I'm trying to use odds data from bookmakers to estimate the expected number of goals in a game. We have these known facts:
- P(o4.5) = 0.573
- P(o5.5) = 0.458
- P(o6.5) = 0.279
P(o4.5) is the probability that there will be more than 4.5, P(o5.5) more than 5.5 and so on. The probability that there will be less than 4.5 is the inverse: 1 - P(o.45).
Can you from these facts estimate the expected number of goals in the game? Something like
P(oX) = 0.5
What is the value of the X variable? Is the information given above enough to figure it out? Is it enough if you make some assumptions like on the shape of the goal distribution and so on?