We have all watched sport series based on winning the best of seven — or first team to win four games.
I consider two teams: Team A and Team B. Given the probability of Team A winning any one game, ; therefore, Team B has
probability of winning any one game.
The two teams have eight possible outcomes:
4-3, 4-2, 4-1, 4-0,
0-4, 1-4, 2-4, 3-4
Using hypergeometric probability, I calculate the likelihood of each of the 8 outcomes given each Team A probability (0.0 to 1.0).
Formula
The formula is as follows for a 7 game series:n = specific total number of games played for a given winning outcome ( total for a 4-2 series)
Permutations
The expression![Rendered by QuickLaTeX.com \frac{(n-1)!}{3!(n-4)!}](https://www.mathpax.com/wp-content/ql-cache/quicklatex.com-3f317dbb5406a48cccba145b13a004f3_l3.png)
![Rendered by QuickLaTeX.com n = 6](https://www.mathpax.com/wp-content/ql-cache/quicklatex.com-3d2be3c689ade1e0ee7061a94fc5ac8f_l3.png)
Example
Given:
The live chart looks best on a laptop or desktop screen. If viewing on a mobile device select ‘Request Desktop Website’ and use landscape orientation of the device.
Static Plots
![All Outcomes](http://khoitsmahq.firstcloudit.com/images/BestOfSeven.png)
![Winning Outcomes](http://khoitsmahq.firstcloudit.com/images/BestOfSevenWin.png)
Using PLOTLY live plots
Each chart series can be toggled off and on
by clicking its legend entry.
On a desktop device, reset the chart to full scale
by reloading the web page.
On a mobile device, reset the chart to full scale
by double tapping.
![All Outcomes](http://khoitsmahq.firstcloudit.com/images%2Fauto%20scale.png)
![Winning Outcomes](http://khoitsmahq.firstcloudit.com/images%2Freset%20axes.png)
This chart too looks best on a laptop or desktop screen. If viewing on a mobile device select ‘Request Desktop Website’ and use landscape orientation of the device.
Team A Winning Outcomes
The best of seven series steers the odds of winning in favor of the winning team. See table and chart below.
Game p(A) | Series p(A) |
0.50 | 0.50 |
0.60 | 0.71 |
0.70 | 0.874 |
0.80 | 0.967 |
0.90 | 0.997 |
1.00 | 1.00 |
This chart too looks best on a laptop or desktop screen. If viewing on a mobile device select ‘Request Desktop Website’.
Reference