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Math Help - help solving poisson calc

  1. #1
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    help solving poisson calc

    i believe number of goals scored in a soccer match is poisson.

    suppose some1 is offering odds of over 2.5 goals is 2.12 and under at 1.802. i want to know what they think the mean score is.

    the no commission implied probability is

    1/2.12=0.47

    1/1.802=0.55

    =0.47/0.47+0.55=0.46

    then use the poisson formula here

    i guess P < 3 = 0.54
    x = 0, 1, 2
    e = 2.71828
    μ is ur answer

    P(x; μ) = (e^-μ) (μ^x) / x!

    so u need 0.54=[(2.71828^-μ) (μ^0) / 0!]+[(2.71828-μ) (μ^1!) / 1]+[(2.71828^-μ) (μ^2) / 2!]

    can any1 help me solve this or even better where can i find a formula for the mean.

    would be amazing if there was something i could use in excel to solve this also.

    many thanks
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  2. #2
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    Re: help solving poisson calc

    Quote Originally Posted by subs View Post
    i believe number of goals scored in a soccer match is poisson.

    suppose some1 is offering odds of over 2.5 goals is 2.12 and under at 1.802. i want to know what they think the mean score is.
    Don't quote odds here, they mean different things in different contexts

    the no commission implied probability is

    1/2.12=0.47

    1/1.802=0.55

    =0.47/0.47+0.55=0.46
    OK now we have probabilities of 0.46 for 3 or more goals and 0.54 of 2 or fewer goals.

    then use the poisson formula here

    i guess P < 3 = 0.54
    x = 0, 1, 2
    e = 2.71828
    μ is ur answer

    P(x; μ) = (e^-μ) (μ^x) / x!

    so u need 0.54=[(2.71828^-μ) (μ^0) / 0!]+[(2.71828-μ) (μ^1!) / 1]+[(2.71828^-μ) (μ^2) / 2!]

    can any1 help me solve this or even better where can i find a formula for the mean.

    would be amazing if there was something i could use in excel to solve this also.

    many thanks
    The equation you need to solve is:

    \sum_{n=0}^2 \frac{e^{-mu}\mu^n}{n!}=e^{-\mu}[1+\mu+\mu^2/2]=0.54

    This almost certainly has no simple closed form solution for \mu so you will need to solve it numerically (or graphically).



    CB
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  3. #3
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    Re: help solving poisson calc

    Quote Originally Posted by CaptainBlack View Post
    Don't quote odds here, they mean different things in different contexts
    sorry

    The equation you need to solve is:

    \sum_{n=0}^2 \frac{e^{-mu}\mu^n}{n!}=e^{-\mu}[1+\mu+\mu^2/2]=0.54

    This almost certainly has no simple closed form solution for \mu so you will need to solve it numerically (or graphically).
    please could u give me a hint or a resource that i can use to educate myself on how to do that.

    can it be done with a downloadable tool? solver or something?

    excuse my ignorance, (not stupidity - i did my maths exams a year early at school and got an A) but in your opinion , if i just used a simple ratio or something as an approximate do you think i would be more than a few % off the exact answer?

    is this bothering people because it is gambling related? if so i understand your hesitation, but i feed my young family like this and have done so for 2 years, over thousands of plays.

    it is very important to me.

    thank you for your understanding.
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  4. #4
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    Re: help solving poisson calc

    Quote Originally Posted by subs View Post
    sorry



    please could u give me a hint or a resource that i can use to educate myself on how to do that.

    can it be done with a downloadable tool? solver or something?

    excuse my ignorance, (not stupidity - i did my maths exams a year early at school and got an A) but in your opinion , if i just used a simple ratio or something as an approximate do you think i would be more than a few % off the exact answer?

    is this bothering people because it is gambling related? if so i understand your hesitation, but i feed my young family like this and have done so for 2 years, over thousands of plays.

    it is very important to me.

    thank you for your understanding.
    In this case the answer is about 2.515.

