Expected value calculator: what a price is worth against your own probability
- Expected value of the stake
- $12.50
- The price as decimal odds
- 2.50
- Break-even probability the price implies (%)
- 40.00
- Your probability minus the break-even, in points
- 5.00
Every figure on this site comes out of the prices you type and the arithmetic printed beside them. There is no feed, no price of our own and no third-party data: the site holds no odds at all, only the method for reading the ones you already have. Conversions are exact, not approximations, and the American-to-probability step is written out on each page so you can check it by hand.
The prices above are a worked example ($12.50). Type the two you are actually looking at and every line re-computes.
Download the Expected Value Calculator worked example (CSV)
Give it a price and the probability you would put on that outcome, and it returns the decimal odds, the break-even probability the price implies, the gap between the two in percentage points and what a stake is worth on average at those numbers. At plus 150 with a 45% probability and 100 at risk, the break-even is 40%, the edge is five points and the expected value is 12.50. The figure is an average over many repetitions of the same arithmetic, not a forecast of any single outcome.
Expected Value Calculator: what people ask about the arithmetic
What is expected value here?
The average result per stake if the probability you supplied were exactly right and the same situation repeated indefinitely. It is arithmetic over your own assumption, so it is only as good as that assumption, and it says nothing about any particular event.
What is the break-even probability?
The probability at which the price is worth exactly nothing either way. It is the implied probability of the price, and if your own number is below it the expected value is negative however attractive the price looks.
Should I use the raw price or the vig-free price?
Use the raw price you would actually get, because that is what you would be paid. The vig-free price is for comparing markets and for testing whether your own probability differs from the market's; the no-vig calculator on this site produces it.
Does a positive number mean this makes money?
No. It is the average of an arithmetic model built on a probability you supplied, and this site makes no claim about income of any kind. A wrong probability produces a confidently positive number that means nothing at all.
Where the method behind this calculator comes from
Wolfers and Zitzewitz, Prediction Markets (Journal of Economic Perspectives, NBER working paper 10504). Sets out the standard reading of a market price as a probability, and the conditions under which that reading holds.
Wolfers and Zitzewitz, Interpreting Prediction Market Prices as Probabilities (NBER working paper 12200). Where the price-as-probability reading breaks down, which is the caveat under every figure on this site.