Sports betting falls under the category of gambling throughout the world. The situation is no different in the rest of the world, by the way. Nevertheless, this creates a slightly distorted picture. It creates the impression that luck alone determines winning or losing. And although there are certainly many factors in areas where the bettor cannot influence the outcome, which can cause even largely safe bets to fail, while the occasional big win might be possible with underdog bets, it is still possible to bet based on mathematical principles.

The theory is both simple and effective. If a bet has a positive expected value, you'll inevitably make a profit at some point as the number of bets increases. Losing bets are thus taken into account, as are winners whose returns outweigh the losses. And if a bet has a fundamentally positive expected value, which can be determined through a mathematical calculation in conjunction with the current odds, this is referred to as value betting.

Today's sports betting guide will, of course, focus on the mathematics behind sports betting. We'll not only show you exactly how to calculate such value bets, but also how betting odds can be converted into probabilities. This will lay the foundation for your betting behavior to gain a mathematical foundation. Move away from gut feeling (emotion) and toward sustainable betting with common sense and reason (rationality). While luck and bad luck may still play a role, as we'll now show you, they're ultimately just two additional factors that can be calculated using the techniques in this sports betting strategy.

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Basics of Value Betting & Positive Expected Value

It's essential to know that all non GamStop casinos odds are always based on probabilities. At least, in the first instance. So, if the untouched odds appear online at your chosen bookie, they are mathematically calculated so that the bookmaker would make a profit regardless of the outcome. This is possible because the payout ratio is never 100%, but rather between 90 and 95%, depending on the provider—sometimes even lower.

For example, assuming a 50:50 situation exists in a 2-way system, with very few exceptions the following odds distribution will probably always be found: 1.90 for both tip 1 and tip 2.

However, bookmakers' odds are constantly evolving once they're online. This is a highly fascinating topic overall, one that will eventually warrant its own sports betting guide, as odds developments can, in turn, favor a number of other value bets if you learn to roughly anticipate the movement through knowledge of the background. At this point, however, it should be briefly mentioned that a bookmaker's odds always develop according to the market principle of supply and demand. This means: If, in the aforementioned 50:50 situation, two-thirds of all bettors suddenly bet on Tip 1, while Tip 2 is hardly played, the odds for Tip 2 will rise to make it more attractive, while, conversely, the odds for Tip 1 will decrease – even though the 50:50 starting position remains virtually unchanged.

However, upon closer inspection, the idea behind this becomes clear very quickly: the bookies ensure that they ultimately make a profit regardless of the outcome. And instead of the extremely large profit that would be generated with a two-thirds vs. one-third distribution if tip 2 comes out, but the likely loss for tip 1, these adjustments rarely result in a truly large profit, but instead, the bookies win with practically every single tip, which also explains the success and proliferation of betting shops, sports betting platforms, and providers.

Long story short: Odds are always based on mathematics. And that means, conversely, that bets that are also based on mathematics can result in winnings in this system. Because even though 95% of all people who regularly place sports bets lose money, there are also those 5% who make a small profit every month. So let's now turn a ignore to how this works in theory.

Calculate and determine value bets – follow these three steps

So let’s get specific by considering the following three steps.

• (1) Calculate probabilities of occurrence
• (2) Calculate expected value
• (3) Only play bets with positive expected value

The first step: calculating probabilities of occurrence

So, before we delve into the mathematical formulas that you can use to determine whether a bet is value or to convert betting odds into probabilities, let's first move on to the first step. This involves calculating probabilities of occurrence.

The good news is: you don't have to win every ticket to make a profit at the end of the month. Quite the opposite. Losing tickets are already factored into the strategy. The bad news, however, is that you have no choice but to carry out a thorough analysis for every game you want to bet on in order to determine the approximate probability of each outcome. If we stick with the example of the 50:50 situation, we have a 50% probability of either winning or losing – provided we are using a 2-way system. If a draw is added to the 3-way system (usually listed as Tip X), another variable is added that must be taken into account. And anyone who follows football regularly knows that statistically speaking, not every third game ends in a draw, meaning that in the classic 3-way system the same 33.3% probability of occurrence can be applied to all three ways – even in perfectly even matches.

Instead, it's always about looking at a number of factors that narrow down a potential outcome of the game. For example, you can consider the following aspects:

• What is the current standings/place in the world rankings?
• What is their current form? (e.g., looking at the last five games)
• How did the last duels between the two teams/players end?
• Does the location of the event matter? (e.g., home advantage)
• Could one of the two sides be particularly motivated? (e.g., because they want to return the favor)
• Who has the physical advantage? (Fitness, freshness, length of the break; especially in the Bundesliga, for example, the team that played internationally during the week is likely to be far more stressed)
• In team sports: Is a team missing one or more key players? (suspended or injured)
• Were there any coaching changes or other external influences?
• Has either party regularly fallen short of expectations recently?
• Does either side have something to make amends for?
• How do the relevant experts assess this encounter?

Of course, there are countless other aspects you can (and should) consider. These questions should therefore primarily be understood as food for thought to get the analysis rolling. The real art then lies in learning to translate all of these answers into concrete figures.

For example, you might notice in a football match that the home team is significantly lower in the table, but now, with their own fans behind them, they're playing against an opponent they haven't lost to in years. The picture might gradually become clearer that things will be tough for the visitors again this time, if you notice, for example, that their midfielder is serving a yellow card suspension. Add to that the fact that the home team's new star striker used to play for the opposition and has more than a few scores to settle, which could boost his motivation to score here immeasurably.

