What the uplift is worth
An uplift pays in full when the selection wins and pays nothing when it loses, so what it is worth depends on how often it wins and on how much stake the cap lets through. This page does both calculations on the sampled boosts and shows why the second one is the one that surprises people.
- the market price
- 2.50
- the boosted price
- 3.00
- the uplift if it wins
- 5.00
- the implied chance
- 40.0%
- added expected value
- 2.00
- as a share of the stake
- 20.0%
An uplift is worth the price difference multiplied by the stake, but only when the selection wins. Averaged across win and loss it is worth the price difference multiplied by the stake multiplied by the chance of winning, which on a 2.50 to 3.00 boost and a 10.00 stake is 2.00.
Two numbers, and the gap between them
The first number is the one an offer advertises without saying so: the money the uplift adds if the selection wins. The second is the one that matters over a month: the same money averaged across every outcome.
Worked example / sample C, the 2.50 to 3.00 boost
- market price 2.50, boosted price 3.00, uplift 0.50 of price
- a 10.00 stake, fully inside the cap
- if the selection wins: 10.00 x 3.00 = 30.00, against 25.00 unboosted
- the uplift paid: 5.00
- the chance of winning, taken as the market own implied chance: 1 / 2.50 = 40.0%
- added expected value: 10.00 x 0.50 x 0.40 = 2.00
Using the market implied chance rather than a tip or a model is deliberate: it is the only probability in the transaction that both sides have already agreed on, and it means the reader can reproduce the number from the two prices alone.
The share of the stake is what the cap decides
The added expected value of 2.00 is fixed by the cap, not by the stake. Raising the stake inside the cap raises the value proportionally; raising the stake above the cap does not raise it at all. This is the single most useful sentence on the desk, and the maximum stake is where it is proved.
| Stake | Boosted at 3.00 | At market 2.50 | Added expected value | Share of stake |
|---|---|---|---|---|
| 10.00 | 10.00 | 0.00 | 2.00 | 20.0% |
| 20.00 | 10.00 | 10.00 | 2.00 | 10.0% |
| 100.00 | 10.00 | 90.00 | 2.00 | 2.0% |
The same offer is worth twenty per cent of a 10.00 stake and two per cent of a 100.00 stake. Nothing about the offer changed between the rows.
Converting the uplift into a per-unit figure
Because the added value is proportional to the price difference and inversely proportional to the market price, the cleanest summary is a single number per unit of boosted stake.
Worked example / the mean offer in sample B
- mean market price 2.75, mean boosted price 3.17
- the uplift per unit of price: 3.17 - 2.75 = 0.42
- the market implied chance: 1 / 2.75 = 36.4%
- added value per 1.00 of boosted stake: 0.42 x 0.364 = 0.153
- the mean cap: 15.8
- added value per offer: 15.8 x 0.153 = 2.42