# The Seven Game Series: A Mathematical Primer

Posted on 04/14/2011 by

The Playoffs are about to begin and so I thought it was appropriate to break out some nice topical mathematical models.

Image Courtesy of xkcd.com

Previously, I wrote a series of pieces on how to build a probability model for a seven game playoff series using the Binomial theorem (see here, here and here).

The basics of the model are below in table form:

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):

For team A and team B playing in a seven game playoff series ,with A being the higher seed first you need to know the win probability margin of team A beating team B at a neutral site.How you work this out is up to you but the simplest possible model would be using winning percentage. For example,

Team A: .750 Winning Pct.

Team B: .650 Winning Pct.

Margin A-B = .100 (now go look it up)

%TeamA beats TeamB @ neutral site = .100 + .500=.600

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

Probability of Team A winning a seven game playoff series as the road team= 68.4%

See, It’s simple.

One of the items that came up as I built the model was the varying significance of Homecourt advantage (and the point of this post actually). You can see this here:

But even more clearly here:

So the math is clear. The more even two teams are facing each other in a seven game series, the more important home court advantage becomes . For dead even teams home court is worth almost half a win.

But that’s only who wins. What about likely series lengths? This I’ve done previously as well and bear in mind there is a bit of a twist as well.

So many ways to take this

The change in series format from 2-2-1-1-1 to 2-3-2 in the NBA finals influences the outcome. Luckily I’ve crunched the ridiculously long probability equation required for this previously.

(Image courtesy of xkcd.com)

But it looks prettier as a graph:

What do we learn here? Home team winning in 5 (if the home team is better) or losing in six (if worse) seem to be the smart bets unless the teams are even in which case the bet is home team in 7.

And now the 2-3-2 format:

And of course the pretty chart:

What do we learn here? For the the 2-3-2 Home team winning in 6 and not 5 (if the home team is better) or losing in five not six (if worse) seem to be the smart bets unless the teams are even in which case the bet is home team in 7.

Now please keep in mind that this blog does not in any way shape or form promote the practice of gambling. This information is provided solely for your amusement and cultural enrichment.

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