I want to add a little explainer here on how to actually calculate the geometric mean of odds. At least I’m pretty sure how this works—please correct my math if I am not right!
Say you have four forecasts given in probabilities: 10%, 30%, 40%, and 90%.
Now, if you’re like me, it is easier to think with probabilities instead of odds, so you will want to transform it back. This is done using p = o/(o+1).
p = o / (o + 1)
p = 0.731110446 / (0.731110446 + 1) = ~42%
Note that this result (~42%) is different from the geometric mean of probabilities (~32%) and different from the mean of probabilities (~43%).
I want to add a little explainer here on how to actually calculate the geometric mean of odds. At least I’m pretty sure how this works—please correct my math if I am not right!
Say you have four forecasts given in probabilities: 10%, 30%, 40%, and 90%.
First you must convert to odds using
o = p/(1-p)O1 = 0.1/(1-0.1) = 0.111111111 O2 = 0.3/(1-0.3) = 0.428571429 O3 = 0.4/(1-0.4) = 0.666666667 O4 = 0.9/(1-0.9) = 9
Now that you have odds, use the geometric mean. The geometric mean is the nth root of the product of n numbers.
geomean(O1, O2, O3, O4) = 4th root of O1 * O2 * O3 * O4 = 4th root of 0.111111111 * 0.428571429 * 0.666666667 * 9 = 4th root of 0.285714286 = 0.731110446
Now, if you’re like me, it is easier to think with probabilities instead of odds, so you will want to transform it back. This is done using
p = o/(o+1).p = o / (o + 1) p = 0.731110446 / (0.731110446 + 1) = ~42%
Note that this result (~42%) is different from the geometric mean of probabilities (~32%) and different from the mean of probabilities (~43%).