What EV means, how to remove the book's margin to get a fair price, how to calculate the edge on a bet, and why a positive EV bet still loses most of the time at long odds.
Expected value is the only concept in betting that separates a good bet from a bet that won. It measures the price, not the result.
A bet is positive EV when the chance of it winning is higher than the chance the price implies. That is the entire idea; the rest is arithmetic.
American odds convert directly. For a negative number, implied probability is the odds divided by the odds plus 100 — so -150 is 150/250, or 60%. For a positive number, it is 100 divided by the odds plus 100 — so +200 is 100/300, or 33.3%.
Do this to both sides of a market and the total will exceed 100%. That excess is the book's margin.
If one side implies 55% and the other 50%, the total is 105%. Dividing each by 1.05 gives 52.4% and 47.6% — a fair market that sums to 100%. Those are the numbers your model has to beat.
Skipping this step is the most common error in amateur EV calculation, and it manufactures edges that do not exist. Every bet looks better against a vigged price.
Edge is your probability minus the de-vigged market probability. If your model says 56% and the fair price says 52.4%, the edge is 3.6 percentage points.
Expected value in money terms is your probability times the profit if it wins, minus the probability of losing times the stake. At +100 with a 56% model probability: 0.56 × $100 − 0.44 × $100 = $12 per $100 wagered.
A play at +500 with a model probability of 23% is strongly positive EV — the fair price would be around +335 — and it loses more than three quarters of the time. If you judge that bet by whether it won, you will conclude a good process is broken.
This is the hardest part of EV betting in practice. The feedback loop is slow and noisy, and the only defence is tracking closing line value alongside results.
The market is a very strong estimator, especially on main lines in major leagues with heavy volume. If your model disagrees with a well-traded market by a wide margin, the base case is that your model is wrong, not that you have found a large edge.
Genuine edges are usually small, appear in less-traded markets, and disappear as the price moves. An enormous apparent edge on a main line is almost always stale data, a mismatched line, or a team you have mis-mapped.