Friday, June 17, 2011

Empirical Measure of Reliability: Part Three

The NBA Finals ended last weekend with the Dallas Mavericks beating the Miami Heat in six games. This is an outcome that a significant minority of the Twitter users predicted -- specifically, it was the second-most common prediction (out of eight logical possibilities) with 24.8% of users choosing it.

What's interesting is to see how the predictions of the crowd selectively followed the probabilities implied by the odds posted by Las Vegas sports books. In the graph (click t0 enlarge), we see the possible outcomes along the bottom, with those most favorable to Miami on the right and those most favorable to Dallas on the left. The house (red line) gave Miami a modest edge in the series, and the probabilities hint at a Gaussian with a peak centered on "Miami winning in seven games." If we ignore the "Dallas in six" position, it looks like the crowd largely went with the gambling odds, choosing a peak that was nearby (Miami in six instead of seven) and then following a course somewhere between Response Matching and a Winner Takes All preference for the favored outcome.

However, the crowd deviated from that in one big way by giving far more credence to the "Dallas in six" outcome (and slightly more to "Miami in six" and slightly less to "Miami in seven"). It is specious to read too much into this single instance, but it looks like the crowd -- a significant minority of them -- got smart in a way that Las Vegas underestimated. Do those Dallas-in-six people have some special talent, or did they just get lucky? I'll take a look next time at how the Dallas-in-six predictors differed -- or didn't -- from the other predictors. Is there a smart gene somewhere in their writing?

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