    Probably the best way to deal with this is to use Excel to tabulate

    e^{-\mu}[1+\mu+\mu^2/2]-0.54

    over the range 0 to 5 for \mu and look for the location of the zero (you could also plot the curve in Excel)

    CB
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  5. #5
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    Re: help solving poisson calc

    thanks for the reply, i'll play around with this.

    the trouble is that the over 2.5 goals is less likely (0.46) so the answer of 2.515 seems wrong. it should be less than 2.5 (0.54). maybe u made a little mistake at the end?

    i'll see if i can get excel to do this for me...
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  6. #6
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    Re: help solving poisson calc

    Quote Originally Posted by subs View Post
    thanks for the reply, i'll play around with this.

    the trouble is that the over 2.5 goals is less likely (0.46) so the answer of 2.515 seems wrong. it should be less than 2.5 (0.54). maybe u made a little mistake at the end?...
    No its OK, that is just the way the Poisson distribution is.

    CB
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  7. #7
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    Re: help solving poisson calc

    Quote Originally Posted by subs View Post
    sorry



    please could u give me a hint or a resource that i can use to educate myself on how to do that.

    can it be done with a downloadable tool? solver or something?

    excuse my ignorance, (not stupidity - i did my maths exams a year early at school and got an A) but in your opinion , if i just used a simple ratio or something as an approximate do you think i would be more than a few % off the exact answer?

    is this bothering people because it is gambling related? if so i understand your hesitation, but i feed my young family like this and have done so for 2 years, over thousands of plays.

    it is very important to me.

    thank you for your understanding.
    solve Exp&#91;-x&#93;&#40;1 &#43; x &#43; x&#94;2&#47;2&#41; &#61; 0.54 - Wolfram|Alpha
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  8. #8
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    Re: help solving poisson calc

    ... that's horrible.

    so in this type of example, poisson is a waste of time really. and i'd get much closer by just using a sort of ratio.

    like (1-0.04)*2.5=2.4

    * pure frustration *
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    Re: help solving poisson calc

    thanks mr fantastic - that looks like a really useful tool.
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  10. #10
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    Re: help solving poisson calc

    Quote Originally Posted by subs View Post
    ... that's horrible.

    so in this type of example, poisson is a waste of time really. and i'd get much closer by just using a sort of ratio.

    like (1-0.04)*2.5=2.4

    * pure frustration *
    The way to do it is get the number of goals scored in a large-ish number of games add up the goals and divide by twice the number of games.

    CB
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  11. #11
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    Re: help solving poisson calc

    Quote Originally Posted by CaptainBlack View Post
    The way to do it is get the number of goals scored in a large-ish number of games add up the goals and divide by twice the number of games.

    CB
    yea, already do this but with many more factors (until my sample sizes are too small to be meaningful). the distribution for a predicted high scoring game, 1 sided game (where a thrashing may occur), or when the game is not important (entertainment factor) etc is going to have different distributions to an average sort of game.

    i was trying to get a better idea of what the enemy's numbers look like for a particular set of variables... gives me the ability to do sanity checks. its going to be harder than i had hoped.

    i've come a long way in 2 years but now i'm getting out of my depth. been trying to find someone for some quality work, but so far got poseurs scamming me for money and wasting my time.

    maybe i need to get down to my local university... hmmmm.

    thank you gentlemen.



    Peace is not merely a distant goal that we seek, but a means by which we arrive at that goal. - by Martin Luther King Jr.
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  12. #12
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    Re: help solving poisson calc

    just for curiosity's sake, i used trial and error with a poisson calculator and got 2.437 which is way better than 2.515. don't really understand that, i mean it is the same formula, right? then again, i'm not the sharpest tool in the shed because my rubbish formula (which is from a stats site) is even worse according to rolframalpha.


    the calculator is useless because i have thousands of these to do. i think i need a solver of some kind that can do this automatically. may have a look down this road.





    Peace is not merely a distant goal that we seek, but a means by which we arrive at that goal. - by Martin Luther King Jr.
    Last edited by subs; July 14th 2011 at 11:22 AM. Reason: spelling
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