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Expected value, variance, and sample size

The arithmetic of long-run outcomes, and why short samples are close to uninformative.

Expected value is the probability-weighted outcome minus cost. If your probability estimate is 55% against a price implying 52%, the difference is the estimated edge — before fees, and only as good as the estimate itself.

With a small theoretical edge, a large number of observations is needed before results can be distinguished from noise. Short-run results are dominated by variance.

Estimated probabilities carry error. Treating a point estimate as certain is the most common analytical failure in this area — which is also why this site publishes no confidence scores it cannot substantiate.

Want this applied to a specific market? The SportsWager Analyst will walk through the arithmetic. It explains method only — never picks.

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