Expected value: when a price is worth betting

Expected value, or EV, is what a bet returns on average if you could place it many times. Multiply the chance of winning by what a win pays, then subtract the chance of losing times the stake. A positive result means the price pays more than the risk deserves. A negative one means it pays less.

EV depends on your probability, not the book's. The price is fixed when you bet; your estimate of the chance is the part you bring. A wrong estimate gives a wrong EV, however careful the arithmetic.

Say you rate a side at 55% and it is offered at +100, even money. A win pays 1 unit and a loss costs 1 unit. EV = 0.55 × 1 − 0.45 × 1 = +0.10 units per unit staked, or 10%.

Now the same 55% at -110. A win pays 100 / 110 = 0.909 units. EV = 0.55 × 0.909 − 0.45 × 1 = +0.05 units, or 5%. The same view of the game is worth half as much at the worse price. Price is half the bet.

At -125, a win pays 0.8 units. EV = 0.55 × 0.8 − 0.45 = −0.01. The same view, now slightly negative. Somewhere between -110 and -125 the bet stops being worth making.

Edge is usually stated as the gap between your probability and the market's fair probability, in percentage points. EV is the return that gap produces at the price you can actually get. A 3-point edge on a heavy favourite and a 3-point edge on a longshot have different EVs and very different swings.

That is why a pick should show both a probability and a price. On our picks, edge is measured against the de-vigged market price, and the pick is graded at the price it was posted.

A +5% EV bet at -110 still loses about 45% of the time. Expected value shows up only across many bets, and a run of losses on positive-EV bets is a normal part of betting them. That is a reason to size small, not a reason to doubt the arithmetic after five bets.

It is also why your estimates need checking. If you think you are making +5% bets but your results and your closing line value say otherwise over hundreds of bets, the estimates are the likely problem.

The same formula works at any price. Say you rate an underdog at 35% and it is offered at +210. A win pays 2.1 units. EV = 0.35 × 2.1 − 0.65 × 1 = +0.085 units, or 8.5%. Break-even at +210 is 100 / 310 = 32.26%, so your estimate sits 2.74 points above it.

That bet loses 65% of the time if your estimate is right. Underdog bets with positive EV produce long losing runs as a matter of course, which is why staking on them needs more patience and smaller units than staking on favourites at the same EV.

The weak point of any EV calculation is the probability you put into it. A number you feel is right is not an estimate. An estimate has a method behind it, a rating, a model or a market you trust, and it has a record you can check.

One honest method is to start from the no-vig market price and adjust only where you can say why: a lineup change the market has not priced, a weather forecast you trust more than the market does. If you cannot name the reason for the adjustment, the market's number is probably the better one.

Any pick service can claim positive EV. The check is the graded record. On the Strategies board, each strategy shows its ROI in units and its average closing line value next to the number of graded picks. A strategy whose picks were truly positive EV should show positive CLV over a large sample. Judge it on that, win or lose.