Understanding Odds & Payouts — American, Decimal & Fractional
Odds are the language of sports betting. They simultaneously communicate probability and payout. Yet odds are expressed in three different formats globally—American, decimal, and fractional—creating confusion. Understanding all three, converting between them, and calculating true probability is essential for comparing value across sportsbooks and markets.
The critical insight: odds don't just tell you payout; they encode the sportsbook's assessment of true probability, adjusted for their margin. Understanding this distinction is the first step toward identifying mispriced bets.
American Odds Format
American odds (used in US sportsbooks) use plus and minus signs. This format directly shows your profit on a standard bet.
Negative odds (favorites): -110 means risk $110 to win $100 profit. -200 means risk $200 to win $100. The larger the negative number, the higher implied probability.
Positive odds (underdogs): +110 means risk $100 to win $110 profit. +200 means risk $100 to win $200. The larger the positive number, the lower implied probability.
Formula for implied probability from American odds:
Negative odds: Probability = |Odds| / (|Odds| + 100)
Example: -150 → 150 / (150 + 100) = 150/250 = 60%
Positive odds: Probability = 100 / (Odds + 100)
Example: +150 → 100 / (150 + 100) = 100/250 = 40%
Decimal Odds Format
Decimal odds (popular in Europe and Australia) express your total return including your stake. This format is simpler mathematically.
1.50 decimal odds means if you risk $100, you get back $150 total ($50 profit plus your $100 stake).
Formula: Implied Probability = 1 / Decimal Odds
Example: 1.50 → 1 / 1.50 = 0.667 = 66.7%
To convert American to decimal:
Negative odds: Decimal = 1 + (100 / |American Odds|)
-150 → 1 + (100/150) = 1 + 0.667 = 1.667
Positive odds: Decimal = 1 + (American Odds / 100)
+150 → 1 + (150/100) = 1 + 1.50 = 2.50
Fractional Odds Format
Fractional odds (common in UK and horse racing) show profit as a fraction of your stake. 5/1 means risk $1 to win $5 profit (total return $6).
Formula: Implied Probability = Denominator / (Numerator + Denominator)
Example: 5/1 → 1 / (5+1) = 1/6 = 16.7%
To convert American to fractional:
Negative odds: 100 / |American Odds|
-150 → 100 / 150 = 2/3
Positive odds: American Odds / 100
+150 → 150 / 100 = 3/2
Implied Probability: The Critical Concept
Implied probability is what the odds suggest about true likelihood. It's crucial because sportsbooks build in margin. The true probability of an event might be 60%, but odds might imply 62% (the extra 2% is the sportsbook's profit margin).
Example: If you calculate true probability at 55% but odds imply 52%, the bet has positive expected value. You think it's more likely to win than the odds suggest.
Sum of all implied probabilities on a market exceeds 100%—this excess is "overround" (the sportsbook's margin). On a -110/-110 market, implied probabilities sum to about 104.76% (4.76% overround).
Calculating Payouts
For American odds:
Negative: Payout = Stake × (100 / |Odds|) + Stake
Example: $100 at -150 → $100 × (100/150) + $100 = $66.67 + $100 = $166.67 total ($66.67 profit)
Positive: Payout = Stake × (Odds / 100) + Stake
Example: $100 at +150 → $100 × (150/100) + $100 = $150 + $100 = $250 total ($150 profit)
For decimal odds:
Payout = Stake × Decimal Odds
Example: $100 at 1.667 → $100 × 1.667 = $166.70 total
Comparing Odds Across Sportsbooks
Different sportsbooks offer different odds on the same event. This variation is crucial—a half-point difference on a spread or slight odds difference on a moneyline substantially impacts long-term profitability.
Example: Compare a -110 favorite at one book vs. -120 at another. The -110 version is objectively better (requires less risk for same profit). Over 100 bets, this difference adds up significantly.
Shopping for odds is essential. Professional bettors maintain accounts at 5-10 sportsbooks specifically to access the best odds on each bet. Sportsbooks now offer "odds boost" promotions, further increasing variation.
Understanding No-Vig Odds
No-vig odds (or fair odds) represent true probability without the sportsbook's margin. These don't exist in the real sportsbook market, but calculating them helps identify true value.
The formula requires both sides of a market. If one side is -110 (implied 52.38%) and the other is -110 (implied 52.38%), true odds before margin would be around 50%/50%.
Using no-vig calculations, you can compare your probability estimate to fair odds, identifying which bets have positive expected value.
Converting Probability to Odds
If you estimate true probability at 55%, what American odds represent fair value?
For favorites (>50%): American Odds = -100 / (Probability - 1)
55% → -100 / (0.55 - 1) = -100 / -0.45 = -222 approximately
For underdogs (<50%): American Odds = (100 / Probability) - 100
45% → (100 / 0.45) - 100 = 222 - 100 = +122 approximately
True Probability vs. Sportsbook Probability
Sportsbooks don't always correctly estimate probability. If you can estimate probability better than sportsbooks, you've found an edge. Your goal is identifying situations where:
Your probability estimate > Implied probability from odds
Example: You estimate a team at 60% to win. Odds imply 56%. Positive expected value +4%. This is a bet worth making repeatedly.
Expected Value Calculation
Formula: EV = (Probability of Win × Payout) - (Probability of Loss × Stake)
Example: You estimate 55% probability. Odds are -110 (implied 52.4%).
Stake: $100. Payout if win: $190.91
EV = (0.55 × $190.91) - (0.45 × $100)
EV = $105.00 - $45.00 = $5 positive EV
This bet has +EV. Over 100 such bets, you'd expect about $500 profit (before accounting for variance).
Common Odds Mistakes
Mistake 1: Confusing decimal and American odds. 1.50 decimal is -200 American, not +150. Always confirm format.
Mistake 2: Not accounting for vigorish. A -110 bet requires 52.4% accuracy to break even, not 50%. Many bettors overestimate their win rate.
Mistake 3: Betting on high-payoff underdogs thinking probability is higher than it is. +300 odds imply only 25% probability. If you think it's 35%, it's good value. If you don't, it's a sucker bet.
Mistake 4: Not shopping for odds. Settling for -120 when -110 is available costs 0.9% immediately. Over time, this is devastating.
Odds Conversion Quick Reference
-110 American = 1.91 Decimal = 10/11 Fractional = 47.6% Implied
-150 American = 1.67 Decimal = 2/3 Fractional = 60% Implied
+150 American = 2.50 Decimal = 3/2 Fractional = 40% Implied
+200 American = 3.00 Decimal = 2/1 Fractional = 33.3% Implied
Related Reading: Learn how to identify value betting, master line shopping techniques, or explore statistical modeling.