Applying Poisson Distribution To Sports Betting

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 2015/2016 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 2020 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.