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How to calculate how often I win a middle

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  • Carni
    New Member
    • May 2014
    • 9

    How to calculate how often I win a middle

    I've got a model that gives me totals for basketball, and with it I use it to calculate the probabilities of winning overs and unders. Let's ignore odds and say I've got a profitable middle where I'm betting:
    Over 210.5 (% chance of being over 210.5 = 57.6%)
    Under 215.5 (% chance of being under 215.5 = 47.8%)

    (As I said, let's ignore odds, but if the over was paying 1.99, and the under 1.99, this would obviously be a +EV middle with some risk (i.e. no pure arbitrage)).

    My question is: given the probabilities I have above, how do I calculate the % chance I win both bets? I feel like intuitively the answer is: (1-(1-P(over)-(1-P(under)) = 5.4% [equivalently (1-P(lose over)-P(lose under))], but I'm not at all sure.

    Anyone have better ideas?
    Last edited by Carni; 25 October 2017, 03:47 PM. Reason: [Edited to give the equivalent expression in square brackets]
  • blackswan
    Member
    • Sep 2014
    • 99

    #2
    I'm not sure if more information is required regarding the probability distribution, but if I had to come up with a number I get 5.4% as well.

    Total ------ Under - Over
    215.5 ------ 47.8% - 52.2%
    210.5 ------ 42.4% - 57.6%
    Difference -- 5.4% -- 5.4%

    Comment

    • Carni
      New Member
      • May 2014
      • 9

      #3
      Originally posted by blackswan View Post
      I'm not sure if more information is required regarding the probability distribution, but if I had to come up with a number I get 5.4% as well.

      Total ------ Under - Over
      215.5 ------ 47.8% - 52.2%
      210.5 ------ 42.4% - 57.6%
      Difference -- 5.4% -- 5.4%
      Thanks for chiming in Blackswan. I've done it a few different ways and that's the result I get. It makes sense when I draw it out diagrammatically.

      Comment

      • guthrybill
        New Member
        • Oct 2020
        • 2

        #4
        Thank you for your advice. Really useful

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