest advantages game-by-game that effect is quite modest as well. A 19-game season series magnifies just a 51%-49% advantage in each game to a roughly 5-3 advantage overall, at 62.5%. You only need a 62% chance of winning each game of that season series to have a 90% chance of winning the series itself. Seven games really isn't enough to get away from the small-sample-size effects. Or, in other words, every World Series is pretty much a toss-up, assuming both teams were above-average MLB teams from that year.

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