FanPost

The Math Behind Home-Field Advantage

Yesterday Jesse cited TwinsGeek on the importance of home-field advantage in a playoff series. Both agreed that it wasn't all that important, and they were both right.

TwinsGeek said that it might give the Twins an extra 10-15% chance of winning a single game, which is true, but this doesn't directly tell us how important home field advantage is over an entire series. Jesse said it was really more about games one and two at home, which is also true, but again, doesn't give us any numbers to work with.

So how important is home-field advantage really? Well, it probably adds only about 3-6% to a team's chance of winning a series, depending on the length of the series and how important you estimate home field advantage to be for a single game. Click through the jump to see where this number comes from.

I originally became interested in this problem because I was wondering how important a certain game in a playoff series is given the series standing at the start of the game. I wanted to be able to define how the result of each game adds or subtracts from a team's chance of winning a playoff series, analogous to how the WPA stat defines how each play in a game impacts a team's chance of winning that game. This would give us a way of comparing the importance of, say, Kirby's game 6 walk-off in 1991 versus Kirk Gibson's epic 2-out, come-from-behind shot in Game 1 of the '88 series*. In order to figure all of this out, I first needed to calculate the probability that a team will win a series given the series standing and whether or not they had home field advantage.

So to begin, we first need an empirical measure of how important home field advantage is for a single game. I looked at all the playoff games played since 1903, and found, like TwinsGeek did, that the home team wins about 55% of the time (actually just slightly less than this). This would give the average team a 10% home advantage, or we could use his 15% mark for the Twins this year.

Next we need to look at all of the different outcomes for a series, and find the probability for each one. So, for example, the probability that the home team sweeps a seven game series would be 0.55 * 0.55 * 0.45 * 0.45 = 0.061. So I wrote up a little program that would play out all of the remaining possibilities of a given series, and then, for each team, add up the probabilities of the scenarios in which they won.

Using a 10% home-field advantage, I found that the home team should win a 5-game series 51.9% of the time and a 7-game series 51.5% of the time. Using a 15% home-field advantage, the home team should win a 5-game series 52.9% of the time and a 7-game series 52.4% of the time.

At this point, the Twins are pretty much guaranteed to get home-field advantage in the first round, and statistics would say that this improves their odds of making it to the ALCS by about 3.8-5.8%. So, they are really just battling over the last two weeks to improve their odds of making it to the World Series by about 3.0-4.8% if they make it to the ALCS, or really, by about 1.5%-2.4% overall. Of course, these are just idealized statistics, so you're entitled to believe that home-field advantage in the ALCS could be make or break for the Twins based on whatever logic you choose.

*In case you're curious, Kirby's home run was worth a 0.36 WPA and winning game 6 increased the twins odds of winning the series by 55% (either their season ended or they had a 55% chance of winning game 7 at home). So, statistically, that at bat added 20% to the Twins chances. Gibson's home run was worth a whopping 0.87 WPA and winning game one of a 7-game series adds about 31% to a teams chance of winning the series. So his at bat added a total of 27% to the Dodgers chances of winning the series in '88.