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Sports Betting Math

Mathematical Betting Strategies

In order to fully understand sports betting, you need to understand the math, which is why we’ve put together this guide here. We will run you through the essential sports betting math skills required.

While knowing your sports can help, mathematics is the more crucial element when it comes to making winning bets – just ask any pro. By looking at the sportsbooks calculate their odds/lines and the formulas that you can use to calculate your winning probability and value, we’ll leave you with the skills needed to get ahead of the game.

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Sports betting math – the basics

Math is involved in every single element of sports betting, from the odds calculation to winning probability and the stats of the teams and players that you are betting on. This applies to both pre-match markets and live betting on sport. The deeper you go, the more mathematics is required and the more complex the theories and formulae can get. That being said though, even getting a grasp on the most basic elements of sports betting math can really help you get off to a good start and increase your chances of placing winning wagers. As an example, let’s start off with the odds and lines.

Sports betting math – behind the odds and lines

The first thing that you need to know in sports betting is how much you stand to win, and the easiest way to do this is by reading the odds and lines. Here in the US, American odds is the most commonly used format and has been specifically designed to allow bettors to calculate their potential payout.

There are two types of numbers that you have to deal with when it comes to American odds – positive and negative odds/lines. With positive number odds and lines, the stated amount tells you how much profit you stand to make from a $100 stake. With negative number odds, the stated amount tells you how much you would have to bet in order to yield a $100 profit.

Let’s take a look at an example below using an NBA game: 

Grizzlies -150

Celtics +130

Calculating implied probability

While understanding how to read odds and lines is important in terms of calculating your potential payout, the most important thing when it comes to the basic math behind sports betting is in calculating your implied probability. The formula for calculating implied probability from American odds is a little complex. If we use the Celtics +130 odds as above the formula is as follows:

100/ (Odds + 100) = Implied probability

100/ (130 + 100) = 0.434 (43.5%)

The good news is that there are plenty of betting sites odds and lines calculators out there to help you to calculate the implied probability at the click of a button. The most important thing with implied probability is simply to know it and know how best to use it going forward.

The sportsbooks implied probability vs reality

One of the most important things to be aware of when it comes to sports betting math is that the implied probability that you can calculate from the odds is the sportsbook’s implied probability and not the real one. Confused? Allow us to dig a little deeper.

Let’s use the above example again and take a closer look with both the odds and implied probability represented: 

Grizzlies -150 (60)

Celtics +130 (43.5)

You may have already noticed that 60+43.5 = 103.5%. The more switched-on among you will be aware that it’s impossible for the total probability of anything to be greater than 100%. There is a reason behind it, and to understand that, we have to understand the overround.

Understanding the overround

The overround refers to the extra margin that the sportsbooks add to their odds in order to secure a profit for themselves regardless of what the outcome is. Let’s once again use the above example, where the sum total of the probability based on the total odds is 103.5%. That additional 3.5% is essentially the markup that the bookies have added to the real odds and probability in order to protect their profits.

Using implied probability to find the most valuable sportsbook

Now that you know about the existence of the overround and implied probability, you can use that to find more valuable bets and the most valuable sportsbook overall. By looking at a sportsbook’s odds and lines across various different sports markets and betting lines, you can now calculate how much they mark up on their odds and lines on average. If we refer again to the above example, 103.5% is actually pretty good. The market average, in general, has been falling in the US as competition continues to grow in many states, but generally speaking anything under 110% can be considered pretty good.

Sports betting math – Expected Value

So far the sports betting math that we have gone over covers most of the basics, but now we’re going to dive into an equation that is the bread and butter of most professional gamblers – Expected Value (EV). This refers to the calculation used to determine how much profit or loss you would make on the same bet time and time again. As a result, positive EV bets are considered to be worthwhile, while negative EV bets are not. But how does it work exactly? Let’s take a look …

EV in basic terms

Before we get down to the actual mathematical specifics of it, let’s first take a look at how EV works using the easiest of all gambling examples – the coin toss. If you were to bet $10 on heads in a coin toss using the real odds of +100 (50% probability), your expected value would be zero, as if you were to bet $10 on repeated coin tosses at +100, you would on average win the same amount as you would lose.

However, let's now say that the person tossing the coin wants to make things more appealing to you, and offers you odds of +110 for heads. If you’re still wagering $10 every time, the EV of your bet has now risen to +0.5, indicating that you would now end up on average making $0.50 profit per coin toss.

