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Poisson distribution in betting is used to calculate the frequency of
any occurrence in a game. In this article, you👄 will learn how to calculate the
probability of any score in football, and how to use it to calculate who👄 is likely to
win.
What is Poisson Distribution in Betting?
Poisson distribution was developed by
19th century French mathematician Siméon Denis Poisson.👄 It is a probability theory that
uses historical sports data to predict the outcome of a sports event. It measures👄 the
likelihood of how many times an event will occur during a specific period.
This may
seem complicated to someone who👄 has no background in maths, but it is actually a fairly
simple method. To put it simply in terms of👄 football betting, Poisson distribution can
help you predict how likely each number of goals scored is.
Why is Poisson Distribution
Important?
When👄 bookies set their odds, it is important to know how likely any event
is, based on past performance. Bookies do👄 not simply come up with odds out of the blue.
They use mathematical models. If you want to take a👄 scientific, mathematical approach
to betting, you should calculate for yourself how likely you think a specific game
event, or set👄 of events will be. That is the first step to finding value. If you have
found something that is more👄 likely to happen than what the bookies predict, that is
what value is.
Poisson distribution in betting is particularly relevant for👄 games like
football, where scoring happens on an incremental scale. It helps you determine the
likelihood of each possible score.
The👄 Poisson distribution is commonly used to
calculate the likelihood of a specific score in football, as well as a win,👄 lose or
draw. You need to first calculate your league’s average goal expectancy, along with the
attack strength and defence👄 strength for both sides.
How to calculate goal
expectancy
Your team's goal expectancy depends on your team’s attack strength and
defence strength,👄 and as well as that of the opposite team.
In our example, we will use
the data from the 2024-2024 English👄 Premier League to calculate a hypothetical match
between Manchester City and Liverpool. Manchester is the home team, while Liverpool is
👄 the away team.
Before calculating these, we need to know:
The total home goals scored
by all EPL teams
The total away goals👄 scored by all EPL teams
The average number of
home goals and away goals per match for the whole league
We need👄 to calculate
Manchester City’s:
Home goal average
Average goals allowed per home match
We need to
calculate Liverpool’s:
Away goal average
Average goals allowed per👄 away match
These
stats are easy to find at the Premier League’s official site.
Calculating Attack
Strength
With these results, we can easily👄 calculate attack strength for the home and
away team. Attack Strength is the team’s average number of goals, divided by👄 the
league’s Average number of goals.
Home
Manchester City’s Attack Strength: 3.00 ÷ 1.53 =
1.96
Away
Liverpool’s Attack Strength: 1.78 ÷ 1.147 =👄 1.55
Calculating Defence
Strength
Calculating Defence Strength is just as easy. Simply divide the team’s average
number of goals allowed by the👄 league’s average number of goals allowed.
Manchester
City’s Defence Strength: 0.63 ÷ 1.147 = 0.55
Away
Liverpool’s Defence Strength: 0.63 ÷
1.532 =👄 0.41
Goal expectancy
Now that we have determined each team’s Attack Strength
and Defence Strength, we can calculate each team’s likely score.
Manchester👄 City goal
expectancy
To determine how many goals Manchester City will likely score, we need to
multiply Manchester City’s Attack Strength👄 by Liverpool’s Defence Strength and the
league’s average number of home goals.
That gives us:
1.96 × 0.41 × 1.532 =
1.23
Liverpool👄 goal expectancy
To determine how many goals Liverpool will likely score,
we need to multiply Liverpool’s Attack Strength by Manchester City’s👄 Defence Strength
and the league’s average number of away goals.
That gives us:
1.55 × 0.55 × 1.147 =
0.997
Average goals scored👄 in the match
Manchester City: 1.23
Liverpool: 0.997
Using
the Poisson Formula to calculate the likelihood of each possible score
Now that we have
👄 each team’s home and away defence and attack strengths, we can easily use them with the
Poisson formula to calculate👄 the probability of any possible outcome.
The Poisson
Formula
The Poisson Formula is:
P (k events in interval) = (λk e –λ) /👄 k!
In this
formula:
P is the probability
is the probability k is the number of occurrences in the
interval (number of goals)
is👄 the number of occurrences in the interval (number of
goals) λ is the expected number of goals
is the expected number👄 of goals e is Euler's
number (e = 2.71828…)
is Euler's number (e = 2.71828…) k! is the factorial of k
Poisson
👄 Calculator
Using this formula, you can calculate the probability for any number of
goals. However, there are plenty of online calculators👄 which will make the job simpler.
To use the calculator, fill in each possible score (limit yourself from 1 to👄 5)
separately in the top in “Event occurrences”, and the expected average goals score per
match in the bottom, in👄 “Expected event occurrences”.
That gives us the following
probability for Manchester City Goals:
That gives us the following probability for
Liverpool City👄 Goals:
Predicting the match outcome based on these probabilities
To get
each possible score, simply multiply the probability of each possible score👄 by each
team by the probability of each possible score by the other team. This gives you the
following distribution:
As👄 you can see, the most likely score is 1 – 1, or 1 – 0
followed by 0 – 0👄 or 0 – 1. Given the defence averages of both teams, it is easy to see
how these would be👄 very likely scores.
How Bookies Convert Estimated Chance Into
Betting Odds
Bookies use Poisson distribution to calculate betting odds for outcomes in
👄 various markets. You can do the same by converting your calculated probabilities into
odds. The calculations are quite simple.
