How to calculate implied probability from odds

Implied probability is the likelihood of a particular outcome occurring as suggested by betting odds, expressed as a percentage. It represents what the bookmaker's odds imply about the chance of an event happening, rather than a direct forecast or guess.

Calculating implied probability involves converting betting odds into a percentage. This conversion allows bettors to understand how likely the bookmaker thinks an event will happen and compare that assessment to their own analysis or other odds formats. The relationship between implied probability and betting odds serves as the foundation for evaluating bets. A bettor who believes the true probability of an event exceeds the implied probability indicated by the odds may have identified a value bet. Conversely, a bet becomes unfavorable when the implied probability surpasses the bettor's estimate.

What are the main types of betting odds formats?

The three main types of betting odds formats are American (Moneyline), Decimal, and Fractional. Each format represents the payout relative to the stake differently, and each converts to implied probability using distinct formulas.

American odds

American odds appear as positive or negative numbers. Positive odds (e.g., +150) show how much profit you would make on a $100 bet. Negative odds (e.g., -200) show how much you need to bet to win $100.

For positive American odds, the implied probability formula is:

$\text{Impli}$

$\text{ed Probability}=\frac{100}{\text{Odds}+100}$

For negative American odds, the implied probability formula is:

$\text{Implied Probability}=\frac{|\text{Odds}|}{|\text{Odds}|+100}$

Decimal odds

Decimal odds are popular in Europe and represent the total payout (stake plus profit) for each $1 bet.

$\text{Implied Probability}=\frac{1}{\text{Decimal Odds}}$

Fractional odds

Fractional odds are common in the UK, shown as a fraction (e.g., 5/1), indicating profit relative to stake.

How do you calculate implied probability from American positive odds?

To calculate implied probability from American positive odds, divide 100 by the sum of the odds plus 100.

Example: +150 American Odds

A +150 American odds means a $100 bet wins $150 profit.

$\text{Implied Probability}=\frac{100}{150+100}=\frac{100}{250}=0.40\text{ or }40\mathrm{\%}$

This calculation suggests the bookmaker views the outcome as having a 40% chance of occurring.

How do you calculate implied probability from American negative odds?

To calculate implied probability from American negative odds, divide the absolute value of the odds by the sum of the absolute value plus 100.

Example: -200 American Odds

A -200 American odds requires a $200 bet to win $100 profit.

$\text{Implied Probability}=\frac{200}{200+100}=\frac{200}{300}=0.667\text{ or }66.7\mathrm{\%}$

This calculation indicates a stronger favorite with approximately a two-thirds likelihood of winning.

How do you calculate implied probability from decimal odds?

To calculate implied probability from decimal odds, divide 1 by the decimal odds value.

Example: 2.50 Decimal Odds

Decimal odds of 2.50 mean a $1 bet returns $2.50 total (including stake).

$\text{Implied Probability}=\frac{1}{2.50}=0.40\text{ or }40\mathrm{\%}$

he straightforward reciprocal calculation matches the positive American example above, demonstrating how equivalent odds across formats yield the same implied probability.

How do you calculate implied probability from fractional odds?

To calculate implied probability from fractional odds, divide the denominator by the sum of the numerator and denominator.

Example: 3/2 Fractional Odds

Fractional odds of 3/2 show $3 profit on a $2 stake.

$\text{Implied Probability}=\frac{2}{3+2}=\frac{2}{5}=0.40\text{ or }40\mathrm{\%}$

This format yields the same 40% probability as the previous examples for equivalent odds.

What is overround in betting odds?

Overround, known as vig or juice, is the bookmaker's built-in profit margin embedded in betting odds. It is calculated as the amount by which the sum of implied probabilities for all outcomes exceeds 100%.

A two-outcome event like a coin flip would have fair odds summing to 100% implied probability. Bookmakers set lines so they total 105-110% (e.g., 55% + 52% = 107%), ensuring profit regardless of the result. This overround inflates each individual implied probability above the true likelihood, making direct comparisons between bookmakers difficult without adjustment.

A lower overround (e.g., 104% vs. 108%) means less vig distortion, so the implied probabilities are closer to the bookmaker's actual assessment of chances.

How do you calculate overround?

To calculate overround, sum the implied probabilities across all outcomes and subtract 100% to find the vig percentage.

$\text{Overround}=(\sum \text{Implied Probabilities})-100\mathrm{\%}$

How do you calculate no-vig or fair probability?

To calculate no-vig or fair probabilities, first convert all bookmaker odds to implied probabilities, sum them to find the total, then divide each individual implied probability by this total to normalize it back toward 100%.

$\text{No-Vig Probability}=\frac{\text{Implied Probability}}{\text{Total Implied Probability}}$

Example: Soccer Match

Consider a match with Arsenal Win at 2.10 decimal odds, Chelsea Win at 3.40, and Draw at 3.60.

Step 1: Calculate implied probabilities.

$\text{Arsenal}=\frac{1}{2.10}\approx 47.6\mathrm{\%}$

$\text{Chelsea}=\frac{1}{3.40}\approx 29.4\mathrm{\%}$

$\text{Draw}=\frac{1}{3.60}\approx 27.8\mathrm{\%}$

Step 2: Sum the implied probabilities.

$\text{Total}=47.6\mathrm{\%}+29.4\mathrm{\%}+27.8\mathrm{\%}=104.8\mathrm{\%}$

Step 3: Calculate no-vig probabilities.

$\text{Arsenal No-Vig}=\frac{47.6\mathrm{\%}}{104.8\mathrm{\%}}\approx 45.4\mathrm{\%}$

$\text{Chelsea No-Vig}=\frac{29.4\mathrm{\%}}{104.8\mathrm{\%}}\approx 28.1\mathrm{\%}$

$\text{Draw No-Vig}=\frac{27.8\mathrm{\%}}{104.8\mathrm{\%}}\approx 26.5\mathrm{\%}$

The adjusted probabilities sum to 100%, revealing the bookmaker's estimated true odds without margin.

What are common mistakes when calculating implied probability?

The most common mistakes bettors make when calculating or interpreting implied probability include:

1. Ignoring the vig or overround by treating implied probabilities as true chances despite their sum exceeding 100%, which overstates bookmaker assessments.
2. Mixing up odds formats by applying decimal formulas to American odds or vice versa, yielding incorrect percentages.
3. Failing to shop odds across sportsbooks for better value.
4. Confusing implied probability with personal true probability estimates.
5. Using outdated odds without considering context like injuries, weather, or lineup changes.

How do you avoid implied probability calculation errors?

To avoid implied probability calculation errors, follow these practices:

1. Sum implied probabilities across all outcomes to spot and adjust for vig by dividing each probability by the total for fair odds.
2. Double-check the odds format before calculating and use the precise formula for that format.
3. Compare current lines from multiple sportsbooks using odds comparison tools.
4. Form your own probability models from data or analysis separate from bookmaker odds.
5. Refresh calculations with live updates as odds change.
6. Practice with simple examples like coin flips to grasp break-even thresholds. Fair odds would be 50/50, but vigged odds at -110 on each side equal approximately 52.4% implied probability each.
7. Track your win rate against implied probabilities over time to refine betting strategy.