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The Player Line / The minutes
The estimate that does most of the work
Why the expected minutes decide the price
Of the two numbers in a projection, the minutes figure is the one that moves. A rate drifts by a decimal over a season; a player either starts or does not, and a manager either keeps him on or takes him off at sixty minutes. The estimate that does most of the work is the least certain thing in the market.
Desk spec
- central estimate
- 78.0 min
- band
- 66 to 90 min
- price at 66
- 3.63
- price at 90
- 2.45
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 answerExpected minutes are the largest source of error in a single-player price. Moving the estimate from 78.0 to 66.0 minutes changes the fair price from 2.93 to 3.63, and moving it to a full 90 changes it to 2.45: a swing of 1.18 of price driven by twelve minutes of absence, not by anything the player does per minute.
Three things that decide the minutes
The team sheet is the first: whether the player is named in the starting eleven at all, which the sample answers 308 times out of 400. Rotation, a knock picked up in training and a manager's plan for a midweek fixture all move this number before anything is priced. The substitution is the second: a starter who is taken off on sixty minutes contributes little more than a substitute who comes on at thirty, and the projection has to blend the two. The third is the injury, which is the only one of the three that cannot be modelled at all - a player who pulls up in the eighth minute turns every estimate into a returned bet.
The samples split the estimate into the cases a reader actually meets. Of the 400 markets, 369 saw the player take the field, 331 saw him play at least sixty minutes and 297 saw him complete the match. Those are four different populations of the same bet, and only the first of them is close to the estimate the price was built from.
What the samples show
Sample B - what the minutes estimate actually resolved to across 400 markets
| Case | Markets | Share | What it does to the projection |
|---|
| Named in the starting eleven | 308 | 77.0% | The estimate's baseline case |
| Took the field at all | 369 | 92.25% | Adds 61 substitute appearances |
| Played at least 60 minutes | 331 | 82.75% | Removes 38 early substitutions |
| Completed the match | 297 | 74.25% | Removes the stoppage-time withdrawals |
| The estimate's central case against the completed match | 78.0 | against 90.0 | Twelve minutes = 0.48 of price |
sample J - twelve minutes, in price
expected minutes 78.0 -> output 1.21 -> fair price 2.93
expected minutes 66.0 -> output 1.03 -> fair price 3.63
expected minutes 90.0 -> output 1.40 -> fair price 2.45
the difference between the central estimate and a full match:
1 / (1.40 x 0.40816) ... expressed as price, 2.93 against 2.45 = 0.48
= 0.48 / 2.93 = 16.4% of the central price
on a 10.00 stake:
the central price returns 29.30; the full-match price returns 24.50
so a book that assumed a full match underprices the same player
by 4.80 on every 10.00, if the projection is right.
sample B - the minute estimate against the population
of 400 markets, the projection's baseline case (a start) happened 308 times
so the model's "expected" case failed to happen 92 times = 23.0%
of the 308 starts, 24 were replaced before sixty minutes
and a further 14 were withdrawn in stoppage time
of the 61 substitute appearances, 38 played fewer than thirty minutes
the projection is therefore an average over populations that differ
by up to an hour of pitch time, and the price is set on the average.
a reader taking the bet holds the tail: 92 of 400 of these
bets never had the player on the pitch for the estimate at all.
Five questions about the minutes
- Whether the projection names the expected minutes, or hides them behind a per-appearance rate.
- Whether a substitute appearance counts towards the same estimate as a start, or is modelled apart.
- What the operator does with the estimate when a player is a doubt on the team sheet.
- Whether the price is re-quoted if the player is withdrawn before the match starts.
- How the operator treats stoppage time, which is neither a full ninety nor a substitute's thirty.
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