The NBA playoff buyout

Category: Statistics

Published: 01/14/2009 09:09 a.m.

*The idea from this came from Jeff Atwood's Unfinished game question and explanation.

So, you think you know basketball. Let's take last years Final for example. Say you are a big Laker fan, and you make a bet for $100 ($50 each) with a friend of yours that the Lakers will beat the Celtics. So, you watch the games and things start off rocky and after 4 games you are worried. The Lakers are down 3-1. You want out of the bet. How do you go about proposing a split of the $100?

You could be tempted to do it this way. The remaining possibilities that matter are as follows:

Celts win g5 Lakers win g5, Celts win g6 Lakers win g5, Lakers win g6, Celts win g7 Lakers win g5, g6, and g7

or in another wording: C, LC, LLC, or LLL.

As a Laker fan, you need LLL to happen. Using this logic, you have a 1 in 4 chance of winning. And it looks right. If your friend would agree, I'd take the $25 and run.

But lets say I am the Celtics fan. I don't agree with giving you $25. I only offer $13. Am I trying to rip you off? No. Actually, I am giving you $0.50 as a bonus. Here is why.

There are many more real situations, assuming all of the games were played out.

CCC, CCL, CLC, CLL, LCC, LCL, LLC, and LLL. A total of 8.

And notice the only one that gives the Lakers a championship is the last one, LLL. So your real odds as a Laker fan are 1 in 8. But, since the series ends after a Celtics win, many people forget to consider all the options. So, if you are ahead of a bet, and someone wants a buyout, make sure you do the right math. (Or, if you are a Celtics fan, just have some faith and take the whole $100 home after game 6.)