Odds that add up to 96% do not give an answer that is 96% right
The disclosed probability mass, published beside every odds table.
- Read as
- If a seller publishes probabilities covering most of the outcomes, an expected value over those is approximately correct and can be published with a caveat.
- Actually
- The missing mass is not a small error term. An expected value over part of a distribution is an exact answer to a question about a different product, and the undisclosed part is where the largest outcomes usually sit.
Suppose a table publishes probabilities summing to 0.96 and the outcomes it names are worth $40 to $150. Averaging over those gives something between $40 and $150 — and it is a confident-looking figure.
Now suppose the undisclosed 4% is a single item worth $5,000. Its contribution to the true average is $200, which is larger than the entire figure computed from the disclosed part. The published number would not be slightly low; it would be wrong by a factor of three.
Nothing in the disclosed portion signals this. The missing mass is missing precisely because the seller did not publish it, so its size cannot be inferred from what was published. Any confidence attached to the partial figure would have to be invented.
So no expected value is produced. What is produced instead is the disclosed mass itself, stated as a percentage, and a note of exactly what is absent. That is a smaller claim and a true one, and it is enough for a reader to see that the product's own disclosure does not support the arithmetic its marketing invites.
The method behind this figure
Randomised purchase economics — box-economics v1.0.0. Its formula, assumptions and limitations are published in full on the methodology page.
Related: Mystery box and pack EV calculator, Recorded boxes and packs, Methodology, Glossary