To calculate👄 the chance of a Manchester City
win , we add all the red squares from the table above: that gives👄 us an estimated
chance of 0.4142, or 41.42%
, we from the table above: that gives us an estimated
chance of👄 0.4142, or 41.42% To calculate the chance of a Liverpool win , we add all the
green squares from the👄 table above: that gives us an estimated chance of 0.29867, or
29.87%
, we from the table above: that gives us👄 an estimated chance of 0.29867, or
29.87% To calculate the chance of a draw, we add all the yellow squares👄 from the table
above: that gives us an estimated chance of 0.286118, or 28.61%
To convert each of
these chances into👄 odds, we use the following formula:
Odds = 1/ (probability)
That
gives us the following odds:
Manchester City win: 1/ (0.4142) = 2.4390
1/👄 (0.4142) =
2.4390 Liverpool win: 1/ (0.29867) = 3.3333
1/ (0.29867) = 3.3333 Draw: 1/ (0.286118) =
3.4483
You can convert these👄 to American or fractional odds, but decimals are easier to
work with. The calculator on our page about implied probability👄 should help you do the
maths faster.
Advantages of Poisson Distribution in Betting
Using Poisson distribution
in betting has many advantages. First👄 of all, it helps you understand how odds are set
in the first place. By adding up the likelihood of👄 various possibilities, bookies are
able to set up relatively accurate odds. You can do the same and compare your result👄 to
what the bookies are presenting. Betting lines are not only set by using these
equations. Popular matches in particular👄 often see the odds offered (betting lines)
change, as more money comes in on a particular outcome.
That is one example👄 of how you
can use Poisson distribution to beat the bookies. Comparing your own odds to the ones
offered by👄 the bookies is part of a sound betting strategy.
Limitations of Poisson
Distribution in Betting
Poisson distribution is a mathematical formula that👄 offers
estimated probabilities, not certainties. The more data it has to rely on, the more
accurate it can get. On👄 the other hand, no squad is the same for each match of the
year.
A player’s injury or absence can make👄 a huge difference in how the entire squad
will perform. At the beginning of the season, most teams also have👄 a different line-up
than the year before. This makes setting odds using data from a previous season
problematic. Still, that👄 does not necessarily put you at a disadvantage, since the
bookies also have fewer data to rely on.
As the season👄 goes longer, it becomes easier
to predict, since there is more current data available.
It is not so hard to create
👄 your own Poisson distribution calculator with Excel; in fact, you do not need to
download one from an external site.👄 This step-by-step guide will show you how to make
your own.
1. Calculate your team’s expected goals
First, calculate your team’s expected
👄 goals. That is the team's average attack strength × the other team’s defence strength ×
average goals per match. Below,👄 we calculated Manchester City’s expected goals at
1.23.
Check out: Expected Goals Explained.
2. Create the following table in Excel:
3.
Go to👄 the square next to 0, and right click.
4. Click on formulas> Insert Function >
Poisson.Dist
5. Fill in:
X = B5 (or👄 click on the number next to 0)
Mean = 1.23 (Your
team’s expected goals)
Cumulative = FALSE
6. Move the cursor to the👄 bottom right of C5
and use the plus cursor to drag the formula down.
This gives you the Poisson
distribution for👄 0 to 5 goals of the expected goal average which is 1.23. You can
combine the results of your team’s👄 probabilities to get a distribution that looks like
this (the same as the above).
Here at ThePuntersPage we have a full👄 range of football
statistics that you may also like to check out ranging across all the major countries
and leagues:
Player👄 Stats
Team Stats
Profit & Loss Stats
Streaks & Trends
Poisson
Distribution FAQs How do you use Poisson Distribution in football? Poisson distribution
uses👄 probability to determine the odds of any score, based on both team’s past
performance and league averages. First, you need👄 to calculate each team’s attack and
defence strength and multiply them by the league average. Next, you use the Poisson
👄 formula to determine the likelihood of any individual score. How do you predict
football scores? One way to predict football👄 scores is with Poisson distribution. This
is a mathematical way to estimate the probability of any score. It is based👄 on both
team’s past performance and league averages. Use it to calculate each teams the
likelihood of each possible number👄 of goals for a team, and multiply that by the
likelihood of each possible number of goals for the other👄 team. How is goal expectancy
calculated in football? Goal expectancy in football uses the following formula: Attack
Strength of the👄 team × Defence Strength of the other team × the league’s Average Number
of Goals. How do you calculate the👄 attack strength of a football team? Attack Strength
is the team’s average number of goals divided by the league’s Average👄 number of goals
for that season. How do you calculate the probability of winning a football match?
Using Poisson distribution,👄 the probability of winning a football match is the sum of
the probabilities of each individual possible winning score. How👄 do you make your own
odds? To make your own odds, first calculate or estimate the likelihood of an event,
👄 then use the following formula: Odds = 1/ (probability). Compare your odds to your
bookie's odds to see if they👄 offer any value.
ThePuntersPage Final Say
It can be a bit
of work understanding how to calculate odds for various game outcomes.👄 Once you
understand Poisson distribution, it becomes much simpler. Luckily, our calculators, as
well as the Excel method explained in👄 this article, can help you. Knowing estimated
odds and comparing them to the bookies odds is a sure path to👄 finding value in
betting.
