Ask ten people what "positive EV" means and you will get ten answers, most of them some version of "it means the bet is good." That is not wrong, but it is not useful either. The concept is arithmetic, and the arithmetic is worth understanding, because it is the difference between a strategy and a hunch.
The number a price implies
Every price contains a probability. When a book offers +142, it is quoting odds that imply a specific chance of the outcome happening. Convert it:
Implied probability = 100 / (odds + 100)
So +142 implies 100 / 242, or 41.3%. That is the book's number — or more accurately, the book's number plus its margin.
The number the model produces
Our models establish the probability independently, using over 10,000 data points per game and no knowledge of where the line sits. Suppose the model returns 45.8% for that same outcome.
Those two numbers disagree. The book is pricing a 41.3% chance; the evidence says 45.8%. That 4.5-point gap is the entire opportunity.
Turning the gap into dollars
Expected value on a $100 position:
- Win 45.8% of the time, collecting $142 profit
- Lose 54.2% of the time, dropping $100
(0.458 × 142) − (0.542 × 100) = 65.04 − 54.20 = +$10.87
Every time you take that position at that price, you are buying something worth about $110.87 for $100. Not on any single occasion — on any single occasion you either win or you don't — but across a long run of similar positions.
What this does not mean
It does not mean the position wins. A 45.8% chance loses more often than it wins. You can take twenty consecutive genuinely +EV positions and lose money on all twenty. Nothing about the maths prevents that.
What it means is that the price is wrong in your favour, and that repeatedly buying mispriced things is the only durable approach anyone has ever found. The edge shows up in the aggregate or not at all.
This is why sizing matters as much as selection, and why we pair every opportunity with a Kelly-based stake. Finding the edge is half the problem. Surviving the variance long enough for it to appear is the other half.