Predicting the First Round of the Playoffs

In this 7 team league, the first round of the playoffs involves the 2^nd through 7^th place teams. The 1^st place team gets a bye into the final weekend double-knockout 4 team tournament involving the three winners of the first round.

In the first round, the 2^nd place team plays the 7^th place team, the 3^rd place team plays the 6^th place team, and the 4^th place team plays the 5^th place team. Each of these is a best-of-5 series.

In my last post, I made a prediction about the regular season standings. So in the first round of the playoffs, team B would play team F, team C would play team D and team E would play team G.

I am interested in the probability of team G winning the best-of-5 first round series and making it to the final weekend tournament.

Team G's regular season win percentage is estimated to be 0.429 and team E's regular season win percentage is estimated to be 0.456. 

So the probability of team G beating team E in one game of head-to-head competition is 0.473.

Team G could win the best-of-5 game series in 3, 4 or 5 games.

The probability of team G winning the series in 3 games is

[ 0.473 * 0.473 * 0.473 ] = 0.106.

The probability of team G winning the series in 4 games is

[ 3 * (1 – 0.473) * 0.473 * 0.473 * 0.473 ] = 0.167.

The probability of team G winning the series in 5 games is

[ 6 * (1 – 0.473) * (1 – 0.473) * 0.473 * 0.473 * 0.473 ] = 0.176.

Adding up these three probabilities, the total probability of team G winning the best-of-5 series against team E is

[ 0.106 + 0.167 + 0.176 ] = 0.449.

So there is a 45% chance that team G will make it to the final weekend tournament in 2013.