Why a composed price is not the product of its legs
Multiply the legs and you have the answer that every calculator gives. The operator returns a shorter number, and the gap is not a fee: it is the distance between two probabilities - the one independence produces and the one the legs actually have.
- legs
- 3, one match
- product of legs
- 5.60
- composed price
- 4.80
- difference
- 14.3%
A same-event combination is priced from the joint chance of its legs happening together, which is not the product of their separate chances. Three legs at 1.60, 1.75 and 2.00 multiply to 5.60 - a 17.86% chance - while the model measures 20.83%, so the composed price is 4.80 and the difference is 14.3% of the price, not a charge added to it.
Independence, and why a match is not independent
Multiplying prices assumes the legs do not affect one another. Inside one event they do: a team that wins has usually scored, a player with two shots on target has usually played most of the match, and an early goal makes both a home win and a high-scoring game more likely. The direction of the correlation is what matters. Positive correlation - legs that happen together more often than chance - makes the true joint chance higher than the product, so the fair price is shorter, and a reader who multiplied has over-estimated the return.
Sample A is that case, and it is the common one, because composing a market out of one match is what customers ask for. The three legs carry a product of 5.60 and a real joint chance of 20.83%. Priced at the product, the leg-set returns 116.65 per 100.00 staked; at 4.80 it returns 99.98. The 0.80 of price is the whole of the difference between the two.
What the samples show
| Leg | Price | Chance alone | What it is |
|---|---|---|---|
| Leg 1 | 1.60 | 62.50% | Home team to win |
| Leg 2 | 1.75 | 57.14% | Over 2.5 goals |
| Leg 3 | 2.00 | 50.00% | A named player, 2+ shots on target |
| All three together, composed | 4.80 | 20.83% | Against 17.86% if treated as independent |
What is not the explanation
It is not a built-in margin on every combination, because the legs already carry their own margins and the composed price is set on top of them rather than from them. It is not a fee for the service of composing, because no charge appears on any statement in sample F. And it is not the operator being cautious about the size of the liability: the payout, not the price, is where a book manages size, and the ceiling on a composed price is a refusal rather than a haircut - see /the-limits.
- Do the legs come from one event, or from several? Legs from different events are closer to independent and the gap should be smaller.
- Does the product of the legs differ from the price by roughly what the correlation would explain, or by much more?
- Are two of the legs, in effect, the same outcome read twice - a win and a win-to-nil, a player to score and the team to score?
- Does the page say the price is fixed at the moment it is offered, or that it may move until the bet is accepted?
- Is the price you were offered the price in the record afterwards, which is the subject of /the-record?