Implied probability calculator: convert betting odds to a win chance

An implied probability calculator turns a betting price into the chance that price is asking you to believe. At -110 that chance is 52.38 percent: win more often than that and the bet pays, win less and it doesn't. The math is two lines, and once you have it, you can read any board.

The formulas

American odds.

• Negative odds: |odds| / (|odds| + 100)
• Positive odds: 100 / (odds + 100)

Wikipedia's moneyline page gives the same relationship through break-even win rates: +300 needs a win 25 percent of the time and -300 needs 75 percent.

Decimal odds. Implied probability = 1 / decimal odds. A price of 1.91 is 1 / 1.91 = 52.36 percent.

Fractional odds. Implied probability = denominator / (numerator + denominator). A price of 5/2 is 2 / 7 = 28.57 percent.

A conversion table

All of these are arithmetic on the price, not predictions.

American	Decimal	Fractional	Implied probability
-200	1.50	1/2	66.67%
-110	1.91	10/11	52.38%
+100	2.00	1/1	50.00%
+150	2.50	3/2	40.00%
+250	3.50	5/2	28.57%

Implied probability is not true probability

The implied probability from a posted price includes the sportsbook's margin. Price both sides of a game at -110 and you get 52.38 percent twice, which adds to 104.76. No game is 104.76 percent likely to end one of two ways. The Wikipedia odds primer notes that the sum of quoted probabilities across all outcomes exceeds 100 percent and the excess is the bookmaker's profit on a balanced book.

To get a probability you can compare against your own estimate, remove that margin first. The devig calculator page walks through three methods, and a 2017 study found the power method outperforms the multiplicative method (American Journal of Sports Science). The fair odds calculator shows a full example from price to fair line.

Odds are worth reading as probabilities because betting odds often beat mathematical models as forecasts (PLOS ONE). Even so, a forecast with the margin still inside it is a biased one.

Using it as a break-even test

The quickest use of implied probability is a yes or no question: do I think this wins more often than the price needs?

• At -110 you need 52.38 percent.
• At +150 you need 40 percent.
• At -200 you need 66.67 percent.

If your honest estimate is 55 percent on a -110 bet, you think you have an edge. If you think 51 percent, you don't, even if you like the team. Your estimate has to come from somewhere other than the price itself. Bookmakers set a price and adjust it only occasionally (Economic Journal), so books differ and sometimes lag. Comparing across them is the plain way to find a price that is out of line, and the expected value calculator turns the gap into a dollar figure.

Parlays

A parlay multiplies prices, which means it multiplies implied probabilities too. Three legs at -110 each pay about +596 (decimal 6.957). The implied probability of that payout is 1 / 6.957 = 14.37 percent, which is 0.5238 cubed.

If each leg were truly a 50 percent shot, the chance of all three would be 12.5 percent and the fair payout +700. The gap between +596 and +700 is the margin compounding across three legs. This is a hypothetical, not a result. Legs from the same game may be correlated, which makes the simple multiplication wrong in either direction.

Futures and fields

A market with many outcomes adds up faster. Four teams priced at +150, +250, +300 and +400 imply 40.00, 28.57, 25.00 and 20.00 percent. That totals 113.57 percent. Real futures markets list far more outcomes, and the overround can be much larger. Same treatment as a two-way market: add them up, then take the excess out before reading any single price as a probability.

In-game and moving lines

An implied probability is a snapshot. A -110 line at noon can be -125 by kickoff, and the number you needed to beat moved with it. The line movement tracker records open, close and every tick between them, so you can see how the implied probability changed rather than guess.

How quant+ shows it

The board can show odds as American, decimal or implied percent, so you can switch formats without redoing math. Next to the best price on each row sits the devigged fair probability, which is the number most bettors actually want when they reach for an implied probability calculator.

Limits

• Implied probability includes the book's margin until you remove it.
• It says what the price needs, not what will happen.
• Prices change. Check the timestamp before using one.
• Rounding matters on long odds, so keep two decimals.

quant+ shows these numbers for information only. It doesn't place bets or connect to sportsbook accounts.

Quant+ is analytics for informational purposes. 21+. If you or someone you know has a gambling problem, call 1-800-GAMBLER.