Statistical modeling of close races

Just a little bit about percentages.

There’s a big fight going on about Nate Silver and statistical modeling and such things. It’s all pretty understandable. People want to believe the best, and the nature of elections means that we don’t get any confirmed info until next Tuesday evening.

But a lot of the concerns I’ve heard are about the level of certainty in Silver’s model. It has put the percentage chance of an Obama victory in the upper 70s all week. Right now it’s sitting at 79.0%.

A couple things.

First, during the 2008 campaign I was ultimately more impressed with Sam Wang’s election model, which uses a lot fewer bells and whistles to achieve its conclusions. I find that to be a good thing. I really enjoy Silver’s detailed analysis of the many complex elements that go into election results. And his approach is fantastic for under-polled races. It’s no surprise that he rose to fame in the 08 Democratic primaries. But when there’s a wealth of polling information Wang’s approach, which makes no effort to fiddle, seems more appropriate.

Anyways, the point is that Wang put the race at well above 90%. So Silver is actually pretty conservative in his estimate. And since I’ve been telling my friends for months to prefer Wang, I don’t feel like I’m cherry-picking the result that favors my guy.

Second, I think a lot of people who are upset about the 79% certainty haven’t really thought through what 79% really means.

To use a baseball analogy, the following circumstance carries a 79% chance of victory. You’re the home team, it’s the top of the 8th, and you’re up by one run. Your opponents have one out, and runners on first and second. Now, that’s a good place to be, but it’s pretty obviously not a sure thing. Teams come back from situations like that all the time. Well, 21% of the time to be exact.

Or, how about another one. If you’re the home team and you’re up by one run going into the bottom half of the 7th, you’ve got a 79.4% chance of winning.

I don’t have the numbers, but off the top of my head I’d guess that being up by just a point with five minutes left in a football games gives you the same percentage. Being up by three with five minutes to go in basketball. Being up by one goal at halftime in a soccer game. And so on.

In a game pitting two basically even opponents, even small leads provide huge percentages. Because you’d predict that almost half the time, the leading team will pull further ahead. And since they’re fairly even, most of the rest of the results will clump around simply preserving the status quo. However, these are general truths. Obviously in any given case, a team can go on a 10-0 run. Or Raul Freaking Ibanez can hit a homerun. Or Arsenal can score four unanswered goals (argh).

In the end, we just have to wait a week and we’ll find out for real.

Edit: I see that Silver’s most recent post also uses a sports analogy.  He says 79 percent is equivalent to being down by a field goal with three minutes to go.