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I have a potential prop bet in the making where my opponent has to pick 7 NFL teams not to make the playoffs for this upcoming season. If all 7 of their teams miss the playoffs, they win, if at least 1 of their teams make the playoffs, I win.

I've already gone ahead and calculated the vig free odds for the worst 7 teams to make the playoffs based on the odds off of one of the top online sports books:

Colts: 9.06% Browns: 9.50% Vikings: 11.37% Jaguars: 11.69% Rams: 13.22% Buccaneers: 18.01% Redskins: 18.01%

Now my question is how do I figure out what the odds are of at least 1 of those above teams making the playoffs in order for me to win my bet? Thanks.

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    Of course independence is not going to hold. It is likely some of these teams will play each other. The winner will then have an increased probability of making the playoffs while the losers chances will decrease.2012-08-14

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If we view whether one team will or won't make the playoffs is independent from the performance of other teams, then the chances that all of them not making the playoff is

$\operatorname{Pr}(\text{None Making}) = \operatorname{Pr}(\text{Team 1 Not}) \operatorname{Pr}(\text{Team 2 Not}) \cdots \operatorname{Pr}(\text{Team n Not})$

So $\operatorname{Pr}(\text{None Making}) = (1-9.06\%)(1-9.50\%)(1-11.37\%)(1-11.69\%)(1-13.22\%)(1-18.01\%)(1-\mathbf{18.01\%}) \approx \mathbf{37.58\%}$

So $\operatorname{Pr}(\text{At Least One Made}) = 1 - \operatorname{Pr}(\text{None Making}) \approx \mathbf{62.42\%}$.

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    for the last part of your equation, you did 1-8.01% instead of 18.01% but ya thanks I got the jist2012-08-14