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The Player Line / The market
A market whose subject is a person rather than an event
What a market on one player actually is
A team market asks what a side will do; a single-player market asks what one person will do inside whatever the side does. The difference sounds small and changes the product: the price rests on a projection rather than a result, the settlement rests on a definition rather than a score, and the whole bet can be returned untouched because the person did not take the field.
Desk spec
- subject
- one person
- inputs
- minutes, rate
- line, sample
- 1.5
- settled by
- a definition
the projectionWhat a player is expected to do: an expected-minutes figure multiplied by a per-90 rate. The sample player is expected to play 78.0 minutes at 1.40 shots on target per 90, so the model expects 1.21 of them rather than the 1.40 a full match would imply.
the participation definitionWhat the operator's rules mean by "to play". Across 400 sampled single-player markets the same bets stand 308 times under "named in the starting XI" and 369 times under "takes the field", so the definition decides whether the bet is settled at all.
the confirmationThe source that counts the stat after the match and the audit behind it. 14 of 1,200 sampled markets were corrected after first publication, 5 of them more than an hour later, and 3 after the payout had already been made.
Direct answerA single-player market is a bet whose subject is one named individual's output - a count of shots, goals, passes, points or games won - rather than a team result. It is priced from a projection of that player, its line is set at a round figure above the model's expectation (1.5 against an expected 1.21 on the samples), and it is settled against a definition of participation that the rules must state.
The published market and the requested one
Two forms look alike and carry different risk. A published single-player market is a line the operator offers to everyone - a named player, a stat and a figure - and anybody may take it. A requested one is a line a customer asks for, on a player the operator has not posted; the operator then decides whether to make it at all. The sample month is built out of 8,000 published single-player bets and the 400 requests that reached a market, and the two are counted separately because only the requested market carries the risk that the operator invents the line itself.
The line matters as much as the price. A model that expects 1.21 cannot offer a line of 1.21, because a count is a whole number: the market rounds to a line of 1.5, so the bet is "two or more". The line is therefore a second decision on top of the projection, and moving the line from 1.5 to 2.5 without touching the model changes the price far more than a small change in the projection does.
What the samples show
Sample A - the same player priced three ways
| Line | Bet | Chance at 1.21 | Fair price |
|---|
| 1.5 | 2 or more | 34.10% | 2.93 |
| 0.5 | 1 or more | 70.18% | 1.43 |
| 2.5 | 3 or more | 12.25% | 8.16 |
| The model did not change between the rows | 1.21 | 34.10% | the line sets the price |
sample A - the line is a second decision
the model's mean is fixed at 1.21; only the line moves:
P(1 or more) = 1 - P(0) = 1 - 0.29820 = 0.70180 -> fair = 1 / 0.7018 = 1.43
P(2 or more) = 0.34100 -> fair = 1 / 0.3410 = 2.93
P(3 or more) = 1 - 0.29820 - 0.36082 - P(2)
P(2) = 0.36082 x 1.21 / 2 = 0.21830
so P(3 or more) = 0.12268 = 12.25% -> fair = 1 / 0.12268 = 8.16
a move of one line, from 1.5 to 2.5, changes the fair price
by 5.23 of price without the projection changing at all.
sample B - published against requested
published single-player bets in the month = 8,000
requests that reached a market = 400 of which 308 were accepted
the requested market carries the risk that the line is invented:
a requested line on a player with no sample is priced from a model,
not from a posted market, and the operator may refuse it (31 of 400
in this sample never became a market).
rate of requested to published = 400 / 8,000 = 5.0%
so one bet in twenty on one person is a line the operator had to
invent, and the rest are lines it had already decided to carry.
Five things to establish before taking a line on a person
- That the subject is an individual and not a team unit the page has blurred into one.
- What the line means in whole numbers - "2 or more" against "more than 2" is a different bet.
- Whether the stat is a count the provider publishes or a value the operator computes itself.
- Whether the line may move after the bet is placed, and whether the price is fixed at placement.
- Whether the market is published to everyone or a line that was requested and kept private.
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