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Conditional probability of several events? (sports-related)

  1. Aug 8, 2013 #1
    I'm casually working on determining the probability of a team in a given sport (let's say football) reaching at least a certain level in a season.

    There are two main parts to this: How many games they won in the season, and how far they got in the playoffs. I'd like to assign one final number to each team that designates how well they did in the season, using a cumulative distribution function (eg, a team that wins every game and the championship would have a 1, a team that lost all games would have 0).

    There are two parts to this that I can see:
    - The probability of getting at least n wins during the season. This is easy using a binomial distribution.
    - The probability of making it at least so far in the playoffs. This is also easy.

    What I'm having a hard time figuring out is how to connect them properly. My guess would be that this is a P(B | A) event, where B is making it that far, and A is winning that many.

    I'm having a hard time thinking through how to express B though, since winning playoff games is independent of how many you win in the season, except that season games get you into the playoffs.

    So is it better to think of this as 3 events?
    C - Playoff progress
    B - Getting into the playoffs
    A - Winning x games

    And so this is P(C | (B | A))?

    I always think myself into circles with probability formulae. Any hints, help, insight would be great.
  2. jcsd
  3. Aug 9, 2013 #2

    Stephen Tashi

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    Science Advisor

    That doesn't make sense unless two teams that play each other can both win the game.
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