Chance vs Skill

Hello,

Given a results data set of sport bets of various odds, how do mathematically differentiate between luck and skill?

Also, how do define if a data set is big enough to characterize the population from which the sample is taken?

Quote: jouesurf

Hello,

Given a results data set of sport bets of various odds, how do mathematically differentiate between luck and skill?

Also, how do define if a data set is big enough to characterize the population from which the sample is taken?
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A sample is never the same as a complete population. It just tends to get closer in all of its statistical properties. I say 'tends' because the sample's average can obviously move away from the true population if the new samples include outliers.

For a set of wagers of the same size and odds, the variance is the most useful measure. However, large bets and high odds winners will dominate your variance in sports betting. The answer to your question is more involved than I want to get into here.

One very simple approach is to divide your sample in half 'fairly' and see if the averages are near each other. If one half has a ROI of 110% and the other has an ROI of 92%, then your 101% ROI isn't proving that you are a winning bettor. If your set is large enough that both ROIs are above 100% and close to each other, then you are probably a winner. If you subdivide further, eventually, your ROIs will start to scatter all over and you know that subset is too small to prove anything.

To divide the set 'fairly', maybe sort them by bet size and then odds in a spreadsheet. Then, take even lines to form one subset and odd lines for the other.