What is the Poisson distribution?

If define that an independent Poisson distribution is a probability distribution of a discrete type, it simulates a random variable that represents a certain number of events that have elapsed in a certain time, provided that these events occur with medium intensity and independently of each other.

Of course, to you from this definition, at first glance, nothing is clear and in general what does it have to do with predicting football matches.

Football strategy

The Poisson distribution is a mathematical concept for converting mean values ​​into probabilities. In order for us to correctly apply this distribution, we need to determine the strength of the attack teams, the defense teams and the average values ​​of the goals scored by the league. For example, we know that the PSV team scores at home with Venlo 2.2 goal goal per game. Then according to the Poisson distribution, the probability that the PSV will score 0 goals = 11.08%, 1 = 24.37%, 2 = 26.81%, 3 = 19.66%, 4 = 10.81%, 5 = 4.75%.

To correctly determine the average score of goals scored per team, you first need to determine the attack strength, defense, the average goal value for the league for each team.

Calculation of mean values ​​for league

The first thing to do is to calculate the average value of the goals that were scored at home and away. To do this, we need to take all the goals that were scored by home teams and divided by the total number of matches for the season:

•  Total number of goals in home games / number of matches played for the season.
•  Total number of goals in away matches / number of matches played for the season.

In the English Premier League season, 582/380 were scored at home and for away matches 436/380:

•  The average value of goals scored in home games 1.53
•  The average value of goals scored in away matches 1.14

It’s also necessary to know the average number of goals that teams miss, for this you need to change the average values ​​of the goals scored in some places:

•  The average value of the missed goals in home games 1.14
•  The average value of the missed goals in away matches 1.53

Soccer picks predictions

Now, for example, we will calculate the match Lester – Watford.

Predict the number of goals for Leicester

Calculating the attack power of Leicester

We took the last 8 home matches of Leicester, before the next match (Lester – Watford), to calculate their attack. We need to count the goals scored by Lester’s team at home (10 goals scored). And divide this number by the number of home games: 10/8 = 1.25. Divide this value by the average number of goals scored by the league: 1.25 / 1.53 = 0.81. Attack Power Leicester = 0.81

Calculating the strength of defense for Watford

Take the number of goals that the Watford team missed away and divide by the number of matches played away: 15/8 = 1.875. Take this value and divide by the average value of goals missed by the team in away matches (1.53). 1.875 / 1.53 = 1.22. Defense Force Watford = 1.22

Now we use the formula to calculate the probable number of goals. Leicester: Attack Power Lester x Strength Defense Watford x average number of home goals scored in the league: 0.81 x 1.22 x 1.53 = 1.51. Expected goals for Leicester = 1.51

Prediction expected goals for Watford

Calculating the attack power of Watford

We took the last eight away matches of Watford, before the match (Leicester – Watford), to calculate their attack. It is necessary to take as a basis the goals scored by Watford away (9 goals). And divide this number by the number of away games Watford: 9/8= 1.125

Divide this by the average number of goals scored at 1.14. 1.125 / 1.14 = 0.98. Attack Power Watford = 0.98

Calculating the strength of the defense of Leicester

Took the number of goals conceded by Leicester’s team for the last 8 matches and divided by the number of matches played: 9/8 = 1.125. Divide this value by the average goals scored by the team in home games: 1.125 / 1.14 = 0.98. Strength of Defense Leicester = 0.98

Now we use the formula to calculate the probable number of goals Watford: attack power Watford x strength of defense Leicester x average number of goals in away matches: 0.98 x 0.98 x 1.14 = 1.09. Probable goal Watford = 1.09

Football strategy = Poisson distribution model

Now that we know the mean values ​​of goals of each team, we will use the Poisson distribution formula.

Formula: P (x; μ) = (e-μ) (μx) / x!

Of course, we will not count manually, for this you can substitute your values ​​in the online calculator.

