Point spread to win probability calculator

How a spread becomes a probability

The final margin of a game lands around the point spread, and how widely it scatters is close to a normal distribution. So a team favoured by s points wins whenever the margin is above zero, which happens with probability Φ(s ÷ SD), where Φ is the standard normal cumulative distribution and SD is how far results typically miss the spread.

For the NFL, Hal Stern found the margin over the spread was not significantly different from a normal distribution with mean 0 and standard deviation 13.86 points (“On the Probability of Winning a Football Game”, The American Statistician, 1991). For college football, Ryan Sides and Jane Harvill measured a standard deviation of 15.35 points for games with similar spreads in the 2021 season, and use 15 as the starting point (“Converting College Football Point Spread Differentials to Probabilities”, arXiv:2212.08116, 2022).

Worked example: a college team at −6.5 wins with probability Φ(6.5 ÷ 15) = Φ(0.43) ≈ 66.8%. A fair moneyline for that is about −201, and a fair YES contract on that team would trade near 67¢.

Where the model is wrong

Football scores move in threes and sevens, so real margins cluster on those numbers, and the smooth normal curve spreads that probability evenly. Sides and Harvill adjust for it with historical frequencies; this calculator does not, so treat a result near a key number as approximate.

The spread is the market’s estimate, not the truth: the probability is only as good as the line you enter. The model also ignores ties, which are rare in the NFL and impossible in college overtime rules.

Using it on a prediction market

On Kalshi, Polymarket US and other exchanges a sports contract pays $1 if the team wins, so its price in cents is already a probability. Compare that price with the probability implied by the sportsbook spread: a large gap is usually a difference in the line, the timing or the contract rules, and fees still come off before any edge is real.