Poisson Distribution in Sports Betting – Complete Guide

Patrick Lynch
By Patrick Lynch
Sports & Casino Expert
Updated Jan 18, 2023
Read time 14 min

Several modern betting strategies are devised from mathematical formulas developed decades or even centuries ago.

One such example is Poisson distribution, created in the 1800s by a French mathematician named Siméon Denis Poisson. He originally designed it to outline the probability of an event occurring a certain number of times within a given time or space interval.

However, mathematically inclined punters now use Poisson distribution sports betting to get an edge over the bookie.

In this article, we explain Poisson sports betting. We’ll provide a detailed example, analysis of the right betting markets to use, as well as investigate Poisson distribution’s potential limitations.

What Is Poisson Distribution in Sports Betting?

In sports betting, Poisson distribution involves using teams’ attack and defense stats to predict the most likely scoreline. You can utilize it to determine the likelihood of how often an event will happen during a specific period. So, in essence, it’s a mathematical concept that converts mean averages into a percentage probability.

From there, you get a decent idea of whether a specific betting market is worth pursuing.

Furthermore, you can use Poisson distribution betting to convert the calculated probabilities into odds to determine if you’re getting value for your bet. After all, if the price isn’t right, you will lose money in the long term, regardless of your strike rate.

So before learning how to calculate Poisson distribution for football betting, you need the following information:

  • The total number of home and away goals scored in the league you’re betting on
  • The average number of home and away goals per match in the league

Additonally, you need data specific to both teams when analyzing a game. For example, if you want to bet on a match between Everton and Newcastle United at Goodison Park (Everton’s home ground), you will need the following:

  • Everton’s average goals scored at home
  • Everton’s average goals conceded at home
  • Newcastle’s average goals scored away from home
  • Newcastle’s average goals conceded away from home

Use this information to calculate the home and away team’s Attack Strength and Defense Strength. At this point, you can calculate each team’s goal expectancy and use the Poisson formula.

Eventually, you’re positioned to predict the game’s outcome based on the data you uncover. Finally, you can check the bookmaker’s odds and see if there are any value betting opportunities.

How To Calculate Poisson Distribution for Football Betting

Poisson sports betting is widely used in soccer, although it applies to different low-scoring team sports. Let’s find out how it works in practice by providing an example.

The upcoming Manchester derby between Manchester United and Manchester City at Old Trafford seems like the ideal option.

It is an eagerly anticipated clash between the defending champions City and a United side showing encouraging sides of improvement under a new manager. To begin, we need the average goal expectancy for the English Premier League in the current season and the Attack and Defense Strength of both teams.

You can easily get this information at the official EPL website.  We quickly find the following data:

Now let’s look at the data for the two teams involved in the game:

Calculating Average Attack and Defense Strength

To get a team’s Attack Strength, you divide its average number of goals by the league average.

  • Manchester United’s Attack Strength: 1.88 / 1.63 = 1.15
  • Manchester City’s Attack Strength: 1.75 / 1.22 = 1.43

Therefore, to get a team’s Defense Strength, divide the average number of goals conceded by the league average:

  • Manchester United’s Defense Strength: 0.5 / 1.22 = 0.41
  • Manchester City’s Defense Strength: 0.75 / 1.63 = 0.46

Calculating Goal Expectancy

Next is calculating how many goals each team is likely to score, also known as ‘goal expectancy.’

So to get United’s goal expectancy, we multiply their Attack Strength by City’s Defense Strength AND the league average of home goals scored:

1.15 x 0.46 x 1.63 = 0.86

Getting City’s goal expectancy involves multiplying their Attack Strength by United’s Defense Strength and the league average of away goals scored: 

1.43 x 0.41 x 1.22 = 0.72

Therefore, we get the following expected score:

  • Manchester United 0.86 – Manchester City 0.72

The Poisson Formula

You might then decide there’s enough information to make an educated bet. Options include under 2.5 goals, a 1-1 final scoreline, or a draw. However, you can take things one step further with the Poisson Formula, which helps you calculate the probability of any outcome in the game.

The Poisson Formula is as follows:

P (k events in the interval) = (λk e –λ) / k!

  • P = probability
  • k = how many occurrences in the interval (number of goals)
  • λ = expected number of goals
  • e is Euler’s number, which is 2.71828
  • k! is the factorial of k

So as you can see, the above formula enables you to calculate the probability for any number of goals accurately. Yet, unless you’re highly skilled in mathematics, it is best to use a Poisson calculator.

In order to use your calculator, in ‘event occurrences,’ put in every possible score for both teams. As football is a low-scoring game, it is best to keep things simple and limit it to 0 – 4. Of course, you can go higher if you’re interested in exploring long-odds wagers. But you must include each team’s goal expectancy figure in the’ expected event occurrences’ box.

