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Over/Under Probability Calculator

Turns an expected total and a line into the probability of the over, the under and a push, with fair odds for each side. It uses a Poisson model, so it fits low-scoring sports best.

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How to use it

  1. 1 Enter your expected total, your own projection of goals, runs or points for the game. It must be above 0 and at most 300.
  2. 2 Enter the line from the sportsbook. Half numbers (2.5) cannot push; whole numbers (3) can.
  3. 3 Read the over, under and push chances and the fair odds for each side.
  4. 4 Compare the fair odds with the price your book offers to see which side, if either, is priced better than the model says.

What this model does, and does not do

This is a Poisson model. It assumes the total is a count of independent events that happen at a steady average rate, and it needs that average as an input. You must supply the expected total yourself; the calculator does not know the teams, the weather or the injuries.

A Poisson model is a good fit for low-scoring counts such as soccer and hockey goals. Baseball runs fit more roughly because scoring comes in clusters. You can enter basketball and football totals (up to 300), but treat them as a rough guide: points come in varied sizes, and Poisson understates how widely high-scoring totals spread, so it makes far-from-average results look less likely than they are. Treat the output as a starting point, not a verdict.

How over, under and push are calculated

With mean m, the chance of exactly k in total is e^-m x m^k / k!. The over is the chance the total is above the line, the under is the chance it is below, and a push is the chance it equals the line, which can only happen on a whole-number line. The three always add to 100%.

Fair odds are the odds a bet would pay if the book took no cut (no vig). When there is a push the stake is refunded, so fair odds use only the outcomes that settle: the chance of a side divided by (1 - push chance).

Worked example

A soccer match with an expected total of 2.75 goals and a line of 2.5. The under wins on 0, 1 or 2 goals, which together have a 48.15% chance. The over wins on 3 or more, a 51.85% chance. A half-point line cannot push.

Fair odds are -108 (1.928 decimal) on the over and +108 (2.077 decimal) on the under. If your book offers the over at -105, the model says it is slightly better than fair, but only if your 2.75 is right.

The formula

P(total = k) = e^-m x m^k / k! (m = expected total) Over = P(total > line), Under = P(total < line), Push = P(total = line) Fair decimal odds = (1 - push) / probability of that side

Frequently asked questions

A formula for the chance of each possible count of events when they happen independently at a steady average rate. Goals in a soccer match are the classic example.
It works best for soccer and hockey goals. It is rougher for baseball runs. For basketball and football totals it is only a rough guide, because it understates how widely high-scoring totals spread.
From your own model or research, for example a projection based on team scoring rates. The sportsbook line itself is a reasonable starting point, but then the output only echoes the market.
On a whole-number line, the total can land exactly on the line and the bet is refunded. Half-number lines have no push.
Only the outcomes that settle count, so the probability of a side is divided by one minus the push probability before it is turned into odds.
No. It converts the expected total you enter into probabilities. If the expected total is wrong, so is every number it shows.

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