Friday, November 2, 2012

On Probabilities, College Basketball, and Elections

As Mr. Gillette alludes to in his programming note, Nate Silver—the author of the fivethirtyeight blog—has become quite famous for his election prognostications. He's also become quite controversial.

The controversy stems from his model's assessment that Barack Obama has about an 80% chance of being reelected next Tuesday. Many pundits, particularly Republican ones, think this is crazy (or worse). They point to the fact that national polls have been tied or given Mitt Romney a narrow lead for weeks and say the race is as best a tossup.

Silver's defenders—and Silver himself—respond with some variation of, "the math is the math." They point to the state level polls, which Silver's model relies heavily on, and which currently show Obama with a small but clear and sustained lead in enough swing states to take the Electoral College with relative ease.

In a way, both sides of this argument are right. I think Silver's model's estimate of an 80% probability of Obama winning is highly plausible. But I also think it's fair to label that a "tossup."

To understand why, you need to understand that Silver comes from the world of sports. In particular, he's among the line of people applying "advanced stats" to baseball and other sports to yield stunning new insights: Bill James; sabermetrics; "Moneyball";; etc.

Let's talk about Ken Pomeroy. His superb website ( has for many years been applying advanced, tempo-free statistics to college basketball. His model allows him to create a "win probability" for every game of every season. This win probability largely tracks the Vegas betting odds. It's pretty amazing.

But here's the thing—it turns out that teams with an 80% win probability lose all the time. Not every time, of course, or even most of the time. But they lose with almost clockwork regularity. In fact, they lose about two out of every ten games.

Here's a painful example from last season. Wisconsin versus Marquette, at the Kohl Center, on December 3rd. Wisconsin came into the game 6-1, having utterly destroyed some inferior competition (e.g., an 85-31 victory over Kennesaw State) and having just lost, on the road, by 3 points to preseason #1 North Carolina. Marquette was undefeated but untested. There was cause for worry, as they had just narrowly scraped out a 59-57 win over lowly Norfolk State.

Considering their relative performances and Wisconsin's significant home court advantage, Pomeroy's computer gave Wisconsin an 83.2% chance of winning. Yet Marquette led almost the entire game, opened up a double-digit lead at half-time, and won going away, 61-54. In other words, the 83.2% favorite got whipped.

(I would link to the Pomeroy data, but it's behind a paywall. I encourage you to pay the $20 to get access to it.)

This is important because Nate Silver's model is fundamentally similar to Ken Pomeroy's model. Neither is predicting what is actually going to happen. Rather, both use historical data to spit out a probability that something will happen in the future. And if you follow Ken Pomeroy's model closely, you will know that an 80% favorite is not really a very "big" favorite. Because you will have experienced your favorite team losing as an 80% favorite many times. Indeed, last year Wisconsin lost twice to Iowa, games in which Pomeroy's computer said it had a 98.3 and 81.9 percent chance of winning. Given those percentages, Wisconsin had a 99.7% chance of winning at least one of those games. (This is hard to swallow, given that Wisconsin would have won a share of the Big Ten title if had managed to win just one of those games.)

There is a psychological difficulty in taking this concept of win probabilities and transferring it to elections. In sports, there are often dozens of games going on every single day—particularly in college basketball. So the "probability" aspect of Pomeroy's model makes some intuitive sense because you can watch it play out in front of your eyes over the dozens of results. But there is only one presidential election at a time. So it is not very intuitive to think of the result probabilistically. You have to start thinking about multiple universes, or something.

Anyhow, here's my conclusion based on my experience as a college basketball fan: Obama is the favorite, but he's a precarious and narrow one. His team better show up on game day.

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