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I am attempting to create a formula that takes the decimal odds of there being under 2.5 goals in a soccer match, and returns the estimated number of goals based on this. So far though, I have only been able to do the opposite - when the estimated number of goals are input, it produces the odds of them occurring. In Excel, it is:

=1/POISSON (2, number of goals,1)

Is there any way to reverse this, so that the odds are the input, and the expected goals are the output?

Matt
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  • I've tried replacing the mean in the formula with the only other variables in the equation - the decimal odds and the percentage they imply. Unfortunately, they didn't produce what I need! There's nothing else that's obvious to me at the moment... – Matt Sep 03 '18 at 19:11
  • @Matt Why you´ve divided 1 by the cdf? Why do you not just use the cdf? – callculus42 Sep 03 '18 at 19:36
  • The cdf here is the implied percentage. Dividing it by 1 converts it to the equivalent decimal odds. – Matt Sep 03 '18 at 19:46
  • @Matt You cannot solve the equation algebraically for $k$. Additionally you we have an inequality for instance $v\geq \frac1{\sum\limits_{x=0}^k e^{-\lambda}\cdot \frac{\lambda^x}{x!}}$ where $v$ is a fixed value. You are looking for the maximum value of $k$ which fulfill the inequality. This can be well made with excel. You just insert different values of $k$ in different cells. Then you can see easily at which value of k the odd is smaller or equal to $k$. – callculus42 Sep 03 '18 at 20:50

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