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In sports betting, there is always going to be an element of unpredictability, but that doesn’t mean you want to 🤶 waste your money placing random bets that have no real grounding behind them. You want methods and models that can 🤶 give you some insight into which way a game is likely to go, and one such strategy is known as 🤶 Poisson distribution.

Poisson distribution is a method that works best for calculating statistics in sports where scoring is rare and happens 🤶 in increments of one. This is why it is most widely used in association football, and occasionally in hockey, but 🤶 not really utilised elsewhere – at least, not successfully.

That’s why, in this article, we’re going to focus on the former 🤶 in particular, and why much of what we’ll write will be applicable to football alone. With that said, let’s begin…

What 🤶 Is Poisson Distribution?

Poisson distribution is a method of calculating the most likely score in a sporting event such as football. 🤶 Used by many experienced gamblers to help shape their strategies, it relies on the calculation of attack and defence strength 🤶 to reach a final figure.

A mathematical concept, Poisson distribution works by converting mean averages into a probability. If we say, 🤶 for example, that the football club we’re looking at scores an average of 1.7 goals in each of their games, 🤶 the formula would give us the following probabilities:

That in 18.3% of their games they score zero

That in 31% of their 🤶 games they score one

That in 26.4% of their games they score two goals

That in 15% of their games they score 🤶 three times

This would help the individual to make an educated guess with a good chance of delivering a profitable outcome 🤶 to their bet.

Calculating Score-line Probabilities

Most individuals use Poisson to work out the likeliest scoreline for a particular match, but before 🤶 they can do this, they first need to calculate the average number of goals each team ought to score. This 🤶 requires two variables to be taken into account and compared: ‘attack strength’ and ‘defence strength’.

In order to work out the 🤶 former, you’ll typically need the last season’s results, so that you can see the average number of goals each team 🤶 scored, both in home games and away games. Begin by dividing the total number of goals scored in home matches 🤶 by the number of games played, and then do the same for away matches.

Let’s use the figures for the English 🤶 Premier League 2024/2024 season:

567 goals divided by 380 home games = 1.492 goals per game

459 goals divided by 380 away 🤶 games = 1.207 goals per game

The ratio of the team’s individual average compared to the league average helps you to 🤶 assess their attack strength.

Once you have this, you can then work out their defence strength. This means knowing the number 🤶 of goals that the average team concedes – essentially, the inverse of the numbers above. So, the average number conceded 🤶 at home would be 1.207; the average conceded away 1.492. The ratio of the team average and the league average 🤶 thus gives you the number you need.

We’re now going to use two fictional teams as examples. Team A scored 35 🤶 goals at home last season out of 19 games. This equates to 1.842. The seasonal average was 1.492, giving them 🤶 an attack strength of 1.235. We calculated this by:

Dividing 35 by 19 to get 1.842

Dividing 567 by 380 to get 🤶 1.492

Dividing 1.842 by 1.492 to get 1.235

What we now need to do is calculate Team B’s defence strength. We’ll take 🤶 the number of goals conceded away from home in the previous season by Team B (in this example, 25) and 🤶 then divide them by the number of away games (19) to get 1.315. We’ll then divide this number by the 🤶 seasonal average conceded by an away team in each game, in this case 1.492, to give us a defence strength 🤶 of 0.881.

Using these figures, we can then calculate the amount of goals Team A is likely to score by multiplying 🤶 their attack strength by Team B’s defence figure and the average number of home goals overall in the Premier League. 🤶 That calculation looks like this:

1.235 x 0.881 x 1.492 = 1.623.

To calculate Team B’s probable score, we use the same 🤶 formula, but replacing the average number of home goals with the average number of away goals. That looks like this:

1.046 🤶 (Team B’s attack strength) x 0.653 (Team A’s defence strength) x 1.207 = 0.824

Predicting Multiple Outcomes

If you fail to see 🤶 how these values might be of use to you, perhaps this next section might clarify things. We know that no 🤶 game is going to end with 1.623 goals to 0.824 goals, but we can use these numbers to work out 🤶 the probability for a range of potential outcomes.

If your head is already spinning at the thought, we’ve got some good 🤶 news for you: you won’t need to do this manually. There are plenty of online calculators and tools that can 🤶 manage the equation for you, so long as you can input the potential goal outcomes (zero to five will usually 🤶 work) and the likelihood of each team scoring (the figures we calculated above).

With these probabilities to hand, you can work 🤶 out the bets that are most likely to deliver a profit, and use the odds you get to compare your 🤶 results to the bookmaker’s and see where opportunities abound.

The Limitations of Poisson Distribution

Poisson distribution can offer some real benefits to 🤶 those who desire strong reasoning to support their betting decisions and improve the likelihood of a profitable outcome, but there 🤶 are limits to how far such a method can help you.

