Every guide to betting tells you to look for positive expected value. Very few of them tell you what the number is actually worth once bets settle.
So here is the arithmetic, worked on a real bet, and then the part that matters more: what our own published expected value has actually returned across 51,494 settled positions. It is a lot less than the number says, and the reason is worth understanding before you trust an expected value figure from anyone, us included.
The formula
Expected value is what one unit returns on average if you could make the same bet forever.
EV = p x b - (1 - p)
p is your probability the bet wins. b is what one unit pays in profit
at the offered price. Positive means the bet is worth making, in theory.
Worked on a real position
Kurt Kitayama, FedEx St. Jude Championship, round 2, hole 18. Birdie or better, priced at +520.
- The price implies 16.1%. That is what the book is charging, margin included.
- Our model said 20.6%.
- A +520 price pays 5.20 units of profit per unit risked.
EV = 0.206 x 5.20 - 0.794 = +0.279
+27.9% expected value. A perfectly ordinary positive edge, the kind the board surfaces dozens of times a round.
It lost. He made par.
One bet tells you nothing
That is not a mark against the bet. A position with a 21% chance of winning is supposed to lose most of the time. Judging it by the outcome is the most common error in betting, and it cuts both ways: a bad bet that wins is still a bad bet.
The only honest test is the population. So here is the population that bet belongs to.
Every birdie-or-better position we published between +400 and +700: 5,476 bets, average price +532, average model probability 21.2%.
- Break-even at that price needs 15.8% of them to win.
- 14.5% won.
- Flat staked, that is -10.1%.
Nominal expected value across that group was strongly positive. The realised return was negative. The model was on average about 7 percentage points too optimistic about how often these land, and at these prices that is the whole difference between a profitable market and a losing one.
The same test on everything we publish
Group every settled position by the expected value we published it at, then compare that to what it actually returned.
| Expected value at bet time | Positions | Average EV | Actual return |
|---|---|---|---|
| 5% to 10% | 15,369 | 7.2% | +0.9% |
| 10% to 20% | 15,672 | 14.3% | +1.8% |
| 20% to 40% | 12,132 | 28.2% | -0.1% |
| 40% and above | 8,321 | 85.6% | +19.3% |
Read the first three rows together: 43,173 positions carried an average 15.7% expected value and returned +0.9%.
That is the finding. Not that the model is worthless, the overall book is profitable, but that the expected value number is not a profit forecast. Anyone quoting you a 20% edge, us included, is quoting a number that is conditional on their probability being exactly right.
Why the gap is so large
Expected value inherits every error in the probability, and the price multiplies it.
At +520, being wrong by just 3 percentage points on the probability moves expected value by 19 points. Three points is an unremarkable amount to be off by on a single golf hole. It is also enough, on its own, to erase an advertised edge of 19%.
Longer prices amplify this further. Which is why the largest expected value numbers are the least trustworthy ones: they mostly appear on long prices, where the probability is hardest to estimate and the error is most magnified.
Which is why the best-looking row above proves the least
The 40%-and-above band returned +19.3% across 8,321 positions. That looks like the headline.
It is not, and the reason is this page's own argument turned on ourselves: 92% of that band's entire profit comes from its 50 best results, out of 8,321 bets. Remove fifty outcomes and the advantage disappears. These are long-price markets where a handful of hits carry everything, which is the signature of variance rather than edge.
Quoting that row as evidence would be exactly the mistake this page is about.
What expected value is actually for
It is a ranking signal, not a forecast.
Between two bets, the one with more expected value is more likely to be the better bet. That is genuinely useful and it is how the board is ordered. Reading 16% expected value as 16% return is not supported by our own data, and we would rather say so here than let you discover it at settlement.
The practical version:
- Use expected value to choose between bets. That is what it is good at.
- Do not use it to project profit. Discount it heavily.
- Be most sceptical of the largest numbers, wherever they come from.
- Judge any source on settled results, not on the edges it advertises.
Every position above is on our public results page, wins and losses, so this is checkable rather than asserted.
Every price PropGolf publishes carries its expected value and its settled outcome, including the ones that lost. See the live board.