## Obama 5, Romney 3 in the 7th

Lots of people are following Nate Silver’s election tracking over at 538, especially his top-line estimate of the probability that Barack Obama will be re-elected in November.  Silver has that number at 79.7% today.  Sounds like good news for Obama.  But it’s hard to get a gut feeling for what that number means.  Yeah, it means Obama has a 4 in 5 chance of winning — but since the election isn’t going to happen 5 times, that proportion doesn’t quite engage the intuition.

Here’s one trick I thought of, which ought to work for baseball fans.  The Win Probability Inquirer over at Hardball Times will estimate the probability of a baseball team winning a game under any specified set of conditions.  Visiting team down by 4 in the 2nd, but has runners on 2nd and 3rd with nobody out?  They’ve got a 26% chance of winning.  Next batter strikes out?  Their chances go down to 22%.

So when do you have a 79.7% of winning?  If we consider the Obama-Romney race to have started in April or May, when Romney wrapped up the nomination, we’re about 2/3 of the way through — so let’s the 7th inning.  If the visiting team is ahead by 2 runs going into the 7th, they’ve got an 82% chance of winning.  That’s pretty close.  If you feel the need to tweak the knobs, say the first two batters of the inning fail to reach; with two outs in the top of the 7th, bases empty and a 2-run lead, the visitors win 79.26% of the time, just a half-percent off from Silver’s estimate.

So:  Obama 5, Romney 3, top of the 7th.  How certain do you feel that Obama wins?

Update:  (request from the comments)  Silver currently has Obama with an 85.% chance of winning.  That’s like:  home team up 5-3, visitors batting in the top of the 8th, runner on first with one out.

## The total variation of win probability, or: THE MAGNIFICENT TWINS-TIGERS GAME

Fangraphs has a neat feature:  they’ll make a chart showing how the probability of a home team win varies over the course of a game.  In a “normal” game this probability starts at .5 and slowly makes its way towards 0 or 1 as one team takes a lead and then holds on.

Today’s Twins-Tigers playoff is not a normal game.

The total variation in win probability over the course of a game is a good way of quantifying how much back-and-forth there’s been between the two teams.  You might take it as a loose measure of “excitingness.”

In this game, the Twins have gone from an 80% chance of winning to 20% to 73% to 20%, again up to 83% and then back down to 50%.  That’s a total variation of at least 2.62, all since the 6th inning!

I wonder what the all-time record for total variation in a single game is?  It would have to be a game with multiple extra innings in which runs scored, I’d think.

And we go to the bottom of the 11th, still tied 5-5.  Minnesota with a 64% win probability per FanGraphs.  Joe Mauer coming up third this inning.  Now that my own team is done playing for the year, I am allowed to say:  go Twins.

Update:  In the comments, Michael Lugo proves by science that the Tigers-Twins playoff (total variation:  7.69) was more exciting than game 7 of the 1991 World Series, but less exciting than this.

Update 2: A similar computation carried out in 2005 by Dennis Boznango at The Hardball Times. An even more similar discussion at FanGraphs.