Place matters in sports: Effects of the length of championship series on winning probabilities for the team with home field advantage

In this paper, I address the question of how the length of championship series between two teams can affect the probability that a team wins the series. The geographical element of the question enters through consideration of 'home-field advantage'. This refers to the fact that in championship series, one of the teams has the benefit of one additional game that is scheduled to be played at home. This, coupled with the fact that teams typically have a higher likelihood of winning at home, leads to an interesting and surprisingly complex relationship between the length of a series and the probability of winning that series. Conclusions include the facts that (1) when the team with home-field advantage has a relatively small probability of winning away from home, it will fare relatively better in shorter series, and (2) the probability of winning a series can first become lower, but then become higher, as one progresses from 1-game series to 3-, 5- and 7-game series.