Baseball Q: Extra Inning Home Field Advantage

Wikipedia says:

"Extra innings (or, indeed, a tied final inning) constitute the situation in which the home-field advantage is most pronounced in baseball and softball. Because it bats in the second (or “bottom”) half of an inning, a home team wins the game immediately by taking the lead at any point in the final inning; extra innings present the same situation…

For the visiting team to win, on the other hand, it must score as many runs as possible in the first (or “top”) half of the inning and then prevent the home team from tying or taking the lead in the bottom half."
Do you agree the home team has an advantage? It doesn’t seem so to me - the visiting team had just as many (half-inning) opportunities to score, and if they didn’t, that just reflects the home team’s succesful defensive play - what am I missing?

Nothing. It’s not an advantage. Whoever wrote that is an idiot.

There are strategic considerations involved that favor the last team to go to the plate. For example, suppose you have a runner at second with no outs. Do you sacrifice him to third & then home? That gives you a great chance at one run, and very small chances of getting more than that. If you’re the visiting manager, you have to make a calculated decision–can your pitcher for the bottom of the inning hold with a one run lead? Or are you better off going for hits, getting more runs on average but increasing the chances of getting none?

The home team manager doesn’t have that problem. If the visitors didn’t score in the top of the inning & the game is still tied, he’ll do whatever will maximize the chance of getting one run, because one run wins the game.

It’s a small edge–just a few percentage points. But it’s a real one.

How does the extra-inning winning percentage for home teams differ from the nine-inning winning percentage for home teams?

From a quick Google search, the advantage is about 52% for the home team in extra innings, and about 54% for home teams for the entire game.

From a previous thread here, IIRC, the team that bats first has an advantage over the team that bats second, but not enough to overcome the home team’s larger advantage. This was based on tournaments where there was no real home team.

That was over the course of a whole game, though, not just considering extra (or final) innings. You’d need to separate those two effects here, as well.

The quote in the OP is confusing but there is a strategic advantage.

A baseball team can employ strategies that increase its chances of scoring one run, but which reduce its chances of scoring multiple runs. For instance, if your leadoff hitter hits a double, it is advantageous to scoring one run to have the next batter make a sacrifice bunt. But it makes you less likely to score multiple runs.

In an extra inning the home team has the benefit of always knowing whether they need to score once or multiple times, and so can always adopt the ideal strategy. If the visitors don’t score in the top of the tenth, the home team knows that bunting with a man on second makes sense; if the vistors score twice, bunting with a man on second is insane.

But the visiting team lacks this information; they do not know what the home team will do in their half of the inning.

It’s not a big advantage, but it would confer a very small one.

A shade smaller. That’s really not surprising–there’s a lot more randomness in a series of one-inning games (which is what extra innings effectively is) than in a nine-inning game, so you’d expect winning percentages sliced any which way to trend closer to 50% for extra innings.

I guess my bewilderment is unassuaged. If a home team actually loses more often in extra innings than in regular innings, where’s the extra inning advantage?

Perhaps I’m simply misunderstanding the point of the thread.

Home team advantage over the course of the game is something like .04 runs per inning scored. This translates to about a 54% winning percentage over a nine inning game (more or less, depending on the overall average runs scored that season), which is what’s observed. It translates to a less than 51% winning percentage in extra innings–between 50.5% and 51%, I’d say, based on back of the envelope calculations. This is not what’s observed–extra inning winning percentage for home teams is statistically a shade higher than that. Not much, but significant in the statistical sense.

Let’s throw away the math and get practical.

If you are the manager of a team that is going into extra innings, given the chance, do you choose to go to bat first or second?

I know I want the bottom of the inning because when I bring my team up to bat I know exactly what I am up against. That’s the advantage. Not that it always works out but I want it that way.

Don’t forget that defensive strategy also plays a role in baseball. As the cliche goes, baseball is the only sport where the defense has the ball.

The visiting offense knows exactly how many it must score, but the visiting defense knows to what maximum it must hold the offense. Intentional walks, player positioning (IF/OF in or back), and pitch selection can be tailored to the situation.

The statistics (fewer home wins in extra innings than in nine innings) suggest defensive strategy is as important as offense, or maybe even more important.

That’s true about defensive strategy, but as SCSimmons says, the home win rate should be lower in extra-inning games, because there’s more variance in the small number of extra innings than in a full nine inning game. The stats quoted above show that the home team’s win rate in extra inning games is lower, but not as much lower as would be expected statistically.

Compare these two coin flipping games I just made up :):

  1. Take an unbalanced coin that comes up heads 60% of the time. Flip it nine times. You’ll get more heads than tails 73% of the time.

