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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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