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The Composed Market / Six beliefs, checked
Six things readers assume about a composed price

Six beliefs about composed markets, checked against the arithmetic

Nothing on this desk is about opinion. Each of the six beliefs below is checked against the same samples the rest of the site uses, and the verdict follows the arithmetic rather than the other way round.

Desk spec
beliefs checked
6
false
4
partly true
1
true
1
the composed priceThe number returned for a set of outcomes the customer named. It is not the product of the legs: on the samples 5.60 multiplies and 4.80 is offered, because the legs happen together more often than independence implies.
the requestA customer asking an operator to invent a market. 500 arrived in the sample month, 218 produced a price, 131 could not be priced at all, and the median answer took 3 hours 40 minutes.
the void legA leg that never happens, repaired by re-pricing the combination from its remaining legs. Dividing the price by the void leg gives 4.50 where the real three-leg price is 4.80 - a 6.7% error.
Direct answer

Four of the six beliefs tested here are false, one is partly true and one is true. The persistent errors are that a composed price is the product of its legs, that the difference is a fee, that same-event legs pay better than legs from several matches, and that a void leg is simply divided out of the price.

Belief 1: the price is the legs multiplied

false

The three sampled legs multiply to 5.60 and the composed price is 4.80. The difference is not small: it is 14.3% of the product and 8.00 on a 10.00 stake. The multiplication assumes the legs are independent, and legs inside one match are not.

Belief 2: the difference is a fee for composing

false

No charge appears anywhere in sample F, and the arithmetic does not need one. Priced at 5.60 against a real joint chance of 20.83% the leg-set returns 116.65 per 100.00 staked, a 16.6% loss. The short price is the price at which the bet is fair, not a commission added to a fair one.

Belief 3: legs from one match pay better than legs from several

false

Almost always the reverse, on the samples. Legs inside one match are positively correlated - they co-occur more often than independence implies - so their joint chance is higher than the product and the price is shorter. Legs spread across several unrelated matches are closer to independent and their product is closer to the fair price.

Belief 4: a void leg is divided out of the price

false

10.80 divided by a void leg of 2.40 is 4.50, and the real three-leg combination prices at 4.80. The divided figure is wrong because the correlation between the remaining legs does not vanish with the leg that did: their joint chance is 20.83%, not the 22.22% that 1 / 4.50 implies. The gap is 0.30 of price, 6.7%, or 3.00 on a 10.00 stake.

Belief 5: any two markets the site shows can be combined

partly

Partly true and mostly beside the point. Of 40 documented rules, 22 permit a combination automatically and 11 more are permitted with a person to price them - so most pairs are allowed. But the 7 refusals are not about risk appetite; they are combinations that cannot be settled at all, such as opposing outcomes inside one market or legs resting on two different settlement rules.

Belief 6: a request can be refused

true

Refusal is normal rather than exceptional. In the sample month 96 requests were priced and refused and 131 could not be modelled at all, so 264 of 500 - 52.8% - never reached the customer as a usable price. Only 7 of the 40 terms pages say so.

the arithmetic under the four false beliefs belief 1 and 2, one subtraction: product of the legs = 5.60 composed price = 4.80 difference = 0.80 = 14.3% expected return at 5.60 on 20.83% = 1.1665 -> a 16.6% loss so the difference is not a fee: it is the difference between a market that returns 100.00 and one that returns 116.65 belief 3, same subtraction read the other way: correlated legs pay less, not more, because their joint chance is higher than the product of their chances. belief 4, the void leg: divide 10.80 / 2.40 = 4.50; re-price the three legs = 4.80 the divided figure implies a 22.22% chance where the model measures 20.83%: a 6.7% error, worth 3.00 on a 10.00 stake.
Five ways to check a composed price yourself
  • Multiply the legs and compare the answer with the price quoted. The gap is the correlation, not a fee.
  • Ask whether the legs are from one event. If they are, expect the price to be shorter than the product.
  • Ask for the settlement rule of each leg before agreeing, not after one of them is void.
  • Ask what happens to the combination if a leg does not happen, and whether the stake or the combination is repaired.
  • Treat the stake box as a starting point: the maximum stake on a long combination is the payout ceiling divided by the price.

Read next

The price of legsThe arithmetic behind belief 1The void legBelief 4, in fullThe refusalsBelief 6, by reasonQuestionsThe twelve most common