How to compare my model's odds to bookmaker's prices? I've developed a model for predicting the probability that each horse will win a race.
The output of the model is the predicted probability that each horse will win, the sum of all the probabilities will be 1.
If I were to look at bookmaker prices for a horse race they would look something like this:
3.9, 5.4, 3.95, 6.7, 9, 14
If we took the sum of the probabilities that each horse would win, we'd get something like this:
1/3.9 + 1/5.4 + 1/3.95 + 1/6.7 + 1/9 + 1/14 = 1.027
The odds come out to be over than 1 due to the bookmaker overround. 
This is problematic for me because I need to compare the odds offered at the bookmaker and the probability from my model to determine if there is any value placing a bet.
In order to compare them accurately I will need to either 


*

*Remove the overround from the bookmaker prices (deflate the probabilities)

*Inflate the output of my model to include the bookmaker's overround


Can anyone suggest how to do this accurately from a theoretical point of view?
I believe that doing this linearly - applying the same factor to each horse - is incorrect.
I believe that each horse should take a percentage of the over round based on their odds of winning, the horses that are more likely to win should take a bigger proportion of the overround. Does this sound more correct?
Thanks for your help.
 A: To determine if there is any value placing a bet just take your model's % of a horse and multiply it to the odds offered. If for example your model says horse A has a 25% of winning and the odds offered is 4,10 then you have value. But this is not all. You have to test your model's outcomes. What i mean is check what is the % of winning on the real deal. Here is an example. Your model has predicted a 15% of winning for 105 horses and in reality there are 11 winners out of these 105 horses which equals to 10,5%. So your model overestimates and even if you would get value odds for the initial 15% prediction in reality thats a big loss cause of your model's fault.
I hope you get the message.
A: You are correct to reason that the bookmaker has probably not applied the overround equally to all runners. It's more likely to be a function of that runner's contribution to the book and the amount of money they expect to take on it.
If you have a sufficient amount of data on bookmaker prices and race winners, and assume a specific relationship between a runner's odds and its share of the overround then you can find the parameters of that relationship which maximize the likelihood - in other words, the adjustment to the raw bookmaker probabilities that result in the most accurate predictions of the winners.
