Math & measurement
Expected value (EV)
The practical difficulty is that nobody hands you the true probability. The standard estimate is the de-vigged market consensus: strip the margin from many books' prices and compare the best available price against that fair baseline.
A worked example
Say you judge a team's true win probability at 55% and the best available price is −110, which pays $90.91 on a $100 risk. Expected value = (0.55 × $90.91) − (0.45 × $100) = $50.00 − $45.00 = +$5.00 per $100 staked, or +5%.
Move the same 55% estimate to a +100 price and it becomes (0.55 × $100) − (0.45 × $100) = +$10.00, or +10%. Nothing changed about the team — only the price. This is why line shopping is an edge in itself: identical opinion, doubled expectation.
The break-even threshold
Every price implies the win probability you need just to break even, which is simply its implied probability after de-vigging. At −110 that is 52.38%; at −150, 60%; at +150, 40%. Beat the number and the bet is +EV, miss it and no amount of confidence rescues it.
Because the threshold moves with the price, the same pick can be +EV at one book and −EV at another on the same afternoon. The bet is not the team; the bet is the team at a price.
Where the true probability actually comes from
This is the part that quietly decides whether an EV figure means anything. If you supply your own estimate, your EV is only as good as your model. The more defensible approach is the de-vigged consensus across many books: strip each book's margin, average the fair probabilities, and treat that as the market's best estimate.
Then look for prices that beat it. An EV calculated against a single book's line is close to circular — you are mostly measuring that book's margin, not an edge.
The common mistake: confidence is not probability
"I'm 70% sure" and "this happens 70% of the time" are different claims, and EV only works with the second. Feeding an inflated estimate into the formula produces a large positive number that is entirely an artifact of the input. If your probability estimates were reliably better than the de-vigged market, you would already know it from your closing line value — which is the cheaper thing to check first.
Common questions
- What does +EV mean in betting?
- A +EV (positive expected value) bet is one where the odds pay more than the true probability justifies, so repeating it many times would make money on average. It says nothing about whether any individual bet wins.
- How do you calculate expected value on a bet?
- EV = (win probability × profit if it wins) − (loss probability × stake). At a 55% estimate on a −110 price risking $100: (0.55 × $90.91) − (0.45 × $100) = +$5.00 per $100, or +5%.
- How do I know the true probability?
- You estimate it. The standard approach is to de-vig the consensus across many sportsbooks and treat that fair probability as the market's estimate, then look for prices that beat it. Calculating EV against a single book's line mostly measures that book's margin.
- Can a bet be +EV and still lose?
- Constantly. Expected value is an average over many repetitions, not a prediction. A +5% EV bet at even money still loses about 45% of the time — the edge only shows up across a large sample.
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