There is a betting-site which calculates the "odds" for two teams by how much money is set on each team. For example, 100 people place one dollar each, 75 on team A and 25 on team B. Therefore, the odds are displayed as "75% team A, 25% team B". Team B wins, and all of the 25 people get 3 + 1 dollars.
Assume I have the results of a fairly small number of games (like 100-1000). Results beeing the chances that the site issued and who actually won.
I want to compute how accurate the displayed chances match the actual results. For example, if matches where one team has displayed odds of 30% actually are won by 40% of those teams.
Granted this will not be reliable advice for actually placing bets, but I am interested anyway.
How can I compute how accurate the displayed odds are? How much samples do I need to make sure that the error-margin is fairly small?
If you provide formulas, small explanations would be highly apprechiated. I am bad at math :(
Thank you for your time and have a nice day!