ENWhy Multiplying Two Probabilities Can Mislead in a Multi
Updated
Three things to understand
- Multiplying probabilities is valid only when the events are independent.
- If one event makes another more likely, the true joint probability differs from the product.
- None of this produces a profitable method; it only explains why a simple product can be wrong.
A multi combines several selections into one wager, and a common shortcut is to multiply the individual probabilities to get the combined chance. That works for independent events and fails when the events are linked. This article uses hypothetical numbers to show how, rather than estimates for a real match.
Generated editorial illustration; not a platform screenshot.
Hypothetical numbers only. ACMA describes online in-play betting as prohibited for Australian customers; this article is not a prompt to bet.
The independent case
Flip two fair coins. The chance of heads on each is 0.5, and the result of one does not affect the other. The chance of two heads is 0.5 x 0.5 = 0.25. In this case, multiplying is correct.
Two coin flips share nothing. The outcome of the first has no bearing on the second, which is what independence means.
When events are linked
Suppose, hypothetically, a team has a 0.50 chance of winning a match and its star player has a 0.40 chance of scoring. If the two were independent, the chance of both would be 0.50 x 0.40 = 0.20.
But a team that wins is more likely to have scored through its best player. If, hypothetically, the player's chance of scoring rises to 0.60 when the team wins, the joint probability is 0.50 x 0.60 = 0.30, not 0.20. The product understated it by a third.
Why the product misleads in both directions
Correlation can also run the other way. Two outcomes that tend to exclude each other, such as a team winning and the match finishing with fewer than two goals in total, may have a joint chance below the product, because a win needs at least one goal and each extra condition squeezes the possibilities.
The size and direction of the error depend on how the events are linked. Without knowing that, a multiplication is a guess dressed up as a calculation.
How pricing handles linked outcomes
Where outcomes are visibly related, a price for a combined selection is typically set with the link in mind rather than by multiplying separate prices. That is why a combined price can differ from the product of the individual ones.
This article does not say how any specific provider does it. The point is that a shortcut done at home can differ from a price set with more information.
Three or more legs
With three independent legs of 0.5 each, the joint chance is 0.125. Each added leg multiplies the chance by a number below one, so the combined chance falls quickly. Add a link between legs and the real figure may be higher or lower than 0.125.
A large combined price is therefore not evidence of value. It reflects how unlikely the combination is, as priced, not a likely reward.
What this does and does not tell you
The numbers above are invented to illustrate a principle. They do not describe any match, player, team or market, and they are not estimates of anything real.
Understanding correlation does not make wagering profitable and nothing here implies it can. ACMA describes online in-play betting as prohibited for Australian customers, and this article is not a prompt to bet anywhere.
Questions readers ask
Can I always multiply probabilities to get a combined chance?
Only if the events are independent. If one affects the other, the product can be too high or too low.
What is an example of linked events?
A team winning and its star player scoring. A win makes a goal by that player more likely, so the joint chance differs from the product.
Why does a combined price not equal the product of the single prices?
Because linked outcomes are priced with their relationship in mind. This article does not describe any provider's method.
Can I treat team probabilities like fair-coin probabilities?
No. The coin example has defined probabilities. Team chances are estimates that can be uncertain, and outcomes within one match can be linked.
