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.