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Math Help - Percentage of a percentage

  1. #1
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    Percentage of a percentage

    Hello,
    I'm having a slight problem on a project I'm working on and hopefully this is the right section to post it in.
    This is the problem:
    I want to calculate the probability of a team winning a game.
    Team A vs Team B:
    1) Team A has a 15.625% of winning, 37.5% of drawing and 46.875% of losing. I drew these conclusions from all the games they have played this season up until now.
    2) Team A has a 19.65% if winning, 53.55% of drawing and 26.8% of losing. I drew these conclusions from the home and away games the teams have been playing and their wins/losses (homecourt advantage).

    Up until now, all is fine. The problem arises when I try to assign a different importance to each percentage.
    I assign 70% importance to the games played up until now; and 30% to the statistics about the homecourt advantage.
    In the end I would like to end up with a percentage for a win, draw and loss from all the figures above.
    If someone could be kind enough to explain to me how to do this so I could do this with different values and even more variables (weather, winning/losing streaks, etc.).
    I'm sorry if this is very basic, and to be honest I even feel like I know how to do this but for some reason I can't wrap my head around it.

    Thank you.
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  2. #2
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    Re: Percentage of a percentage

    Hey sardinemaster.

    Have you heard of the Bayesian method of probability and statistical inference? (Specifically with regard to priors)
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  3. #3
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    Re: Percentage of a percentage

    Thanks for your response.
    No, I haven't unfortunately. I went to search for it on google, and I have to admit I got a little lost in all the technicalities.
    I did not pursue math after high school and it looks to me as if this is a little bit more advanced than that!
    If you would be so kind to explain how that method of probability applies to what I am looking for and how to actively use it, using the figure I gave you above I would be very grateful!

    Thank you.
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  4. #4
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    Re: Percentage of a percentage

    Basically you have a distribution and you generalize the choices in that distribution by making each choice be random.

    In your example you have three choices: winning, drawing, and losing.

    In the classical approach this is the distribution.

    But in the Bayesian approach, we allow each choice to have a probability distribution where the probabilities can take on a bunch of values.

    The choice value could have a distribution for example P(Winning Probability = 19.125%) = 1/2 and P(Winning Probability = 15.625%) = 1/2.

    You then do one for drawing and also for losing keeping in mind that all choices must add up to 1.

    This is the basic idea of Bayesian analysis and you can calculate probabilities through Bayes theorems and rules of conditional probability.

    If this is a little over your head just ask a specific question and I'll do my best to give a specific answer.
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  5. #5
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    Re: Percentage of a percentage

    Thanks for your answer.
    Indeed it does seem a little over my head, sorry!
    But I was talking it through with a friend and suddenly it became all so simple!
    I'd like to tell you what I currently think is the answer to my problem and hopefully I'm right.
    1) Team A has a 15.625% of winning, 37.5% of drawing and 46.875% of losing. I drew these conclusions from all the games they have played this season up until now.
    2) Team A has a 19.65% if winning, 53.55% of drawing and 26.8% of losing. I drew these conclusions from the home and away games the teams have been playing and their wins/losses (homecourt advantage).
    The first stats have 70% importance and the second have 30%.
    So, this is what I'm doing (all of this assuming Team A has homecourt advantage):
    (15.626 * 0.7) + (19.65 * 0.3) = 16.8332% This is the percentage of winning.
    (37.5 * 0.7) + (53.55 *0.3) = 42.315% This is the percentage of drawing.
    (46.75 * 0.7) + (26.8 * 0.3) = 40.765% This is the percentage of losing.
    N.B. All these stats of for Team A, but in any case Team B's percentages are just the opposite.

    Would this be the correct method of getting to what I'm looking for?
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