How to Calculate Implied Probability From American Odds

In these formulas, A is the absolute value of the odds—the number without its plus or minus sign. For -135, the absolute value is 135.

The calculation produces a decimal. Multiply that result by 100 to express it as a percentage. For example, +120 becomes 100 ÷ 220 = 0.4545, or 45.45%. A -135 line becomes 135 ÷ 235 = 0.5745, or 57.45%.

The sign also shows how the potential payout is quoted:

• Positive odds show the profit from a $100 wager. At +120, a winning $100 bet earns $120 in profit.
• Negative odds show the amount that must be risked to earn $100 in profit. At -135, the bettor risks $135 to win $100.

For broader context on moneylines, spreads, and totals, see how sports betting odds work. These implied percentages reflect the sportsbook’s posted price and generally include vig, so they are not necessarily a market’s true probability.

For positive American odds, divide 100 by the odds plus 100:

Implied probability = 100 ÷ (positive odds + 100)

1. Convert +150
   • Add 100: 150 + 100 = 250
   • Divide: 100 ÷ 250 = 0.40
   • Convert to a percentage: 0.40 × 100 = 40%
   A $100 wager at +150 returns $250 total: the original $100 stake plus $150 in profit. Winning 40% of identical wagers would produce $100 in average returns per $100 risked, which is the break-even point.
2. Convert +250
   • Add 100: 250 + 100 = 350
   • Divide: 100 ÷ 350 = 0.2857
   • Convert to a percentage: 0.2857 × 100 = 28.57%

Larger positive odds imply a lower probability because the sportsbook offers a bigger payout for a less likely outcome. At +250, fewer wins are needed to offset losing wagers than at +150.

The percentage is a break-even rate, not a prediction. It shows how often the bet must win to avoid a long-term loss at that price. Sportsbook margin, market opinion, injuries, and matchup information can all affect whether the true probability is higher or lower.

For negative American odds, use this formula:

Implied probability = |odds| ÷ (|odds| + 100) × 100

The vertical bars indicate absolute value, which removes the minus sign. For example, the absolute value of -200 is 200.

Convert -200

|-200| ÷ (|-200| + 100) × 100
= 200 ÷ 300 × 100
= 66.67%

A -200 moneyline therefore has a break-even probability of 66.67%. It also requires a $200 stake to win $100 in profit. A winning wager returns $300 total, including the original stake.

Convert -110

|-110| ÷ (|-110| + 100) × 100
= 110 ÷ 210 × 100
= 52.38%

At -110, a bettor must risk $110 to win $100. The line is common around point spreads and over/unders, where the extra 10 dollars reflects the sportsbook’s juice.

As odds become increasingly negative, both the break-even probability and the stake needed to win $100 rise. That makes -200 a stronger market expectation—and a more expensive wager—than -110.

Consider a point spread with both teams priced at -110. The implied probability for each side uses the negative-odds formula:

[ 110 \div (110 + 100) = 0.5238 ]

Converted to percentages, the market looks like this:

The 4.76 percentage points above 100% are the market’s overround, which is associated with the sportsbook’s vig or juice. This built-in margin helps explain why simply winning half of all -110 wagers does not produce a break-even result.

The two 52.38% figures should not be read as the teams’ true chances of winning; opposing outcomes cannot have a combined true probability above 100%. They are break-even percentages based on the posted betting lines. For a balanced two-way market, removing the margin would normalize each side to 50%.

This combined-percentage method is a practical starting point to calculate the sportsbook’s vig and compare pricing across markets.

The percentage converted directly from American odds is the sportsbook’s displayed implied probability. It includes the vig. In a two-way market priced at -110 on both sides, each outcome implies 52.38%, even though both outcomes cannot collectively have a 104.76% chance of occurring.

A fair probability estimates each side’s share after removing that excess. The basic normalization is:

Fair probability = side’s implied probability ÷ total implied probability for all outcomes

For the -110/-110 market, each side becomes 52.38% ÷ 104.76% = 50%. This is a standard way to remove the vig and estimate fair probability.

Both sides—or every listed outcome in a multiway market—must be included. Looking at one line alone can mistake the sportsbook’s break-even price for a true forecast and hides how much juice is built into the overall market. Normalization is still an estimate: it assumes the vig is distributed proportionally rather than revealing the sportsbook’s exact assessment.

For +150 odds, the implied probability is 40%. That percentage is the break-even threshold: a bettor would need to win more than 40% of identical wagers over time to have a positive expected return, assuming the price remains +150.

Suppose an independent analysis estimates the actual win probability at 43%. The estimated edge is three percentage points:

• Sportsbook break-even rate: 40%
• Independent probability estimate: 43%
• Possible edge: 3 percentage points

For a $100 wager, a win earns $150 and a loss costs $100. Using the 43% estimate, the expected value is:

(0.43 × $150) − (0.57 × $100) = $7.50

That works out to a theoretical $7.50 expected profit per $100 wager. It is a long-run mathematical estimate, not a prediction that the next bet will win.

Account for uncertainty

The calculation is only as reliable as the 43% estimate. Injuries, lineup changes, limited data, model assumptions, and ordinary variance can erase a small apparent edge. If the true probability is 39% rather than 43%, the same +150 wager has negative expected value.

Finding possible value also does not determine how much to risk. Stake size should reflect bankroll, confidence, and tolerance for swings. Methods such as fractional Kelly bet sizing can reduce exposure compared with full Kelly, but no bankroll formula turns uncertain estimates into a winning system.