For instance, to get the probability of United scoring 2 goals, you enter 2 in ‘event occurrences’ and 0.86 in ‘expected event occurrences.’ Here are the probabilities for United and City goals:

Likelihood of Scorelines

You can create a chart of the likelihood of different scorelines. You achieve this by multiplying the possible number of goals scored by United by the potential number of goals scored by City.

For instance, the chance of a 0-0 score is 0.42 x 0.49 (round to two decimal places for simplicity) = 0.21.

So here is what the chart looks like:

So as you can see, the most likely score is 0-0, which has a 21% chance of happening, according to this chart.

The next most probable scores are:

  • 1-0 win for United – 18%
  • 1-0 win for City – 15%
  • 1-1 draw – 13%

There is plenty of hype surrounding this fixture, with the consensus being that goals are likely. However, our Poisson-inspired calculations suggest that a low-scoring game is more probable. Therefore, you could get value in the betting markets.

Is the Price Right?

Now it’s time to see whether the markets offer any value bets. For example, the Crypto betting site Stake.com has plenty of options.

As illustrated, the odds for a 0-0 final score are 17.00. Therefore, the bookmaker thinks there is a 5.88% chance of the game ending goalless. However, your Poisson chart suggests there is a 21% chance. Therefore, this is clearly a value bet if you believe in your calculations.

Your model also shows a 54% chance of the game finishing 0-0, 0-1, or 1-0. However, Stake offers odds of 4.40 on the game having under 1.5 goals, an implied probability of 22.72%.

There is even value in the under 2.5 goals market at odds of 2.17, an implied probability of 46.08%. Your model says there is an 80% chance of the game finishing 0-0, 1-0, 2-0, 0-1, or 0-2.

In each case, the game has a maximum of two goals.

Therefore, ultimately, this entry into Poisson distribution sports betting suggests that, contrary to most predictions, the Manchester derby will have few goals.

However, you should perform additional research to see if this is likely the case.

What Are the Best Poisson Sports Betting Markets?

There are quite a few markets you can use when implementing Poisson in sports betting. These include:

  • Moneyline
  • Over/under goals
  • Handicap markets
  • Both teams to score
  • Final score
  • Double chance

It is overwhelmingly used in soccer betting, although it is potentially applicable to other low-scoring sports, such as ice hockey.

Problems With Poisson Betting

There are plenty of advantages to this mathematical method, and it enables you to understand better how bookmakers set their odds and provides insight into the likelihood of certain events occurring.

However, there are also Poisson distribution betting limitations:

  • It is generally only useful for low-scoring team sports like soccer and ice hockey
  • While the math may seem complex, the overall system is basic as it doesn’t account for various factors, including team news, weather, and pitch conditions. An injury to a star player can throw everything out of place, as can weather conditions. For example, a soccer game played in high wind will likely prove chaotic
  • You need a significant amount of data to get an accurate picture. Therefore, you can’t rely on Poisson until a season is a few months old
  • There is little utility in focusing on data from previous seasons, as teams undergo many changes during the off-season. For example, the transfer window in soccer can significantly strengthen or severely weaken teams
  • Poisson only takes into account the result. While a result gives us the final score, it doesn’t always provide an accurate insight into how the game went. For instance, a team could dominate but then miss lots of chances and end up losing 1-0

Poisson Sports Betting: What Is It Good For?

Poisson is a highly useful way of investigating the potential of a game being high or low scoring, and you can use it to determine whether a game is worth additional analysis. Also, it could provide insight into whether a wager offers potential value odds.

For instance, our example of the Manchester derby showed that a low-scoring game was likely, which is the opposite of what the markets said.

Nonetheless, this doesn’t mean Poisson will prove accurate, as there’s always a chance that the heated atmosphere of a game between local rivals will result in a fast and furious affair with lots of goals.

Also, an early score could change everything, as the team that concedes furiously chases an equalizer, leaving themselves open to a counterattack.

However, Poisson doesn’t account for certain on-field and off-field factors that could play a huge role in the game’s outcome. Therefore, it will prove highly accurate in some cases and completely inaccurate in others.

So, as with everything else, you should not view Poisson distribution in sports betting as a panacea. Instead, use it as another tool in your never-ending battle to beat the bookies in the long term. 

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Patrick Lynch
Patrick Lynch
Sports & Casino Expert

Patrick has been a professional writer since 2009. He knows the issues players face when trying to find reputable casinos and performs forensic analysis on every site he reviews. Since joining in 2021, Patrick has had his eyes opened by the potential of the cryptocurrency market. With a background in sports betting, he realizes the possibilities afforded to successful bettors when using digital currency.