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The Mathematical Principles Behind Sports Betting

mathematics in sports betting

If you have an interest in wagering on sports, then you probably take one of three main approaches. If you have a severely analytical mind, then you probably have thought about sports wagering in-depth. You may have read an article or two, to deepen your understanding of how the system works.

However, it’s a likely scenario that you still have many unanswered questions. Most likely, you’ll want to understand the mathematical principles and logic behind sports betting.

The second kind of person who wagers on sports is in it for the thrill. More than likely you’re an extremely intuitive bettor, who glances at the odds, but who tends to follow your gut feeling. You wouldn’t usually dream of reading about the technicalities behind sports betting.

The last kind of person is someone who attempts to turn a hobby into a career. You may have started with an intense love of sports, and now you’re trying to carry it into the business world. No one can blame you for that; we’d all love to make money off our passions.

However, since it’s your bread and butter, you’ll probably spend more time on it. Perhaps, you’ve spent vast amounts of time reading about possible techniques and strategies. Even so, you may not fully understand the mathematics behind sports betting. Whichever kind of person you are, one thing is for sure: you can undeniably benefit from understanding the underlying mathematics behind sports betting. In this article, we’ll be taking a closer look at just that.

Mathematics in Sports Betting

It might not have occurred to many of you that sports betting involves mathematics. Before we take a more in-depth look at mathematics in sports betting, we must discuss whether there’s much mathematics in sports betting.

Sports betting absolutely involves mathematics. However, it may be more than some of you think, but less than others. When it comes to setting odds, in particular, there are many mathematical principles to consider.

The Mathematics of Betting Odds

There’s a few who’ve been wagering on sports for quite some time and who will be aware of the main types of betting odds.

For those of you who aren’t, let’s have a cursory look at the types of betting odds available. The three main types of betting odds that are available on the usual markets are fractional, decimal and American.

Each of these types of odds gets expressed in a somewhat different manner, but they all involve a lot of mathematical concepts. Firstly, let’s have a look at the format in which bookmakers write each of these. This will give us our first insights into the mathematics of sports wagering odds.

American Odds

Decimal Odds

Fractional Odds

Changing Between Formats

How Sportsbooks Work

To fully understand the mathematical principles behind sports betting, we must look at how sportsbooks make money.

Firstly, a principle that adds mathematically and that you need to be aware of is the vigorish. Vigorish is the amount that a sportsbook adds to every wagering transaction. It’s essentially the bookie’s cut.

For example, on a $/€/£10 wager, you usually pay $/€/£11. The $/€/£1 extra is the sportsbook cut or vig for short.

When you lose your money, the bookie takes your $/€/£10 wager and uses it to pay another bettor who won. This way the bookie doesn’t fork out any cash to pay someone but instead gets to keep the vig from both wagers.

This is a principle that many sports bettors misunderstand. It’s also one that is vital for the sports betting industry.

How Bookmakers Set Odds

how bookmakers set odds

Before we look at how bookmakers set odds, we must understand why bookmakers set odds and what odds are.

Bookmakers set odds for two reasons. Firstly, they offer odds so bettors can see, at a glance, who the bookmakers expect to win — the second reason why bookmakers odds is to equalise the number of wagers placed on each team.

The aim of a bookmaker is not only to earn a profit but to convince people who wager on sports to bet equally on each side.

If it weren’t for sports betting odds, the chances are that most people would bet on the favourite contender almost all of the time.

The conception that makes people have is that the favourite is the contender that’s most likely to win. Typically, while the favourite contender may have the most running in their favour, the odds don’t speak much as to the probability of their winning.

So how’re they determined? This is where the mathematical part comes in. Bookmakers apply a sliding scale to two contenders when they come together.

Rather than setting odds on the favourites that are wildly higher than those on the underdog, many bookmakers will “borrow” statistical points from the favourite, and “lend” them to the underdog to provide almost equal odds.

Some other bookies have no qualms about providing odds that are wildly different. They base theirs on the statistical probability of teams winning. If not based on actual probability and statistics, then on the public perception of probability.

They’ll adjust the odds as bettors place their wagers in an effort to get bettors to wager on both contenders equally.

But What About Sports Betting as a Whole?

We’ve now spent quite some time having a look at how mathematical principles take their toll on sports betting odds. We’re sure that you’ve learned several things.

At this junction, you should be aware that all the varying odds formats are mathematically related. You can also convert them into each other format.

You should also know that bookmakers use mathematical principles. They mathematically adjust averages they set on odds to help bettors wager on both contenders equally.

In addition, you know that there’s a profit percentage, called the vig, added to every wager. This is another essential mathematical principle.

The Main Principle Behind Setting Odds

What is the most critical mathematical principle of all? That is quite simply how to calculate the odds themselves. As we’ve mentioned, bookmakers adjust the odds depending on how many people wager on each contender. If more people wager on the favourite, it becomes more expensive to do so.

The odds on the favourite become higher, so the payout also becomes higher in relation to your stake. The odds on the underdog become lower, so the payout becomes higher in relation to your stake and wagers cost less. This is because, as we explained previously, the sportsbook uses the funds from one bet to pay another.

As the sportsbook tries to convince people to bet on the underdog, they make it cheaper to do so. If you bet on the underdog and win, then you’ll earn more because more people believed the underdog would fail.

If you bet on the favourite and win, you’ll win less because everyone already believed the favourite would win. Bets on the favourite become more expensive because the sportsbook requires more money to pay out on bets on the underdog if the underdog wins.

Since betting on the favourites already comes at low odds, the sportsbook won’t require a large amount of money to pay all of the people who placed bets on the favourite if the favourite wins.

This is the central mathematical principle behind sports betting: a simple sliding average, combined with a basic algebraic formula. Since the 1790s, when betting odds were first introduced, this system has served bookies well. It will continue to do so for many centuries to come.


We hope that you’ve enjoyed this article about the mathematical principles behind sports betting. We’re sorry that we couldn’t provide you with even more information. However, to be fair, there are so many mathematical principles involved in the world of wagering on sports, that you’d require a whole book to look at them all in detail. In fact, we recommend that you do just that. There are very many books out there about the mathematics of sports betting. If you wish to become a real expert on the topic, then you’d be wise to give one of them a try. Also, do not forget to check our chart with the bookies with the highest odds for EU, USA and ROW. As for us, thank you for joining us, and may you have nothing but good odds.