Here is a fairly simple question with an equally simple and straightforward answer. How does one convert the odds ratio to the probability of winning in sports handicapping. Crazy as it sounds, this question was right up my high school baseball coach’s alley, as he was also my teacher in probability and statistics (some fun school class I had back in the day). And yes, I did just put fun and school in the same sentence. And no, I wasn’t being sarcastic. He always made baseball fun, whether at practice, driving on a bus to an away game, or in the game itself. And his class was fun as well (at least for me). No idea if he handicapped sports, or if he ever ran equations in his head any time he flashed the bunt or steal sign. Anyway, without further ado…

Flipping a Coin – What are odds?

So, we all probably have no doubt that a coin flip would result in 50% chance of heads and 50% chance of tails. The coin only has two sides. So here, we simple divide our desired outcome (1) by the two possible outcomes (2) and multiply by 100 to give us our answer in a percentage.

1 / 2 x 100

.5 * 100 = 50%

A roll of a die (or singular form of dice)

Die or dice, whatever you want to call the singular form of dice. We have one. It has 6 sides, what is the probability that we get a 3 from rolling it? Well, to answer this, we take the 1 desired result (the 3) and divide it by 6 (the 6 possible outcomes). Then we multiply the answer by 100 to put our answer in percentage form.

Convert Decimal Odds into Probability. If we use the decimal odds of 1.80 for this and use the following equation:. 1 / decimal odds x 100 = implied probability. So, 1 / 1.80 is 0.555 (rounded up to 0.56), giving the mathematical equation of 0.56 x 100 = 56%. This means that odds of 1.80 reflect a 56% chance of that particular outcome.

To convert odds to probability, add the successes and failures to find the total. Then divide the number of successes by the total to calculate the probability. Example: Suppose the odds of a casino game are 2:3. Since 2+3 = 5 we take 5 as the total. Thus the probability is 2/5 = 0.4 = 40%. Convert Fractional odds to probability. The most common form of odds are going to be decimal odds in the UK and here is how to convert decimal odds to probability.These are clear odds to read and for example the 6/5 odds on Liverpool from the example above means that for every 5 units you put on, you will receive 6 back as a profit. Finite Math Mini Presentation 3 Tre Swilling Q.2 Convert the probability 3/7 to odds. Do the same for the probability 0.2. Difference between probability & odds Probability: refers to the likelihood of occurrence of an event. Expressed in percent or decimal - Ranges from 0 to 1 Odds: refers to the chances in favor of the event to the chances against it.

1 / 6 * 100

.1667 * 100 = 16.67%

Here, we have a 16.67% chance of rolling our desired outcome.

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Types of Odds

The most common forms of odds used today are decimal odds, fractional odds and American odds (the moneyline). We will go through each below. First, however, why is this important? Well, by converting the betting odds into something often referred to as implied probability, we can better access the value of a particular market. Do they differ from what we believe the odds of winning should be? If the odds offered to us (the implied probability) are less than or greater than our personal assessment, then this would represent either an increase or decrease in betting value.

Decimal Odds – How to Convert Odds Ratio to Probability in Sports Handicapping

First on the above list, are the decimal odds. These odds are common in Europe. The decimal odds represent the amount that is won for every $1 wagered. Say for example the odds are represented as 2.5, this would imply that for every 1 you wager, you will gain a profit of 1.5 if the outcome was in your favor. Here, to convert odds ratio to probability in sports handicapping, we would have the following equation:

(1 / the decimal odds) * 100

or

(1 / 2.5) * 100

Quickly, doing the math in my head (kidding, I used a calculator), the answer is 40%

Fractional Odds – How to Convert Odds Ratio to Probability in Sports Handicapping

When I think of the odds represented in a fractional format, I automatically think of horse racing. Let’s say the odds of Aggressive Neil to win are represented as 9 / 2, how do we translate? Well the equation is as follows:

Denominator / (Denominator + Numerator) * 100

Or with our 9 /2 example:

2 / (2 +9) *100

Using my overused calculator, I get an 18.18% chance of winning.

American Odds (The Moneyline) – How to Convert Odds Ratio to Probability in Sports Handicapping

Used much in North America for sports such as baseball, basketball, hockey and others, the moneyline is actually not as confusing as one would first think. Each game or match will have teams with either a plus moneyline or a minus moneyline. A +180 for example would imply that for every $100 wagered the winnings would be $180 gross or $80 net. So, the plus moneyline would represent the underdog for the game or match.

