# Implied Probability in Sports Betting

If you want to be an effective sports handicapper, you should understand implied probability for sports betting markets. It is useful information because it gives you the ability to easily understand the true probability of an event’s outcome.

When you recognize the likelihood from a statistical perspective, you can effectively weigh the risk vs. reward equation. This is key because successful gambling is all about value for your betting dollar and understanding how sports betting odds work.

When the potential payout is sufficient based on the amount that you are going to bet, you can feel confident placing a wager. It is satisfying to win a bet that you made with confidence based on implied probability. Even if you lose, you can accept it when you know it was a sound risk.

### How do I calculate implied probability in betting?

The first step is to gain an understanding of the three distinct types of odds that are utilized in sports betting. Moneyline or American odds are the traditional odds for sports betting in the United States.

This is a depiction of the moneyline for a hypothetical game between the Los Angeles Chargers and the Cincinnati Bengals.

• Chargers +146
• Bengals -174

The numbers represent the return or stake for a \$100 wager. If you don’t calculate the implied probability, these numbers would not give you any actionable insight. They let you know that the Bengals are expected to win, but you get no precise insight into the actual probability percentage.

Decimal odds are used in European countries mostly, and this method is very simple and straightforward.

• Chargers 2.46
• Bengals 1.57

These decimal odds tell you how much you would win for every dollar that you bet on each side. The numbers include the stake that will be returned to you along with the profit. With American odds, the original bet amount coming back to you is not included.

Fractional odds are known as British odds because they are popular in the UK. These odds are also used at American horse racing tracks. For the purposes of this example, we will use fictional Super Bowl futures odds for these teams.

• Chargers 15/1
• Bengals 12/1

If you bet on the Chargers, you win \$15 for every dollar you bet. You make a \$12 profit for every dollar you bet on the favored Bengals.

When you use implied probability for sports betting, you convert these odds to a percentage. It will represent the likelihood of the outcome. So, if you calculate a 50% implied probability on a certain bet, it would be successful 50% of the time.

### Implied Probability using American Odds

You can use an implied probability calculator that will convert odds for you. However, you will not be dependent if you learn how to calculate implied probability on your own.

The method that is used to calculate implied probability with positive American or moneyline odds starts with a relatively simple equation. This is the standard formula:

• 100/(American odds) + 100 x 100

Let’s use this for a +300 underdog.

• 100/400 = .25 x 100 = 25

This means that there is a 25% probability of the outcome happening.

There is a different formula used to convert negative American odds:

(odds with minus sign removed)/(odds with minus removed + 100) x 100

Now we’ll use a -300 favorite as the example.

• 300/400 = .75 x 100 = 75

The implied odds are 75%.

### Implied Probability using Decimal Odds

The way that you calculate the implied probability percentage for decimal odds is simpler and more straightforward.

1/(decimal odds x 100) = implied probability

What you see below is an example of the implied probability conversion for decimal odds of 4.0.

• 1/400 = .25 x 100 = 25%

There is a 25% implied probability. This is identical to the probability for the initial example because +300 converts to decimal odds of 4.0. We will explain the methods for converting the different types of odds in another section.

### Implied Probability using Fractional Odds

Fractional odds that are used in England and Ireland are calculated using another rudimentary equation.

(denominator)/(numerator + denominator) x 100 = implied probability

We will use +300 converted to fractional odds of 3/1 to demonstrate.

• 1/4 = .25 x 100 = 25%

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## How to Convert Betting Odds

You can convert any odds type to any other if you memorize the basic formulas. This ability can allow you to fluidly move from one form to another if necessary.

### American to Decimal

To convert positive American odds of +300 to the decimal line, you divide the odds by 100 and add 1.

• 300/100 = 3 + 1 = 4.0 decimal odds

If you want to convert negative American odds of -300 decimal odds, you divide 100 by the American odds without the minus sign and you add 1.

• 100/300 = .33 = 1 = 1.33 decimal odds

### Decimal to Fractional

When you are converting decimal betting odds to fractional odds, you subtract one from the decimal odds to get the numerator, and the denominator is 1. When you do this, it will not be an exact match unless the decimal ends in 0.

4.0 - 1 = 3/1

With a number like 4.5, if you subtract 1, it comes to 3.5/1, and there are no decimal points in fractional betting odds. However, we can simply convert 3.5/1 to 7/2, which is a number that is a commonly used by oddsmakers.

### American to Fractional

It is very easy to convert positive American odds to fractional odds. You simply subtract 1 from the decimal number and add 1 as the denominator.

4.0 – 1 = 3/1 fractional odds

To convert negative American odds of -300 to fractional odds, you divide -100 by the American odds.

-100/-300 = 3.333 or 1/3 fractional odds

### Fractional to Decimal

The fractional to decimal conversion is another simple one. You divide the numerator by the denominator, and you add 1.

Here is a depiction of the formula for converting fractional odds of 3/1.

3/1 = 3 + 1 = 4.0 fractional odds

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## Implied Probability Chart

American OddsDecimal OddsFractional OddsImplied Probability
-500 1.21/5 83.3%
-450 1.222/981.8%
-400 1.251/4 80%
-3501.29 2/7 77.8%
-300 1.33 1/3 75%
-275 1.36 4/11 73.3%
-2251.44 4/9 69.2%
-200 1.5 1/2 66.7%
+100 21/1 50%
+900109/110%
+1000 1110/1 9.1%
+200021 20/1 4.8%
+5000 51 50/1 2%
+10000 101 100/1 1%
+1000001001 1000/10.1%

## Implied Probability in Sports Betting

Now that you have an understanding of the nuts and bolts of implied probability in sports betting, we can look at the practical utilization. Let’s say that you are betting an NFL game at one of the online sportsbooks. You are handicapping games to look for an edge.

You certainly need one because there is a built-in house edge via the sportsbooks margin or vigorish. If bettors place an equal amount of money on both sides of a matchup, the sportsbooks can’t lose because there is a difference between what they have to pay out what they brought in.

For example, let’s say that five people bet \$110 on the over in an NFL game at -110, and five people bet the same amount on the under at -110. The sportsbook is holding 10 x \$110, which is \$1100. It will pay out \$210 to each of the five winners.

That’s \$1050, but the sportsbook was holding \$1100 in wagers placed by these 10 bettors. It makes a \$50 profit, and this is multiplied by thousands if it is a popular bookmaker.

Bet \$5 on NFL, Get \$200 if You Win

The utilization of implied probability can neutralize that edge. A sportsbook will originally set the opening lines based on algorithms with some human adjustment at times. This number is supposed to attract equal betting action on both sides, but it is not foolproof by any means.

A sportsbook will adjust the odds as often as necessary in an effort to balance the action. If more people are betting the over in an NFL game, they will increase the total in increments until they have evened out the action.

So, a lot of people think that you are trying to outsmart the sportsbook when you make a sports wager, but this is really not the case. You are attempting to find weaknesses in the lines that exist because they were set as a response to public betting sentiment.

When you calculate implied probability based on the odds that you are seeing at any given time, they may be different from the true odds. Your own research can be used to help you find flaws in the line, and there is another element that is more concrete.

Very sophisticated algorithms were used to set the lines in the first place. These betting sites are big businesses, and a lot of resources are devoted to the creation of accurate lines. You can calculate implied probability using the opening line and compare it to the percentage for the bettor-adjusted line.

If you bet against the direction of the line movement, you are putting your trust in the bookmaker rather than the public. This is called the “contrarian” approach, and some pro handicappers have found that it is successful over a large sample size.

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