By using a Poisson distribution, combined with an analysis of previous match data, you can predict the likely score in football matches, and then place bets based on those predictions. Our material describes how to calculate the required values of attack and defense forces, and also provides a convenient way to determine them using the Poisson distribution method.

What is Poisson Distribution? It is a mathematical concept for translating means into probabilities for variable outcomes within a distribution. For example, we know that Manchester City scores 1.7 goals per game on average. If we enter this information into Poisson's formula, we find out that this average is equivalent to the fact that Manchester City scores 0 goals 18.3% of the time, 1 goal 31% of the time, 2 goals 26.4% of the time and 3 goals in 15% of cases.

**Poisson distribution: calculating the probability of a game score**

Before using Poisson's formula to calculate the probability of a match score, you need to calculate the average number of goals each team is likely to score in that match. This number can be calculated by determining the attack and defense strength of each team and comparing these indicators. Once you know how to calculate the likelihood of results, you can compare your data with the bookmaker's odds in order to identify potentially profitable betting options.

However, the choice of a range of representative data is extremely important when calculating attack strength and defense strength. If the range is too large, the data will not match the current strength of the teams. However, if the range is too small, it can lead to information distortion due to the frequent appearance of results that differ sharply from other values in the existing dataset. For this analysis, we use data from 38 matches played by each team in the previous Premier League season. This is a sufficient sample size to apply the Poisson distribution.

**Attack Power**

Here, the first step in calculating attack power based on last season's results is to determine the average number of goals each team scored at home and away. To calculate this value, the total number of goals scored last season must be divided by the number of matches played:

- Total goals in a season at home / games played (in a season).
- Total number of away goals per season / number of games (per season).

In the Premier League season 2019–2020. these values were 567/380 for home games and 459/380 for away games. This means that on average, teams scored 1,492 goals in one home game and 1.207 goals in an away match.

- Average number of goals scored at home: 1,492
- Average number of goals scored in away games: 1,207.

The difference between the team average and the league average is **the attack power** .

**Defense strength**

In addition, you need to know the average number of goals that the average team misses. To do this, the above numbers should simply be swapped (since the number of goals that the home team scores will be equal to the number that the away team misses).

- Average number of goals conceded at home: 1.207
- Average number of goals conceded in away games: 1,492

The difference between the team average and the league average is **defensive strength** .

We can now use the above numbers to calculate the attack and defense forces for Tottenham Hotspur and Everton.

**Predicting Tottenham Goals**

Calculating the attack power of Tottenham Hotspur:

- Step 1. Take the number of home goals scored last season by the home team (35) and divide that number by 1,842 home games (35/19).
- Step 2. Divide this value by the average home team goals per season scored by the home team per game (1,842 / 1,492). This will give you an attack power of 1.235.

**(35/19) / (567/380) = 1.235**

Calculation of the strength of defense "Everton":

- Step 1. Take the number of goals conceded in away games last season by the away team (25) and divide by the number of 1,315 away games (25/19).
- Step 2. Divide this value by the average number of goals conceded per season by the visiting team in one match (1.315 / 1.492). This will give you a Defense Strength value of 0.881.

**(25/19) / (567/380) = 0.881**

We can now use the following formula to calculate Tottenham's probable goals (this is done by multiplying Spurs' attack strength, Everton's defense strength and the Premier League's average home goals):

**1.235 x 0.881 x 1.492 = 1.623**

**Predicting Everton Goals**

To calculate the number of possible goals Everton will score, simply use the formulas above, but replace the average home goals with the average away goals.

Everton's attack strength:

**(24/19) / (459/380) = 1.046**

Defense Strength of Tottenham:

**(15/19) / (459/380) = 0.653**

To predict the number of possible goals for Everton, you can use the same method that was used to calculate the probable number of goals that the Hotspur can score (this is a multiplication of the value of the attack strength of Everton, the defense strength of the spurs and the average number goals in Premier League away matches):

**1.046 x 0.653 x 1.207 = 0.824**

**Poisson Distribution: Predicting Multiple Results**

Of course, no game ends with a score of 1.623 versus 0.824 - these are just averages. Poisson Distribution - a formula created by the French mathematician Simeon Denis Poisson - allows you to use these numbers to distribute 100% probability across the range of results for each team.

Poisson distribution formula:

**P (x; μ) = (e-μ) (μx) / x!**

However, we do have the option of using online tools such as the Poisson Distribution Calculator, which is convenient for most of the calculations.

All you need to do is enter various indicators (in our case, we are talking about the number of goals [0-5]), and then the values of the probability that the team will be able to score goals (in our example, Tottenham's average success rate is 1.623, and Everton is 0.824), and the calculator will calculate the probability of such a score for a particular outcome.

**Poisson distribution for predicting match outcomes**

This **table** shows that the odds of Tottenham not scoring a single goal is 19.73%, with a 32.02% chance of a team scoring one goal and 25.99% of two goals. ... On the other hand, Everton has a 43.86% chance of ending the game without a single goal, 36.14% to score one goal and 14.89% to score two. Hoping that one of the teams will score five goals? The probability of this happening for Spurs is 1.85% and for Everton it is 0.14%. At the same time, the probability that one of the teams will score 5 goals is 2%.

Since both outcomes are independent (in a mathematical sense), it can be concluded that the score is likely to be 1–0 - this is the result of comparing the most likely outcomes for each team. If you multiply these two probabilistic values, then the probability of outcome 1–0 will be (0.3202 * 0.4386) = 0.1404 or 14.04%.

Knowing how to calculate the probability of a particular score in a game using the Poisson distribution for betting purposes, you can compare the results of your calculations with the bookmaker's odds to find any discrepancies that you can use to your advantage, especially if you included role in your calculations. relevant situational factors such as weather conditions, injury or home arena advantage.

**Converting probabilities to odds**

From the above example of applying the Poisson distribution formula, we see that the probability of a 1-1 draw is 11.53% (0.3202 * 0.3614). But what if you want to calculate the odds for a draw, not the score of one of the teams? In this case, you should calculate the probability for *all* possible draws: 0-0, 1-1, 2-2, 3-3, 4-4, 5-5, etc.

To do this, you just need to calculate the probabilities of all possible draw combinations and add them. This will tell you the probability of a tie, regardless of the score.

Of course, there are in reality an infinite number of draw opportunities (for example, both teams can score 10 goals), but the chances of a draw greater than 5-5 are so small that they can be neglected for this model.

In the example with our match, adding all the tie results gives a probability of 0.2472 or 24.72%, which corresponds to a true odds of 4.05 (1 / 0.2472).

**Poisson distribution constraints**

The Poisson Distribution is a simple predictive model that does not take into account many factors. Situational factors (eg club circumstances, match status, etc.) and subjective assessment of changes in team line-up during the transfer window are completely ignored.

In addition, the above example of the calculation using the Poisson distribution formula does not take into account the impact of the possible arrival of a new coach on the team's results. It also does not take into account the potential spur fatigue associated with the team's performance in the Champions League. Further, correlations are ignored, such as the generally recognized effect of the football field, which is that teams tend to perform better or worse at certain matches.

All of these factors are especially important in minor league matches, allowing bettors to gain an edge over the bookmakers. However, it is more difficult to gain an advantage in the case of major leagues such as the Premier League, as modern bookmakers have valuable experience and resources in this area. Last but not least, these odds do not include the bookmaker's margin, which is of great importance for the whole process of determining a profitable bet value.

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