How Simple Maths Can Be Used To Beat The Bookies

March 16, 2021

How I used maths to beat the bookies

You don’t have to be an expert gambler to make a profit with an online betting site gamble.

Online betting is big business these days. You can access a bookmaker website through PC, laptop, tablet or Smartphone. There’s also the chance to download the app for ease of use on the move, with most new bookies now offering In-Play betting and the chance to Cash Out for a profit.

Naturally, the house often wins, especially when it comes to In-Play betting where the margins aren’t as tight and that means that punters face an uphill struggle to beat a trader with several algorithms at his hands.

However, it’s important to note that pre-match betting on football matches can yield a profit and you don’t always need to know a great deal about the teams concerned.

While plenty of betting customers have different ways of reading the form and pay special attention to injury information before striking a wager, there are others who simply follow a simple mathematics program.

This can be achieved in a number of ways. You get the bonus “abusers” who will use maths when they receive a free bet to ensure that they bank a profit whatever happens in a football match.

The emergence of betting exchanges means that trading out a free bet for a modest profit is achievable even if the process is slightly complicated with regard to how you do this.

Then something has come along called “Soccermatics”, a concept that has been introduced by a mathematician called David Sumpter who had previously rarely gambled on a sporting event but recently turned his attention towards online betting. soccermatics


In a recent article featuring in “The Economist”, Sumpter has explained the secrets behind his methods, pointing out how the bookmakers price up football matches and suggests different ways that customers with little betting knowledge can emerge with a tidy profit over a long-term basis.

Indeed, a lot of customer losses come from short-termism where a certain method is employed for a short spell only for the person to realise only a small gain or even an initial loss.

However, the methods described by Sumpter should theoretically result in small gains over a long-term basis. Naturally, as confidence (and hopefully profit) grows using a certain methodology, then a larger staking plan can be executed to good effect.
short term long term

Until autumn 2015, Sumpter “had never got over the entry barrier posed by opening up an account and feeding in my credit card details”.

However, in the previous months, he had developed a maths technique to beat the bookies and wanted to deploy one final experiment before sending off his book draft to the publishers. This experiment would hopefully bear fruit and strengthen “Soccermatics” and what it can bring to the greater world of punters.

During the first half of the 2015-16 Premier League season, Sumpter developed a mathematics model and he told The Economist that the model would attempt to predict the outcome of football matches in a more accurate fashion than a bookmaker such as bet365, Ladbrokes or Paddy Power. bet365

Premier league logo


One of the first things recommended by Sumpter (and this very site) is to ensure you have betting accounts with several operators. It simply doesn’t pay (literally) to have one or two bookmaker accounts if you’re serious about making a profit margin over a long-term basis.

The odds differ across the board every time a football match is played. Some bookmakers are prepared to take a position against a certain side, whether it’s just a hunch or based on some statistical model that is being employed within that particular trading room.

It should also be noted that a lot of the time, the prices are dictated by the amount of money going on each team. For example, Arsenal open their 2016/17 campaign against Liverpool and might be chalked up at even money to win.

However, should a bookmaker get a deluge of bets on the Gunners to win the match, they might trim Arsenal to 10/11 or even 4/5, thus reducing the payout every time someone backs the London club.

Now, this deluge of bets might have a story behind it, eg a new Arsenal signing or Liverpool losing one of their best players. Or it might just be that a customer wants to back a favoured team at home and let’s face it, a lot of people like backing the favourites.

Sumpter is keen for everyone to understand the difference between odds and probabilities. So for example, if Arsenal were even money, then that suggests that the Gunners have a 50% chance of winning a football match. If they were 2/1, then they have a 33% chance of winning in the eyes of the bookmaker.

Money lines betting

According to the mathematician, “you need to do the odds-to-probability calculation every single time you place a bet. Before you part with your money, assign probabilities to each potential outcome and compare these with the odds”.

So effectively, you are creating your own “tissue” where you assign the odds for each game before comparing and contrasting with the bookies. He then suggests (naturally) that you should only bet where your implied probability is higher than the bookmaker odds.

There are several models which Sumpter has rejected along the way, with celebrities often making fun predictions which wouldn’t win money over time. The Euro Club index and “expected goals” were also dismissed after being tested out after flimsy results accordingly.

However, the “odds bias model” was unearthed to be the most reliable of all. This was especially the case when it came to backing the draw in big matches where it appears that punters aren’t fond of sitting on the fence.

Indeed, the hype surrounding these matches and the tribalism of Arsenal meeting Chelsea or Manchester United facing Manchester United means that bookmakers take a huge number of bets on one team or another, leaving the draw price to drift and shrewd punters to get on board.

The professor is at pains to point out that modelling systems on football betting need to evolve and be freshly-devised over time. You can’t simply stick to the ethos of “betting on the draw in big matches” as bookmakers will reduce the odds accordingly if enough people start doing this.

The one tip that Sumpter produces for The Economist is the 5/2 about Wales beating Russia during the group stage and he recommends placing bets at these odds on a regular basis.


Backing teams to win at 5/2 or 2/1 naturally requires an element of bravery although it doesn’t actually require you to be right all the time. If you get one selection out of three right by betting at minimum odds of 2/1, then you will guarantee to break even at the very least and make a handsome profit.

We should also resist the temptation to Cash Out even when the offer is tasty, with the bookmaker always offering a cheaper option which doesn’t accurately reflect the odds of you winning on a bet.

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