Conversely, a -180 line essentially means the team is the favorite to win, and to win $100, one would need to wager $180. So, here, how do we convert these odds into the probability of winning in sports handicapping?

Well, in the case of the moneyline, we have the following equation for the plus moneyline:

100 / (plus moneyline +100) * 100 (to put it as a percentage)

Or using the example above,

100 / (180 + 100) *100

Here my calculator gives me a 35.71% chance of winning.

And for the minus moneyline, I basically use the absolute value or (in my simple terms) remove the negative sign in the value. The calculation for chance of winning would then look something like this:

(absolute value of negative line odds) / (absolute value of negative line odds + 100)* 100 (to put it as a percentage)

Or using above example:

180 / (180 +100) *100

And, here, my calculator throws out a 64.29% chance of winning.

Places Online to Convert the Odds Ratio to Probability in Sports Handicapping

Ok, so maybe I should have blurted out the following websites right up front. But now, we at least understand the formulas used to convert the odds ratio to probability in sports handicapping. One webpage I found that calculates these odds into a percentage is from aceodds.com. Here is the link.

Another webpage, I found is from actionnetwork.com. Here is the link.

Moneyline (American Odds) to Percentage Conversion Chart

I personally like the online calculators mentioned above for our topic and mission here. However, you may want a spreadsheet version of the calculations instead. If this describes you, I’ll throw a quick moneyline to percentage conversion chart at the end of this article.

Why Do the Odds that Bookmakers Give You Not Add Up to 100%

So, why is it that the odds that bookmakers offer do not equate to 100% when combined? For example, in major league baseball, let’s say the Seattle Mariners are visiting the Oakland Athletics today. The odds may have the game at Seattle Mariners +120 and Oakland Athletics -130. Do the above equations and we come up with the Seattle Mariners percentage value of 45.45% and the Oakland Athletics percentage value of 56.52%. Add the two and we come up with a total percentage value of 101.97%. What is with this figure? Well, that 1.97% is the bookmakers edge incorporated into the odds, their expected return for setting up the bet.

Why Do the Odds Move Throughout the Day?

So, you probably have noticed the lines moving throughout the day. These lines are not static? In our Seattle Mariners vs. Oakland Athletics game above (which I did grab from a past game played), we again have the odds listed at Seattle Mariners +120 and Oakland Athletics -130. These were not, however, the odds the game opened at. The opening odds were actually Seattle Mariners +107 and Oakland Athletics -127. So, why did this particular sportsbook move the line from +107 to +120 and -127 to -130? Well, most likely the lines moved to entice more action to the Seattle Mariners. The sportsbook wants to “balance the books”, and they will move the lines one way or the other to entice more action to one side of the equation.

In Summary

Hey, sportsbooks are around to make money for themselves. The lines may fluctuate throughout the course of the day in an attempt to match the bets as close to 50% one side and 50% the other. The left over percentage that we described above is how the books make money. Let’s say your assessed probability is of a greater percentage than that of the bookmaker’s implied probability. This creates an opportunity, a value betting opportunity.

And below is the a table of the moneyline to percentage conversion chart mentioned above.

Implied probability is the conversion of betting odds into a percentage. This tells us how often we need to win in order to break-even. Implied probability is used to isolate profitable wagers and calculate the bookmaker’s margin. This guide will teach you how to convert American, Decimal, and Fractional odds into implied probability as well as evaluating how big of an advantage any given sportsbook has over you.

What is Implied Probability

Implied probability is the direct conversion of the betting odds available at a sportsbook into a percentage. Because the bookmaker’s commission is factored in this reveals the break-even percentage. One can only justify placing a bet if they believe it will win more often than the implied probability.

Bookmaker’s adjust their markets in an attempt to attract an even amount of action to both sides of the game. This creates margins between the implied probability and the outcome probability. Taking advantage of this is the key to long-term sportsbetting success.

Let’s start off by taking a look at how we can convert American, Decimal, and Fractional odds into percentages. This will be a direct calculation from the bookmaker’s posted line so their commission will be factored in. This percentage will allow us to determine the break-even percentage.

American Odds into Implied Probability

When converting American odds into implied probability we need to differentiate between plus and minus odds. The calculations will be different for each one. Let’s take a look at the following NFL game:

For minus odds we we will divide the absolute value of the odds by itself augmented by 100. Here is the formula:

IP = Minus Moneyline Odds /( Minus Moneyline Odds + 100)

In the example above the Miami Dolphins have -150 odds to win the game. This means that their implied probability will be 150/(150 + 100) which simplifies to 150/250. This comes out to 0.6 which is 60%. When we have plus odds we will divide 100 by the odds augmented by 100:

Converting Between Probability And Odds

IP = 100/(Plus Moneyline Odds + 100)

The Baltimore Ravens have +130 odds to win the match. Their implied probability is given by 100/(130 + 100) which simplifies to 100/230. This comes out to 0.435 which is 43.5%.

