What is the Excel formula for expected value in betting?

With probability in B2 and decimal odds in C2, expected value per unit staked is =B2*C2-1. Multiply by the stake for expected profit. It comes from weighting the profit if the outcome occurs by its probability and subtracting the weighted loss of stake otherwise.

How do you calculate break-even probability in a spreadsheet?

Divide one by the decimal odds, =1/C2. Expected value is zero at that probability. Comparing a probability estimate with break-even, for example =B2-1/C2, expresses the result in probability points, which is often easier to reason about than expected value directly.

What is a sensitivity grid for expected value?

A table with probability values down one side and odds values across the top, each cell computing expected value with mixed references. Conditional formatting centred on zero shows where the sign flips, revealing how much error in the probability estimate the conclusion can tolerate.

Why is the probability input the weak point?

Because the formula itself is exact arithmetic, so every bit of uncertainty in the result comes from the probability estimate. Small estimated edges are often smaller than the plausible error in that estimate, which a sensitivity grid makes immediately visible.

How to Calculate Expected Value in a Spreadsheet

With a probability estimate in B2 and decimal odds in C2, expected value per unit staked is =B2*C2-1, and expected profit is that multiplied by the stake. A positive result means the estimate implies the price is generous. Add a sensitivity grid, because the result depends heavily on a probability estimate that is uncertain.

The formula in cells

Inputs. Put your probability estimate in B2 as a decimal between zero and one, and the decimal odds in C2. If you have American odds, convert them first with =IF(A2>0, 1+A2/100, 1+100/ABS(A2)).

Expected value per unit. =B2*C2-1. This is the average profit per unit staked if the probability estimate were correct. It comes from weighting the profit if the outcome occurs, odds minus one, by its probability, and subtracting the stake lost otherwise, weighted by the remaining probability. Those terms simplify to probability times odds minus one.

Expected profit. With the stake in D2, =D2*(B2*C2-1).

Break-even probability. =1/C2. The probability at which expected value is exactly zero. Comparing your estimate with this number is often more intuitive than looking at expected value directly: the question becomes whether your estimate is above or below it, and by how much.

Edge in probability points. =B2-1/C2. The gap between your estimate and break-even. This makes the sensitivity discussion below concrete, because it expresses the result in the same units as the input.

Formatting that prevents mistakes

Format probability cells as percentages and odds cells with two decimal places, and add data validation so probabilities must fall between zero and one. The most common spreadsheet error in these calculations is typing a percentage as a whole number, which makes every result absurd.

A layout that stays trustworthy

Separate inputs from calculations. Put everything you type in one clearly shaded block and every formula elsewhere. When a result looks strange, you only need to check the inputs block.

Name the key cells. Named ranges such as prob, odds, and stake make formulas read as =prob*odds-1, which is far easier to audit than cell references.

Record the source and time of each price. A column for where the odds came from and when. Prices change, and a calculation without that context cannot be reviewed later.

Record where the probability came from. A model, a fair probability derived from market prices, a rating system. The expected value is only as meaningful as this input, and the sheet should say what it was.

One row per case. When evaluating many cases, keep one row each with the same columns, rather than scattering calculations across the sheet. It makes sorting, filtering, and later analysis possible.

Using a fair market probability as the input

One common input is the market's own probability with the margin removed, calculated from both sides of the market. Using it produces an expected value slightly below zero at the posted price, which is a useful sanity check on the sheet. A result far from that suggests an error in the inputs or the margin removal.

The sensitivity grid

The formula is exact. The probability estimate is not. A sensitivity grid makes that visible.

Build it. Down the first column, list probability values around your estimate, for example from five points below to five points above in steps of one point. Across the top row, list a few odds values around the price. In each cell, compute =$A5*B$4-1, using mixed references so the formula copies across the grid.

Colour it. Apply conditional formatting with a colour scale centred on zero. The boundary between positive and negative becomes a visible line through the grid.

Read it. If the result flips sign within a point or two of your estimate, the conclusion depends on a level of precision that almost no probability estimate has. If it stays positive or negative across the whole range, the conclusion is robust to reasonable error.

This grid is usually more informative than the single expected value number, because it answers the question that actually matters: how wrong could the estimate be before the conclusion changes?

This page describes calculation and is not betting advice.

Why small edges are fragile

At typical prices, an estimated edge of a couple of probability points is smaller than the uncertainty in most probability estimates. The sensitivity grid shows this immediately: the sign changes inside the range of plausible error. That is not a spreadsheet limitation. It is the honest state of the information.

Frequently asked questions

What is the Excel formula for expected value in betting?: With probability in B2 and decimal odds in C2, expected value per unit staked is =B2*C2-1. Multiply by the stake for expected profit. It comes from weighting the profit if the outcome occurs by its probability and subtracting the weighted loss of stake otherwise.
How do you calculate break-even probability in a spreadsheet?: Divide one by the decimal odds, =1/C2. Expected value is zero at that probability. Comparing a probability estimate with break-even, for example =B2-1/C2, expresses the result in probability points, which is often easier to reason about than expected value directly.
What is a sensitivity grid for expected value?: A table with probability values down one side and odds values across the top, each cell computing expected value with mixed references. Conditional formatting centred on zero shows where the sign flips, revealing how much error in the probability estimate the conclusion can tolerate.
Why is the probability input the weak point?: Because the formula itself is exact arithmetic, so every bit of uncertainty in the result comes from the probability estimate. Small estimated edges are often smaller than the plausible error in that estimate, which a sensitivity grid makes immediately visible.