What percentage chance do you give Miami to win the Finals? 60 percent? 70? 80?

What about each individual game? Do you give Miami an 80 percent shot to win every game of the series? Do you give the home team a 75 percent chance to win each game?

If we have odds for the individual games, we can calculate odds for the entire series. Here are some sample results:

Odds for each game: |
Miami wins series |
San Antonio wins series |

Each game 50-50 | 50% | 50% |

Miami 60% to win every game | 71.02% | 28.98% |

Home team 60% to win every game | 53.2% | 46.8% |

Miami 70% at home, 60% on the road | 81.31% | 18.69% |

The series odds may not be quite what you’d expect based on the individual game odds. But that’s the point of doing the math. If we’re right that Miami has a 60 percent chance to win each game, then their chances of winning the series are a little over 70 percent, not 60 percent. Likewise, if you think Miami has a 60 percent chance to win each game, then it doesn’t make sense to say they have an 80 percent chance to win the series.

So how do you do the math? I’ve saved you the work and created a quick & dirty Excel spreadsheet you can download and play with:

Here’s a screenshot:

Using the spreadsheet is pretty simple. Input values are in yellow — just enter the percentage chance you give Miami to win each game. The final results show up in red. For example, here it is with the home team given a 70 percent chance to win each game:

If you want to see how the math is done, it’s all in hidden rows 17-34, which you’ll need to un-hide to see. There are more elegant ways to do the math, but as the title of the spreadsheet suggests, I used a quick & dirty method to put it together. Enjoy!

**UPDATE:** Since San Antonio won Game 1, I’ve updated the spreadsheet to reflect that in the input values. You can continue to use the tool to show the probabilities for the remainder of the series. I’ll try to keep the spreadsheet updated for the remainder of the Finals.

AhsanDid you use a binomial distribution to calculate the probabilities?

lcoonPost authorNo — as I understand binomial distributions (I’m not a statistician), they are for situations where the probability for success in each trial is the same. That’s obviously not the same in a playoff series — if nothing else, home court advantage changes the odds.

So rather than spend time researching the right way to do this, I just brute-forced it. Every series goes at least four games, and there are only 2^4 = 16 possible outcomes of those four games. So step 1 was to figure out the probability for each of those outcomes. Un-hide rows 17-35 of the spreadsheet and you’ll see it. A19:A34 are those outcomes, and B19:B34 are the probabilities for each, based on the input values in yellow.

Columns C through J, then work through the outcomes for the final three games. The tricky part is: 1) Stopping when one team reaches four wins; and 2) Don’t double-count results incorrectly. For example, Row 20 is MMMS, so Miami enters the fifth game with three wins and needs just one more. Any result where Miami wins the fifth game (MMM, MMS, MSM or MSS) is over after the fifth game, so looking at the permutations of the sixth & seventh games is redundant. So I just count the first one (MMM in C20), and ignore the others in D20:F20.

And since the bottom section is from Miami’s perspective (San Antonio’s is just one minus Miami’s) you’ll note that any trial that has San Antonio winning four games has a probability of zero.

So with that little bit of intelligence built into C20:J34, you just sum across the rows (columns C through J) to add up the possibilities for the final three games, given where we are in the first four games, then multiply that sum by the value in column B, which is the probability we got to that point in the first place. That total is in column K. Add all of those up, and you get the total probability for Miami winning the series, which is the result in G9. The probability of San Antonio winning is just one minus this result, and it’s in G10.

Daniel KazanieckiMr. Coon,

thank you for posting this, many people fall into the “60% chance to win each game, 80% chance to win the series” fallacy. If you ever want to dig even deeper, I guess there is a decreased probability of winning game 2 by whoever won game 1, aka the splitting phenomenon. (In earlier rounds the same applies to games 3-4.)

One more comment on a much more general subject. I’d like to express my gratitude for all your hard work on the FAQ. There are no words for how unique of a resource it became for all NBA fans. Myself, I run a very in-depth CBA-based fantasy league, which automatically means you’re a demigod for all our members: whenever a question is asked (be it renouncing exceptions, repeater tax, or Arenas provision), the answer always starts with “http://www.cbafaq.com/salarycap.htm#Q…”.

Thank you, thank you, thank you, and keep up the good work!

Kind regards from across the Pond.

lcoonPost authorThanks for the kind words!

There are many supposed effects you could build into the analysis — I just don’t know if those effects can be supported with analysis to verify their existence, and in any event, they’re beyond the scope of this tool. But the beauty of giving the user input values is that they can build-in whatever effects they want when they set the individual probabilities.

You can also use this tool to track the probabilities as the series progresses. As I’m writing this San Antonio has won game 1, so change Miami to 0 in cell B9, and you can continue analyzing the probabilities for the rest of the series using whatever criteria you wish.