Expected return in sports predictions

For a set of mutually exclusive modeled scenarios, multiply each scenario probability by the payout produced in that scenario, then add the results. Expected profit equals that expected payout minus the total cost of the plan. If other fees or deductions apply, include them in cost so comparisons use the same net basis.

With decimal odds o and an estimated success probability p, the expected net result per unit allocated is p × o − 1 when the quoted payout includes the returned unit. At odds of 2.20 and probability 0.50, the modeled expected net is 0.50 × 2.20 − 1 = 0.10 units. A different probability estimate changes the answer immediately.

A plan can win often but have negative expected profit if successful payouts are too small relative to losses. Another can win infrequently yet have positive modeled expectation because the payout is large enough. Compare success frequency, expected profit, downside, and return distribution rather than using any one measure as a substitute for the others.

First calculate all prediction combinations, then evaluate what the whole plan pays under each modeled outcome path. Add the payouts from every winning card in that scenario, subtract the cost of all cards, and probability-weight the resulting profit. Adding card-level expected values is valid only when costs and overlapping payouts are handled consistently.

Expected-return calculations are only as credible as their probabilities. Odds-implied probabilities may include a market margin and therefore sum to more than 100%. Normalizing them can provide a baseline, but it does not make them true probabilities. Use calibrated estimates, document their source, and test a range around uncertain inputs.

If an outcome probability might reasonably be 42% to 48%, calculate expected profit across that range. Identify the break-even probability where p × o = 1 and see whether the plausible range clears it. A plan that appears profitable only at the most optimistic edge of the range is less robust than its headline estimate suggests.

When comparing two card sets, keep total allocation, probability model, payout rules, and costs consistent. Then examine expected profit alongside median result, loss frequency, downside percentiles, and concentration. This makes it possible to prefer a plan for its profit profile rather than simply because it contains more cards or a larger maximum payout.