A hand-sized win-rate estimate

Question

Six trades came out as wins (1) or losses (0): 1, 0, 1, 1, 0, 1. You model each as Bernoulli with win probability p, whose mean is p. Use the method of moments to estimate p.

Accepted Answer

Step 1: the sample average. For 0/1 data the average is the fraction of ones: \bar X = \frac{1 + 0 + 1 + 1 + 0 + 1}{6} = \frac{4}{6} = \frac{2}{3} \approx 0.667. Step 2: match the mean. The Bernoulli mean is p itself, so \hat p = \bar X = 2/3. Why so simple. For a yes/no outcome, matching the mean just counts the successes and divides by the total. No algebra beyond a fraction. Takeaway. The method-of-moments estimate of a win probability is the observed win rate: \hat p = 4/6 = 2/3.

A hand-sized win-rate estimate

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