Expected Value in Betting

Expected value converts an edge into money. It is the arithmetic that tells you whether a price is worth taking, and it is simple enough that the difficulty is entirely in the input, not the calculation.

The formula

A 55% chance at +110 gives 0.55 × 2.10 − 1 = +0.155. Every dollar staked averages 15.5 cents of profit over the long run.

Flip it: a 45% chance at −110 gives 0.45 × 1.909 − 1 = −0.141. Every dollar averages a loss of just over 14 cents. The EV calculator runs both directions and shows the dollar figure alongside the percentage.

EV and edge are related but different

Edge is expressed in probability: your number minus the market's fair number. EV is expressed in money: what that gap is worth at the price you can actually get.

They usually point the same way, but not always by the same amount. A five-point probability edge on a heavy favourite is worth much less in EV terms than a five-point edge on a long shot, because the payout multiplier differs. When sizing bets, EV is the more directly useful quantity.

The estimation problem

Here is the honest part. EV is trivially easy to compute and extremely easy to fake.

Every EV calculation requires a win probability, and where that number comes from determines whether the answer means anything. Feed it a probability derived from forty games of relevant history and you get a meaningful result. Feed it a probability derived from a feeling about a quarterback and you get a confident-looking number that is pure decoration.

This is why WeBall pairs every edge with a confidence score rather than publishing edges alone, and suppresses the grade entirely when the sample behind it is too thin to support a number.

A +EV bet loses constantly

This is the hardest thing about betting to internalise emotionally.

A bet with a 55% win probability loses 45% of the time. Over a hundred such bets you would expect roughly eleven losing streaks of three or more. None of that means the edge was fake; it is the ordinary behaviour of a small advantage in a high-variance process.

The practical response is to judge the decision rather than the outcome. Track your closing line value, which measures whether you got a better price than the market settled on — it converges far faster than profit does.

From EV to stake size

Knowing a bet is +EV does not tell you how much to bet. That is what the Kelly criterion is for: it sizes the stake to the size of the edge, then immediately teaches you why nobody should use it at full strength.