Regardless of your analysis, you should ultimately assign a percentage probability to each outcome in the classic 3-way system. This could be 60% for pick 1, 25% for pick X, and 15% for the away team's win.

The second step: calculate the expected value

Now that we've arrived at these percentages, we can calculate the expected value. For this, we need the odds. To do this, log in to your trusted bookmaker and look up the betting odds. These could be, for example, 2.00 for Tip 1, 3.30 for Tip X, and 3.10 for Tip 2.

The whole thing again clearly:

• Tip 1 (Home team win): 2.00 // our calculated probability of occurrence: 60%
• Tip X (draw): 3.30 // our calculated probability of occurrence: 25%
• Tip 2 (Away team win): 3.10 // our calculated probability of occurrence: 15%

The formula you use to calculate the expected value is:

Probability x Odds = Amount in Euro you get back for 100 Euro stake

So let’s do the math:

• Tip 1: 2.00 x 60 = 120 euros
• Tip X: 3.30 x 25 = 82.50 euros
• Tip 2: 3.10 x 15 = 46.50 euros

So, if we choose Tip X, we statistically lose €17.50. With Tip 2, we lose more than half of our money in the long run (€53.50). Only with Tip 1 do we make a profit of €20. This is also referred to as a positive expected value, because this is where the value bets that professional punters look for are found.

The whole thing always depends on a detailed analysis. Another tipster could just as easily consider the away team's league position as the most important criterion, overlook all other factors, and thus find a positive expected value for tip 2, even though, upon closer inspection, this isn't even remotely true.

The third step: only play tickets with positive expected value

In theory, of course, we only make the stated winnings and losses after playing 100 tickets. Statistically speaking, only then would we have won those 20 euros with a 60% probability of occurrence, since we would have won 60 times and lost 40 times. So, to make a profit at the end of the day, you need to completely switch off your emotions and, in a purely rational and cool manner, only play bets with a positive expected value. And that can sometimes be the market whose probability of occurrence is just 10%. In other words, out of 100 of these bets, you would lose 90 times, but you would make those 10 times as much profit, so that the bottom line remains in the black.

The tricky thing is that probability has no memory, which is why this 90:10 distribution doesn't necessarily settle after 100 games. You could theoretically lose 200 or 500 times in a row before you get several winning tickets in a row. This is precisely why it's important to always choose the right stake based on your bankroll so you don't go broke. We'll explain how to do this in a separate article in due course. For these purposes, all you need to remember is that from now on, it should be absolutely taboo for you to place bets that don't have a positive expected value.

Last but not least, there are two more things you should keep in mind.

1. If the bookmaker has done his job perfectly, then the three odds that go online first will not have a positive expected value in any of the three scenarios.
2. Almost all bookies deduct a so-called betting tax from your winnings. This means that if you bet €100 at odds of 2.00, you won't receive €200, but rather around 5% goes to the tax authorities. In this example, that's ten euros, meaning you'd only receive €190 instead of €200 at odds of 2.00. If this is the case with your online bookmaker, you should definitely factor this into your calculations beforehand by multiplying the result in euros by 0.95 (with a betting tax of 5%) in the formula from the second step. With the €120 for Tip 1, the positive expected value would remain (result: €114).

Convert Betting Odds into Probabilities

Last but not least, you can also do the opposite, which often makes it easier for beginners to decide for or against a sports bet. Namely, by converting the betting odds you find at your chosen bookmaker into probabilities. We've prepared a formula for this as well:

100% betting odds = bookmaker's probability of occurrence in percent

Let's look at an example using real odds. A favorite is playing at home against the visitors, who are underdogs. The odds distribution in the classic 3-way system looks like this:

Tip 1: 1.50
Tip X: 4.33
Tip 2: 6.50

So let’s take a look at what the formula just presented spits out:

• (1) 100% 1.50 = 66.7%
• (2) 100% 4.33 = 23.1%
• (3) 100% 6.50 = 15.4%

This means that a positive expected value exists wherever you believe the actual probability of the respective event exceeds this percentage. For example, if you believe the 66.7% probability for a home team to win is reasonable, then the bet is playable.

However, caution is still advised when converting betting odds into such probabilities. Firstly, the betting tax is missing here. And secondly, that 66.7% would mean a zero-to-zero outcome. To generate a profit, you have to be able to exceed these percentages – ideally significantly. So, if you see 70% for Tip 1, it's still questionable whether you should really risk this bet, whereas an assessment that even 75% could be invested in this bet would be a crystal-clear decision.

Conclusion

In this article, we've shown you how to calculate value bets. We've presented you with a three-step guide that you should follow, without exception, for every game you want to bet on, provided you want to be one of the 5% of people who make a profit from sports betting. We've also shown you the formula for translating betting odds into probabilities. It's important to note that this “translation” should by no means be seen as a shortcut that will save you from all the aforementioned questions in the analysis process. The more meticulous you are in your analysis and the more numbers and data you incorporate, the more accurate your probabilities will ultimately be. And that means even more precise bets and, ultimately, more secure winnings.

We wish you much success with your sports betting and hope we have encouraged you to sharpen your own betting behavior with these applications of mathematics in sports betting in the future and to take it to a higher level.