Key among these is that Poisson distribution is a relatively 🤶 basic predictive model, one that doesn’t take into account the many factors that can affect the outcome of a game, 🤶 be it football or hockey. Situational influences like club circumstances, transfers, and so on are simply not recognised, though the 🤶 reality is that each of these can massively impact the real-world likelihood of a particular outcome. New managers, different players, 🤶 morale… The list goes on, but none of these is accounted for within the remit of such a method.

Correlations, too, 🤶 are ignored, even pitch effect, which has been so widely recognised as an influencer of scoring.

That’s not to say that 🤶 the method is entirely without merit. Though not an absolute determiner of the outcome of a game, Poisson distribution certainly 🤶 does help us to create a more realistic picture of what we can expect, and can be an invaluable tool 🤶 when used alongside your existing knowledge, natural talent, and ability to listen and apply all that you hear, read, and 🤶 see.

FAQs

Why is Poisson distribution used for football?

The Poisson distribution is often used in football prediction models because it can model 🤶 the number of events (like goals) that happen in a fixed interval of time or space. It makes a few 🤶 key assumptions that fit well with football games:

Events are independent: Each goal is independent of others. The occurrence of one 🤶 goal doesn’t affect the probability of another goal happening. For example, if a team scores a goal, it doesn’t increase 🤶 or decrease the chances of them scoring another goal.

Events are rare or uncommon: In football, goals are relatively rare events. 🤶 In many games, the number of goals scored by a team is often 0, 1, 2, or 3, but rarely 🤶 more. This is a good fit for the Poisson distribution which is often used to model rare events.

Events are uniformly 🤶 distributed in time: The time at which a goal is scored is independent of when the last goal was scored. 🤶 This assumption is a bit of a simplification, as in reality, goals may be more likely at certain times (like 🤶 just before half-time), but it’s often close enough for prediction purposes.

Average rate is known and constant: The Poisson distribution requires 🤶 knowledge of the average rate of events (λ, lambda), and assumes that this rate is constant over the time period. 🤶 For example, if a team averages 1.5 goals per game, this would be the λ value used in the Poisson 🤶 distribution.

These assumptions and characteristics make the Poisson distribution a useful tool for modelling football goal-scoring, and for creating predictive models 🤶 for football match outcomes. However, it’s important to remember that it’s a simplification and may not fully capture all the 🤶 nuances of a real football game. For example, it doesn’t take into account the strength of the opposing teams, the 🤶 strategy used by the teams, or the conditions on the day of the match.

How accurate is Poisson distribution for football?

The 🤶 accuracy of the Poisson distribution in predicting football results can vary depending on the context, the specific teams involved, the 🤶 timeframe of the data used, among other factors. A recent study examined the pre-tournament predictions made using a double Poisson 🤶 model for the Euro 2024 football tournament and found that the predictions were extremely accurate in predicting the number of 🤶 goals scored. The predictions made using this model even won the Royal Statistical Society’s prediction competition, demonstrating the high-quality results 🤶 that this model can produce.

However, it’s important to note that the model has potential problems, such as the over-weighting of 🤶 the results of weaker teams. The study found that ignoring results against the weakest opposition could be effective in addressing 🤶 this issue. The choice of start date for the dataset also influenced the model’s effectiveness. In this case, starting the 🤶 dataset just after the previous major international tournament was found to be close to optimal.

In conclusion, while the Poisson distribution 🤶 can be a very effective tool for predicting football results, its accuracy is contingent on a number of factors and 🤶 it is not without its limitations.

What is the application of Poisson distribution in real life?

The Poisson distribution has a wide 🤶 range of applications in real life, particularly in fields where we need to model the number of times an event 🤶 occurs in a fixed interval of time or space. Here are a few examples:

Call Centres: Poisson distribution can be used 🤶 to model the number of calls that a call centre receives in a given period of time. This can help 🤶 in planning the staffing levels needed to handle the expected call volume.

Traffic Flow: It can be used to model the 🤶 number of cars passing through a toll booth or a particular stretch of road in a given period of time. 🤶 This information can be useful in traffic planning and management.

Medical Studies: In medical research, it can be used to model 🤶 rare events like the number of mutations in a given stretch of DNA, or the number of patients arriving at 🤶 an emergency room in a given period of time.

Networking: In computer networks, the Poisson distribution can be used to model 🤶 the number of packets arriving at a router in a given period of time. This can help in designing networks 🤶 and managing traffic.

Natural Phenomena: It’s also used in studying natural phenomena like earthquakes, meteor showers, and radioactive decay, where the 🤶 events occur randomly and independently over time.

Manufacturing: In manufacturing and quality control, the Poisson distribution can be used to model 🤶 the number of defects in a batch of products. This can help in process improvement and quality assurance.

Retail: In the 🤶 retail sector, it can be used to model the number of customers entering a store in a given period of 🤶 time, helping in staff scheduling and inventory management.

Remember that the Poisson distribution is based on certain assumptions, such as the 🤶 events being independent and happening at a constant average rate. If these assumptions don’t hold, other distributions might be more 🤶 appropriate.

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