# The Seven Game Series Model in Table Form

Posted on 09/08/2010 by

Over Labor day weekend, I took it upon myself to build a probability model for a seven game playoff series using the Binomial theorem (see here and here). I’ve been told the math  made peoples eye’s bleed so I’m going to try to simplify it for your enjoyment.

Not quite what I had in mind

The basics of the model are below(warning math content):

For team A and team B playing in a seven game playoff series ,with A being the higher seed  we have:

AbB= Marginal Probability Team A beats TeamB @ neutral site (Note that this could be the differences in win percentages, head to head matchups, win production or simply what the octopus says)

Ah= %TeamA beats TeamB @ Home

Ah: Probability of Team A winning @ home = AbB + HCA

Br: Probability of Team B winning on the road

and Ah+Br =1

Ar: Probability of Team A winning on the road= AbB + (1- HCA)

Bh: Probability of Team B winning @ home

and Ar+Bh =1

The equation for the 4 game set is:

(Ah+Br)^4= Ah^4+4*Ah^3*Br+ 6*Ah^2*Br^2+4*Ah*Br^3+Br^4

The equation for the 3 game set is:

(Ar+Bh)^3= Ar^3+3*Ar^2*Bh+ 3*Ar*Bh^2+Bh^3

As for the equation for team A winning the series?

Prob of Team A winning the series=

Prob of winning 4 Home games

Prob of winning 3 Home games * Prob of winning more than no away games

Prob of winning 2 Home games * Prob of winning more than 1 away game

Prob of winning 1 Home games * Prob of winning more than 2 away game

or

Prob of Team A winning the series=

(Ah^4)+

(4*Ah^3*Br)* (1-Bh^3)+

(6*Ah^2*Br^2)* (1-3*Ar*Bh^2-Bh^3)+

(4*Ah*Br^3)*(1-3*Ar^2*Bh-3*Ar*Bh^2-Bh^3)

Note, that my base assumption is that you know the win probabilities Now this is a little complicated but we can all understand a simple table. As before please note I capped out win probabilities at no better than 90% and no worse than 10%. This was done as the best team ever record wise still managed to lose 9 of 82 games (and the worst team ever still won 11 of 82):

With this in hand you too can figure out out who’d win a playoff series (as long as you know a way to work out the win % margin between Team A & Team B). The simplest possible model would be using winning percentage. For example,

Team A: .750 Winning Pct.

Team B: .650 Winning Pct.

A-B = .100

Probability of Team A winning a seven game playoff series as the home team= 74.4%

See, It’s simple.

Now if you wanted to use a more complex model for the margin you could build one. Or use mine:

%TeamA beats TeamB @ neutral site  = 4*(Pace Adjusted WP48 Team A-Pace Adjusted WP48 Team A) + .500 ( go here for more detail)

As a bonus, here’s the above table as an google doc. Now you to can play at home.

I promise I’ll get back to lighter fare in the next couple of days.