How the expected value (ev) calculator works
Expected value is what a bet is worth on average if it were placed many times at the same price with the same true chance of winning. A positive figure means the price is bigger than the chance deserves; a negative figure means the bookmaker's margin is working against you.
- Work out the profit if the bet wins: stake multiplied by the decimal odds, minus the stake.
- Multiply that profit by your win probability, and the stake by the probability of losing.
- Expected value is the first minus the second. Divide by the stake for the figure as a percentage of the outlay.
Worked example
£10 at 2.50 with a 45% chance of winning.
- Profit if it wins: £15. Loss if it does not: £10.
- EV = 0.45 × £15 − 0.55 × £10 = £6.75 − £5.50 = +£1.25.
- That is +12.5% of the stake; the break-even price for a 45% chance is 2.22.
The result is only as good as the probability you put in. A price cannot be value against a guess.
Questions
- Where does the win probability come from?
- From something other than the price itself: a model, a de-vigged consensus of sharper books, or a record you have measured. Using the bookmaker's own implied probability returns an EV of exactly the margin, always negative.
- Is a positive EV bet a good bet every time?
- It is a bet that pays on average. Any single result can lose; the value shows up over many bets, and only if the probability estimate was right.
- What is the break-even price?
- The decimal odds at which EV is zero for your probability: 1 divided by the probability. Anything above it is value on your numbers; anything below is not.
