Determining Fair Odds

The Difference Between Implied Probability and Fair Probability

What is Implied Probability

Implied probability is the probability suggested directly by the odds offered by a sportsbook, including the sportsbook’s built-in margin (vig or juice). It represents the likelihood of an event as perceived by the sportsbook and inherently includes a profit margin, making it slightly skewed or inflated from the actual likelihood.

For example, consider a standard sportsbook line with -110 odds on both sides of a spread:

Hawks +4.5: -110
Magic -4.5: -110

Converting -110 to implied probability, we get 52.38%. Adding both sides together, the total is 104.76%. It's not possible for the sum of all possible outcomes to be above 100%. However, this is how all sportsbook odds are set. The difference between 104.76% and 100% is the built-in margin sportsbooks use to profit, often called the margin, vig, juice, or overround.

What is Fair Probability

Fair probability, on the other hand, refers to the genuine likelihood of an event occurring. Understanding the difference between fair and implied probabilities helps bettors identify discrepancies and spot bets with positive expected value (+EV).

How to Determine the Fair Probability of a Bet

There are two main approaches to finding the fair probability, often called fair odds, or de-vigged odds. Top-Down and Bottom-Up.

Top-Down

• Using a sharp sportsbook's odds to determine the probability of winning and "de-vigging" the line to find the fair odds.
• Finding discrepancies based on outliers compared to the fair odds as determined from the sharp sportsbook.

Bottom-Up

• Creating your own model/algorithm to determine the probability of winning based on any number of factors.
• Using your model's probability compared to the odds sportsbooks are offering to find a +EV edge.

The DarkHorse Odds Bet Finders support a Top-Down approach to +EV betting.

De-Vigging Sportsbook Odds

Removing the vig from sportsbook odds is essential to determine the fair probability of an event accurately. There are several common devigging methods, each used based on specific assumptions about how sportsbooks apply their margin.

Sportsbooks generally don't distribute their margins evenly across all outcomes. Instead, they strategically allocate the vig based on several factors, resulting in uneven distributions. Key reasons why sportsbooks might not evenly distribute the vig include:

• Favorite-Longshot Bias: Bettors tend to overvalue "longshots" and relatively undervalue favorites. This may lead a sportsbook to disproportionately inflate margins on longshots due to bettors' tendencies to overvalue unlikely outcomes.
• Market Popularity: Certain popular teams attract significantly more public money, making a perfect balance impossible.
• Risk Management: If a sportsbook has significant exposure on one side, they may adjust margins unevenly to balance their liabilities or discourage further bets on specific outcomes.
• Sharp vs. Public Money: Sportsbooks often differentiate between sharp (professional) bettors and public (casual) bettors, applying uneven margins to manage risks associated with sharper betting action.

All of these factors and more need to be taken into consideration when de-vigging odds in an attempt to determine the fair odds for a specific bet.

Common Devig Methods

Multiplicative

• How it works: Implied probabilities are adjusted proportionally to their size, preserving the ratio between outcomes.‍
• When to use: Commonly used for evenly matched events or when no specific market insight suggests uneven margin allocation.
• Also Called: Tradidtional or normalization.

Additive

• How it works: The margin is subtracted equally from each outcome’s implied probability.‍
• When to use: Useful for events with similarly competitive odds, though less accurate if implied probabilities differ significantly.‍
• Also Called: Equal Margin

Power

• How it works: Raises each implied probability to a power so that the total probability equals 100%, which slightly reduces larger probabilities more than smaller ones. This assumes the sportsbook’s margin skews toward favorites.‍
• When to use: When the market or sport shows a consistent favorite-longshot bias and you believe the margin is not evenly distributed.
• Also Called: Exponential method

Shin

• How it works: Uses Shin’s formula to estimate the level of insider trading in a market, then adjusts probabilities accordingly. It assumes the overround is partly due to asymmetric information, disproportionately affecting shorter odds.‍
• When to use: When betting in markets susceptible to insider knowledge (e.g., lower-tier horse racing, niche sports) or when you suspect asymmetric information is influencing prices.
• Also Called: Shin’s Insider Trading Adjustment

Goto

• How it works: Adjusts implied probabilities based on a parameter that accounts for the uneven distribution of margin between outcomes, often fitted from historical market data.‍
• When to use: When historical pricing data suggests sportsbooks bias the vig toward one side of the market, and you can estimate that bias.
• Also Called: Least Squares Method, Goto’s Margin Allocation

Probit

• How it works: Converts implied probabilities into z-scores using the inverse normal distribution, subtracts an equal margin in z-space, then converts back to probabilities. This allows for a non-linear margin removal, which is often more realistic for skewed odds.‍
• When to use: When odds are significantly skewed (heavy favorite vs. longshot) and you want a margin removal method that preserves the natural shape of the probability distribution.
• Also Called: Normal Model Method

Worst Case Method

• How it works: Uses all the methods listed above and chooses the worst case scenario.‍
• When to use: Best for being conservative in determining the fair odds or there is not enough market insight to clearly choose a different method.

Practical Example:

Consider a sportsbook line with odds:

• Home Team: +246 (implied probability: 28.90%)
• Away Team: -276 (implied probability: 73.40%)

Total implied probability = 28.90% + 73.40% = 102.30%

Using the Multiplicative method:

• Fair Odds Home Team = +254
• Fair Odds Away Team = -254

Using the Additive method:

• Fair Odds Home Team = +260
• Fair Odds Away Team = -260

Using the Power method:

• Fair Odds Home Team = +264
• Fair Odds Away Team = -264

Using the Shin method:

• Fair Odds Home Team = +260
• Fair Odds Away Team = -260

Using the Goto method:

• Fair Odds Home Team = +264
• Fair Odds Away Team = -264

Using the Probit method:

• Fair Odds Home Team = +261
• Fair Odds Away Team = -261

Using the Worst Case method:

• Fair Odds Home Team = +264 (from Goto and Power)
• FairOdds Away Team = -264 (from Goto and Power)

Understanding and properly applying these devig methods significantly enhances your ability to estimate accurate fair probabilities, enabling better betting decisions and greater long-term profitability.