Baseball’s World Series is played over the best of seven games. The first

two games are played at the home field of one team (we will call

this one team A), the next three at the home field of team

B, and the last two at the home field of team A. Given that

teams are more likely to win games on their home fields, does

this give team A an advantage?

Keith Burgess-Jackson argues that neither team has an advantage:

Every Series goes either four, five, six, or seven games. We

don’t know at the outset how many games it will

go. Suppose it goes four games. Then there will have been two

games in each team’s park. No advantage. Suppose it goes

five games. Then there will have been three games in team

B’s park and two in team A’s park. Advantage to team

B. Suppose it goes six games. Then there will have been three

games in each team’s park. No advantage. Suppose it goes

seven games. Then there will have been four games in team

A’s park and three in team B’s park. Advantage to

team A.Let’s take stock. In two of the scenarios, there is no home-field

advantage. In one scenario, the team that begins at home has an

advantage. In one scenario, the team that begins on the road has

an advantage. It’s a wash! Where’s the overall

advantage?

Is he right, or does team A have the advantage? The answer is below the fold.

Team A has the advantage. The easiest way to see this is to imagine

what would happen if all seven games were always played instead

of stopping when one team gets four wins. Then team A would

have the advantage since it plays one more game at home. But

once a team reaches four wins, playing the remaining games makes

no difference to which teams wins the Series, so team A has the

same chance of victory in the “stop at four” and in the “play all seven”

formats. So team A has the advantage in the “stop at four”

format that is actually used.

A second way to see it is to consider what would happen if home field

advantage was absolute. Then each team wins all their home

games and team A wins the Series in game 7. So team A has

the advantage again.

For people who are not convinced, I have calculated the actual

probabilities in the table below (this requires that your browser

supports Javascript). The home team has won 57% of the games in

World Series play^{1}, so there is a 57% chance the Series score will be

1-0 after game one and a 43% chance it will be 0-1. The score will be

1-1 after two games if either B wins with the score 1-0 (43% of

57%) or if A wins with the score 0-1 (57% of 43%). The total is

49% (43% of 57% + 57% of 43%). Similarly you can work out the

probability of each Series score and add up the ones where A

wins to work the chance of A winning the Series and see that A

has a 52% chance of winning the seven game Series. The

calculations assume that the results of the games are

independent—that there is no such thing as “momentum” where

the winner of a game is more likely to win the next game.

You can experiment by entering different percentages for home field

advantage or different formats for the sequence of home and away

games. (Press ‘Enter’ after changing values to have the table

update.) Notice that the format makes no difference to A’s

chance of winning the Series—it’s the same with BBBAAAA as it

is with AAAABBB.

Now there are some possible explanations for the extra four-game Series.

For example, I assumed that the teams are evenly matched except for

home field advantage, but if one

team is better than the other, that increases the chance of a four

game Series. (Try entering 67 and 47 as the percentages that A and B

win at home.) Trouble is, that *decreases* the chance of a

seven game Series. (Try it—the *p* value even goes down.)

Similarly, if there is “momentum” and winning one game makes a team

more likely to win the next game, that makes four-game Series more

likely but seven-game Series *less* likely.

The only way that there can be a sixth game is if the score is 3-2

after five games. For the Series to go on to seven games, the team

that is behind must win the sixth game. Remarkably, that has happened

31 out of 49 times or 63% of the time instead of the 50% you would

expect. I can’t think of a good reason why this would

happen. If you can, leave a comment.

**Update 30 Oct:** Included result of 2004 Series.

^{1} The results of all the

games are available from this site.

I collected the results for the 78 world Series that used the AABBBAA

format for games (the Series from 1924 to 2004 except for 1943 and

1945) and put them in this file so you do your own

calculations if you are so inclined.

^{2}

Alan Abramowitz has article

on home field advantage. While he finds that the team with home field

advantage

wins more often, he argues that this is not because they get to play

the seventh game at home:

playing game seven at home does not appear to be a significant

advantage in the World Series. … Moreover, since the 2-3-2 format was

introduced in 1924,

the home team has won only 16 of 31 seventh games (52 percent), far

below the 57 percent success rate of the home team in all World Series

games.

I don’t think 52% is “far below” 57%. In fact, if the home team had

won just two more of those seventh games the success rate would have

*more* than 57%. If you do a statistical test (the Fisher

Exact Test) you will find that the difference between 52% and 57%

is not even close to being statistically significant, so it is wrong

for Abramowitz to reject the notion that the advantage comes from the

extra home game. (He also miscounts the number of wins for the home

team in game seven—it is actually 17 of 32, or 53%.)