## How Important is Home Field Advantage in the World Series?

The World Series is coming up. The Tigers will have the home field advantage (HFA) since the AL won the All-Star game. How much does this help them? How much does this increase their probability of winning the series? I calculated the probability of the team with the HFA of winning in  4, 5, 6, and 7 games assuming that the home team wins 54% of the games and then added them up. It turns out to make only a small difference.

I used 54% because that is close to the historical average. If the series were to go 4 games, the probability of the team with the HFA winning would be .54*.54*.46*.46 = .062 (assuming the two teams are equally matched). The .46 is used for games 3 and 4 since the HFA team is now the road team and the chance of them winning in the other team's park is .46 (1 - .54). So the HFA team will sweep 6.2% of the time.

Things get more complicated for a 5-game series. If the HFA team wins such a series, they must win game 5, so we can only consider cases when their sole loss comes in game 1, 2, 3 or 4 (See Table 1 below). So there are 4 ways this can happen. Table 2 below shows the probability of the HFA team winning a 5-game series in the four cases where the other team wins 1, 2, 3 and 4 (if they lose game 1, for example, the chances of them winning in 5 games is 0.46*0.54*0.46*0.46*0.46 = 0.024). Those four cases add up to .115, meaning that the probility that the HFA team wins in exactly 5 games is 11.5%.

For six game series, we again have to remember that the HFA team can only win them if it wins game 6. Table 1 shows all the different ways this can happen while Table 2 shows the probabilities of each of those cases. Then the total probability of the HFA winning in exactly 6-games is .169. The same thing was done for the chances of the HFA team winning in exactly 7-games, which turned out to be .169 as well.

So below we have the chances of the HFA team winning in exactly 4, 5, 6, and 7 games

4 Game Series  .062
5 Game Series .115
6 Game Series .169
7 Game Series  .169

The total is .5152, meaning that the HFA team wins 51.52% of the series. In a thousand years, the HFA team would win about 30 more times or one more than the other team about every 33 years.

Table 1

Table 2

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