Probability of winning the World Series

I thought I'd calculate the probability of winning the world series since I'm taking a 4000 level statistics class, and I have that kind of time. Using the negative binomial distribution, X ~ NB(r,p), where r is the number of successes you need and p is the probability of success on each individual try, you can determine the probability of any team winning a odd-numbered finite series of games. The negative binomial distribution is used, because it guarantees a success (win) on the very last try.

The negative binomial distribution uses the formula: _x-1C_r-1p^r(1-p)^x-r where x is the total number of games played.

We always hear from sports anchors about the chance of winning a game series after you win game 1, and most of them use past real-world data to say that a team has x percent chance of winning the series when they have a 1-0 lead. Let's remember that chance is not the same a probability, as chance uses some subjectivity and past real-world results to determine its numbers, whereas probability uses pure mathematics to obtain a solution.

Obviously the probability of either team winning when the series is at 0-0 (or tied at any point) is 50%. This is true even using the negative binomial distribution. But, now that the Cardinals have a 1-0 lead the probability of them winning the World Series is 65.625%. This is calculated using p = 0.5 (50% - equal probability of either team winning), and does not use any real-world subjectivity such as momentum, home-field advantage, player match-ups, etc.

UPDATE: Now that the Rangers have won game 2, tying the series at 1-1, the probability of either team winning the series goes back to 50%.

You can play with the probability of winning a series below. Have fun!

Probability of winning a series

This is a game series.

has/have won games.

has/have won games.