Or use our Poisson calculator, designed specifically for the site. There you must enter from above the average value of the goals scored by the teams at home and away, in the columns of the match score for the two teams, take into account who plays at home and away, then click on the “calculate” button and at the bottom you will see the probabilities for this match by:

• for the 1 × 2 market;
•  Handicap for teams A and B (-1.5, -2.5, -3.5);
• Total is more / less (1.5, 2.5, 3.5);
• Correct score prediction, three probable scores for match

Poisson distribution for match forecast Lester-Watford

When you put the value into a simple Poisson calculator, you will get:

For Leicester (1.51): 0 – 22.09%, 1 – 33.35%, 2 – 25.18%, 3 – 12.67%, 4 – 4.78%, 5 – 1.44%

At Watford (1.09):     0 – 33.62%, 1 – 36.64%, 2 – 19.97%, 3 – 7.25%,   4 – 1.97%, 5 – 0.43%

From these figures it follows that the probability of goals scored by Leicester: 0 goals = 22.09%, 1 goal = 33.35%, etc.

According to Watford, 0 goals = 33.62%, 1 goal = 36.64%, etc.

You will say: “What to do with this?”. Further, it is necessary to translate this data into odds.

For example, in order to know the probability of 1-0, we need to multiply the probability of Lester by 1 goal by the probability of Watford’s 0 goals: 0.3335 x 0.3362 = 0.1121 x 100% = 11.21% to score 1-0.

You can also count the probability of Leicester’s victory. To do this, you need to add all scores prediction that will indicate the victory of the home team. To add 1-0, 2-0, 3-0, 4-0, 5-0, 2-1, 3-1, 4-1, 5-1, 3-2, 4-2, 5-2, 4-3, 5-3, 5-4, you must first multiply the goal value with each other, as in example 1-0. It turns out that the victory of Leicester is 49.55%. But in order not to consider this all manually, I would advise using our Poisson distribution calculator.

Asian handicap predictions

With the Poisson distribution, we can accurately determine the forecast for Asian handicap. For example, let’s take the Leicester-Watford match again. We want to define -1.5 to Leicester. To do this, we need to scores a match that suits this handicap. It is: 2 – 0; 3 – 0; 4 – 0; 5 – 0; 3 – 1; 4 – 1; 5 – 1; 4 – 2; 5 – 2; 5 – 3.

We take into account the probability of only up to 5 goals for each team, since the odds after 5 goals are too small and they have little effect on the result.

To begin with, you need to find out the probabilities of the corresponding possible match scores, in order to overcome the probability of one another:

• 2-0 = 8.46%
• 3-0 = 4.2%
• 4-0 = 1.6%
• 5-0 = 0.48%
• 3-1 = 4.6%
• 4-1 = 1.7%
• 5-1 = 0.52%
• 4-2 = 0.95%
• 5-2 = 0.28%
• 5-3 = 0.1%

Now have to add this values: 8.46 + 4.2 + 1.6 + 0.48 + 4.6 + 1.7 + 0.52 + 0.95 + 0.28 + 0.1 = 22.89%

This means that AH -1.5 Leicester = 22.89%. To know whether to bet, you need to test the models with your calculating probabilities.

Total goals predictions

We can use the same strategy with Poisson distribution to calculate probabilities of total goals. We need to know the probabilities of total under 2.5 at Leicester – Watford match. To do this, take match scores which suitable to total under 2.5:

• 1-0
• 2-0
• 0-0
• 1-1
• 0-1
• 0-2

Than need determine every match score probabilities:

• 1-0 = 11.2%
• 2-0 = 8.46%
• 0-0 = 7.4%
• 1-1 = 12.2%
• 0-1 = 8%
• 0-2 = 4.4%

Now need to add this values: 11.2 + 8.46 + 7.4 + 12.2 + 8 + 4.4 = 51.66% to total under 2.5 in match Leicester – Watford.

With Poisson distribution, you can accurate predict football matches at all betting markets: draw no bet, both team to score and so on.

If you correctly determine the number of expected team’s goals, you can accurately predict matches using the Poisson distribution. In the following articles, the topic of predicting football matches using mathematical models will be more fully disclosed.

Now you to know about Poisson. This only one step to the professional betting way. Without bankroll management, you can’t beat the bookie.

Read the next article about “Kelly Criterion“. Probabilities, Poisson and Kelly work together in betting world.