Cover Probability & EV

Why a simple normal curve gets this wrong

Scores are whole numbers and some margins happen far more often than their neighbours. In the NFL a game lands on exactly 3 or 7 much more often than on 4 or 5, because of how touchdowns and field goals add up. That is why buying a half-point from -3 to -2.5 is worth so much more than buying from -5 to -4.5. A smooth bell curve treats every point the same and misprices exactly the lines bettors care about.

This calculator uses a separate outcome distribution for each league and market, fitted to final scores against closing lines from seasons before 2026:

• Football (NFL, college, CFL): a normal curve re-weighted at each margin or total by how often that number actually occurs. CFL borrows the NFL shape.
• Basketball (NBA, college, WNBA): a normal curve, because scoring is frequent enough that no single margin dominates.
• Baseball and hockey: each team's score is drawn from a count model (negative binomial runs, Poisson goals), so run lines, puck lines and low totals get realistic push and tie behaviour. A tie after regulation is settled by one run or goal.

How the numbers are worked out

For a spread bet, let M be your side's final margin and s your spread. You win when M + s > 0, push when M + s = 0 and lose otherwise. Expected profit per unit staked is:

EV = P(win) × (decimal odds − 1) − P(lose)

Pushes return the stake, so they add nothing and cost nothing. Quarter lines (like -2.75) are split half on each neighbouring half-line. The fair price is the American price at which EV is exactly zero, and break-even win % is the share of graded (non-push) bets you need to win at your price.

With A market line, the two prices are de-vigged to a fair chance at the market number, the distribution is centred so it reproduces that chance exactly, and then it is read at your number. That is the same method we use to compare an emailed line with the close.

Related: half-point value, no-vig calculator, EV calculator, spread to moneyline.