Decimal Odds into Implied Probability

This is the easiest odds format to convert into implied probability. The only thing you need to do is take the reciprocal of the odds by dividing it into 1:

IP = 1/Decimal Odds

Manchester United have 1.36 odds to defeat Swansea. Their implied probability is represented by 1/1.36 = 0.735 = 73.5%. You would need to win this wager 73.5% of the time in order to break even. Swansea’s match odds are 9.50 which means their implied probability is 1/9.50 = 0.105 = 10.5%. You would need to win this wager 10.5% of the time in order to break even.

Fractional Odds into Implied Probability

Fractional odds can be converted into implied probability by dividing the denominator by the sum of the denominator and numerator:

IP = denominator/(denominator + numerator)

Let’s take Bournemouth with 10/11 odds against Watford. The numerator is 10 and the denominator is 11. We will retrieve the implied probability with 11/(11+10) = 11/21 = 0.524 = 52.4%. If you believe Bournemouth have more than a 52.4% chance of emerging victorious then you would be making a good bet!

Bookmaker Margins

You should have noticed that in the calculations above the implied probability for all sides of a given betting market do not add up to 100%. This surplus reflects the bookmaker’s margin. Their odds to not represent the statistical probability of an event. Knowing how to calculate bookmaker margins is crucial to ensuring that you are not getting ripped off. The larger the margin the more advantage the bookmaker has over you.

Calculating Bookmaker Margins

The margin will be expressed as a percentage above or below 100%. A market that is deemed fair would sit exactly at 100%. In order to calculate a bookmaker’s margin on a given betting market by summing the implied probability of all possible outcomes. Let’s look at an example:

In the match between Norwich and QPR the set of possible outcomes have odds of 1.80, 3.80, and 4.75 respectively. Converting these into implied probabilities gives us the following values:

1/1.80 = 0.556 = 55.6%

1/3.80 = 0.263 = 26.3%

1/4.75 = 0.211 = 21.1%

Next we will take the sum of all possible outcomes: 55.6% + 26.3% + 21.1% = 103%. The implied probability is 3% higher than a theoretical fair market. This means the bookmaker’s margin for this betting market is 3%.

What is a Good Margin?

As bettors we want to find bookmakers that offer the lowest margins possible. The industry average for most spreads, moneylines, and totals is around 5%. Anything higher than this should be avoided as you are putting yourself at an unnecessary disadvantage.

Removing Vig/Juice from Moneylines

Since implied probabilities are direct conversions of betting odds into percentages the bookmaker’s margin is factored in. The implied probability represents how often you would need to win a wager of those odds in order to break even. We can perform an additional calculation to remove the margin to get the true probabilities.

Start off by calculating the implied probabilities of all possible outcomes for the betting market you are working with. Let’s use the money line market for this NFL match between the Buffalo Bills and Philadelphia Eagles:

The Buffalo Bills implied probability is 1/2.70 = 0.370 = 37.0% and the Philadelphia Eagles implied probability is 1/1.50 = 0.667 = 66.7%. Next we will sum up the implied probabilities of all possible outcomes in order to evaluate the bookmaker’s margin. Here we have 37.0% = 66.6% = 103.7% for a margin of 3.7%. In order to calculate the true probabilities we will need to make it out of 100%. This is accomplished by dividing the implied probability by the sum of the implied probabilities of all possible outcomes:

True Probability = Implied Probability/(Bookmaker Margin + 100%)

Convert Probability To Odds Calculator

This means the true probabilities are 37.0%/103.7% = 0.357 = 35.7% for the Buffalo Bills and 66.7% / 103.7% = 0.643 = 64.3%. The sum of your true probabilities should add up to 100% (which is the case here).

Profitable Sportsbetting

To become a winning sportsbettor one must place wagers that hold positive expected value. There exists a margin between the real life winning percentage of a given betting market and that implied by the bookmaker’s odds. In the next guide we will discuss how to create a projection model in order to estimate the real winning percentages of multiple betting markets. Comparing these numbers to the implied probabilities we learned how to calculate today will reveal which wagers have the most value.