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Sports betting math – the EV formula

The above example makes things simple and can be calculated at a glance. Odds and lines of +110 being offered on a coin toss is also far from realistic. So how then does calculating the EV work for a real-life sports bet? It’s actually fairly simple, and the formula for calculating your EV is as follows:

(Profit x Winning probability) - (Loss x Losing probability)

The profit figure above is found by calculating your total potential returns from your bet and then subtracting your stake. Your loss figure is equal to the money you are staking on your bet, as that is the total amount you stand to lose.

If we once again use the example from earlier, and we decide to place $10 on the Grizzlies at -150 with an implied winning probability of 60%. To find your profit, you would first need to convert -150 into decimal odds, which is 1.67. Your total returns would then be $10 x 1.67 = $16.70. If you subtract the $10 from that $16.70, you get a total potential profit of $6.70.

Your EV calculation for this bet would therefore be as follows:

(6.7 x 0.6) - (10 x 0.4) = $0.02

This means that you would stand to make a $0.02 profit were you to repeat this bet, which admittedly isn’t much. However, if we refer back to the section above, it’s important to remember that this is the sportsbook’s implied probability and therefore not necessarily the real one. Therefore, you could use your own knowledge, twinned with math, to calculate the real implied probability. Which could alter the outcome significantly one way or the other.

Calculating EV using the real implied probability

You might decide that the Grizzlies actually have a 70% chance of winning and the Celtics just 30%. If this were the case, your EV for a $10 bet on the Grizzlies at -150 would be as follows:

(6.7 x 0.7) - (10 x 0.3) = $1.69

If you look at this example, you can see how big a difference a seemingly small disparity between the sportsbook’s implied probability and the real one can make with regards to your EV. However, it could also work the other way as well. For example, if the real probability of the Grizzlies winning is actually just 55%, then your EV would be:

(6.7 x 0.55) - (10 x 0.45) = $0.80

Sports betting math – finding the real probability

The above examples are all well and good, but how can you use sports betting math in order to calculate the real probability? This is where things can get a little bit more complicated, and your knowledge of sports and what’s happening with the sportsbooks comes into play.

The main thing that you do have to go on is the sportsbook’s overround. If we refer again to the earlier example, we remember that the sportsbook’s odds and lines total combined probability was 103.5%. We therefore know that 3.5% has been added to the total realistic probability. In an ideal world, we would like to think that 1.75% has simply been added on to the probability of each outcome. Sadly, it’s never that straightforward.

If you want to find the true probability, then you will need to use your sports knowledge and get extremely technical. You could weigh up factors such as the strength and attacking values of each team in numbers, for example.

Does this render the EV calculation useless?

Even if you don’t go as far as to calculate the accurate realistic probability of your outcome coming to pass, the EV calculator is far from useless. It still gives you a very good indicator of how valuable your bet is. More crucially, it can be used to help you to find the most valuable sportsbook for each bet. Something that is crucial for a number of popular strategies, including no-risk matched betting.

Sports betting math – the verdict

We’ve dug deep into the basics and essentials of sports betting math throughout this article here today. We therefore hope that we have left you with some knowledge as to how you can use maths to enhance your chances of placing winning wagers and taking advantage of sportsbook promotions. Just remember that when it comes to sports betting math, you can never stop learning. It might be a long journey, but once you start, the only directions you can move in are onwards and upwards.

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Sports betting math FAQ

🔢 How do you do sports betting using math?

Like it or loathe it, sports betting and math are massively interlinked in multiple ways. While you might like to think that your knowledge of sports is the key to making winning bets, it’s not worth much without the math skills on your side. Fortunately, the betting and math guide here at PromoGuy is on hand to help you out.

🤔 How does the math work with betting odds?

There are many ways math works in betting odds/lines, and the more you understand, the more it can help you. There are two main angles you need to think of here - your point of view and that of the sportsbooks. If you’re interested to find out more about how you can use math to your advantage in sports betting, then head on over to our guide here at PromoGuy. The guide outlines how you can use math to take advantage of sportsbook new user promos, as well as other offers.

💸 How are sports betting payouts calculated?

The answer to this largely depends on the odds and lines format that you are using. There are three main odds formats used to calculate betting payouts and winnings in the world today – fractional, decimal, and American. Discover how each one works in our guide by following the link to our site at PromoGuy.

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