  2. Take an unbalanced coin that comes up heads 70% of the time. Flip it once. You’ll get more heads than tails 70% of the time.

So even though the coin in game 1 has a smaller strategic advantage per flip, it wins its game more often because the game has more flips. In baseball, the home team can have a smaller advantage per inning in a normal inning compared to an extra inning, but still win more nine-inning games.

Edit: I’m not sure whether this effect is true for baseball or not, but it seems to be, given the percentages in SCSimmons’ post.

You’re not the only one confused. If it’s true that if the home team wins 54% of the time overall, but only 52% of extra-inning games, then extra-inning situations can only be described as a reduction of the overall homefield advantage, rather than an advantage in and of itself for the home team.

It just depends on the level you’re looking at. A home team is more likely to win a nine inning game than an extra inning game, but a home team is more likely to “win” a single extra inning than they are a single normal inning.

The home team’s advantage in a single extra inning is more than their advantage in a single normal inning, but that advantage is overwhelmed by the fact that more normal innings are played than extra innings.

Has anyone ever compiled the home-versus-road win-lose-draw percentage by inning, for each inning from the first through EI?

Here’s what I get:

 INN:      1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26
AWAY:  0.223 0.198 0.206 0.218 0.208 0.219 0.212 0.213 0.262 0.209 0.210 0.208 0.212 0.203 0.204 0.200 0.202 0.195 0.190 0.212 0.300 0.308 0.167 0.000 0.500 0.000
HOME:  0.264 0.216 0.233 0.235 0.231 0.236 0.231 0.230 0.205 0.228 0.232 0.231 0.227 0.249 0.221 0.248 0.242 0.220 0.222 0.152 0.050 0.231 0.000 0.250 0.000 0.000

HOME:  0.5435
AWAY:  0.4503

The ninth inning is a special case, since the home team often doesn’t bat at all. I removed those cases from the statistics, which is why that inning shows a lead for AWAY. The sample size obviously gets pretty small beyond 20 innings, so you should probably ignore those.

As has been pointed out, if the home team has a better chance of winning a given inning, they have an even better chance of winning a nine inning game. Logically, a small one-inning advantage should make it even likelier that you’re going to win a nine-inning game. But once the game becomes just a one-inning game, your chances of victory drop back to the chances of winning one inning; you blew your shot at winning the nine-inning contest.

Think of it in terms of a seven game series. Suppose we were to say that in any given game the Yankees have a 2-to-1 shot of beating the Orioles. What’s the Yankees’ chance of winning a 7-game series?heir

About 84%, actually. Much better than the per game chance. But if you arrive at Game Seven, the equivalent of an extra inning, with the series tied 3-3, then New York’s chances go back to 66%, because now it’s just a matter of their advantage in one game.

So it is with home teams and innings.

Those are very interesting numbers, Omphaloskeptic. This appears to best support the hypothesis that the chance of a draw in any given inning increases in extra innings, at the expense of the chance of the visitors winning, while the chance of the home team winning any given inning stays pretty much constant. (That is, the deviation in extra innings is comparable in size and much larger than the variation in the mean for the home team single-inning winning percentage.) I think this actually makes sense–the home manager won’t risk losing the game when he has a good chance to force another inning. That is, if the visitors score one in the top of the inning, the home team will focus on maximizing their chance of scoring at least one, rather than taking a smaller chance of getting at least one run but a relatively larger chance of getting two and winning the game right there. Better to play conservatively and live to fight another inning.

The effect looks to be even smaller than I’d thought, though–just barely significant. I’m less sure than I was that it actually exists–I’d need to spend a lot more time crunching the numbers than this is worth spending on to be sure. (Hell, I’ve already spent more time doing that than this is worth …) Home-field advantage in extra innings is, at best, a fraction higher than home-field advantage overall. It probably doesn’t decrease, though, other than the necessary result of having a series of one-inning games.

Keep in mind that there is a selectivity in getting to extra innings. Extra innings means that the teams are tied after 9 innings and playing that game on an equal level. (In major league ball there is much less disparity between two clubs than there may appear.)

If the 2011 Phillies and the 2011 Astros were playing each other for the entire season there would probably be few extra inning games. If the Phillies and the Cardinals were playing each other for the entire season there would probably be a lot more extra inning games because of a more equal match-up. Therefore, it only stands to reason that the outcome of an extra inning game would be closer to 50-50 than the outcome of the typical 9 inning game where the home team had the advantage throughout the game by batting last and some clubs have more talent than others.

If you think about it, a 54% advantage to the home team is huge when you consider that some teams are stronger than others. That means that a significant amount of the time the home field advantage is working in favor of a weak team over a strong team.