Poisson Calculator

- April 25, 2025

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Calculate probability distributions using the Poisson distribution model. This calculator is useful for sports betting, predicting events that occur randomly with a known average rate.

Poisson Parameters

Team A:

Team B:

Team A Average Goals:

Team B Average Goals:

Advanced Options

Maximum Goals to Calculate:

Decimal Places:

Show percentages

Poisson Distribution Results

Most Likely Score

0-0

0.00%

Team A Win Probability

0.00%

Draw Probability

0.00%

Team B Win Probability

0.00%

Exact Score Probabilities

	Team B Goals
Team A Goals	0	1	2	3	4	5	6	7

Goal Distribution Charts

Team A Goal Distribution

Team B Goal Distribution

Result Probabilities

How Poisson Distribution Works

The Poisson distribution is used to predict the probability of a specific number of events occurring in a fixed time period, given the average rate of occurrence.

For soccer/football predictions, we use each team's average goals as the lambda (λ) parameter.

The formula for calculating the probability of exactly x events is:

P(X = x) = (e^-λ × λ^x) / x!

Where:

e is Euler's number (approximately 2.71828)
λ is the average number of events (goals)
x is the number of events we want to calculate the probability for
x! is the factorial of x

About Poisson Distribution in Sports Betting

The Poisson distribution is a statistical model that helps predict the number of times an event will occur within a specified time period. In sports betting, particularly soccer/football, it's used to estimate the probability of specific scorelines.

Key Assumptions

Independence: Goals scored by each team are independent of each other.
Constant Rate: The rate of scoring remains constant throughout the game.
Random Occurrence: Goals occur at random points in time.

Limitations

Does not account for red cards, injuries, or other in-game events that change team dynamics.
Assumes independence between teams' scoring rates, which may not be true in practice.
Does not factor in team psychology, such as defensive strategies after taking a lead.
Recent form and head-to-head records are not considered in the base calculation.

How to Use This Calculator

Enter the average goals for each team (from historical data).
Set the maximum number of goals to calculate probabilities for.
Click "Calculate Probabilities" to generate the distribution matrix and charts.
Use the results to identify value bets by comparing with bookmaker odds.

Understanding the Poisson Calculator

The Poisson Calculator is a handy tool for anyone interested in predicting outcomes, especially in Sports like soccer. It uses the Poisson distribution model, which estimates the likelihood of certain events happening within a set timeframe. This is particularly useful for sports betting, where you can gauge the probability of various scorelines based on average goals scored by each team.

How to Set Your Parameters

To get started with the Poisson Calculator, you'll need to enter some key information. You’ll input the teams’ names and their average goals scored per Game. The average goals are vital, as they help establish the 'lambda' (λ) parameter, which the calculator uses to derive probabilities.

Team A Name: Input your home team.
Team B Name: Input your away team.
Average Goals: Fill in the average goals for both teams.

Advanced Options for Better Predictions

The calculator also offers advanced options for users who want more control over their calculations. You can set a maximum number of goals to consider and choose how many decimal places to display in the results. There’s even an option to show percentages, making the output clearer.

Maximum Goals: Set a range from 5 to 10 goals.
Decimal Places: Choose how precise you want your results.
Show Percentages: This helps in visualising the probability.

Viewing the Results: What to Expect

Once you've input all your data, the Poisson Calculator will provide a range of results. You’ll see the most likely score, as well as the win probabilities for each team and the chance of a draw. The results are broken down for easy understanding, making it simple to see how the teams stack up against each Other.

The Power of the Score Matrix

One of the standout features of the Poisson Calculator is the score matrix. This table gives you a detailed look at the exact score probabilities for all possible outcomes. It displays the likelihood of each team scoring a particular number of goals against one another, offering deeper insights into the match.

Visualising Goal Distribution

Alongside numerical results, the calculator generates charts showing goal distribution for both teams. These visual aids can help you better understand trends, such as which team is more likely to score higher goals based on historical data.

How the Poisson Distribution Works

The Poisson distribution predicts the chance of a certain number of events occurring within a fixed period, assuming a known average rate. In sports, it’s often used to gauge the number of goals scored. The calculator uses the formula:

P(X = x) = (e^-λ × λ^x) / x!

This formula helps you measure the probability of specific events happening, giving you a solid foundation for making informed predictions.

The Importance of Assumptions in Sports Betting

When using the Poisson Calculator, it’s essential to understand some key assumptions. For instance, the goals scored are assumed to be independent events, and the rate of scoring is consistent throughout the game. However, it doesn’t account for factors like red cards or injuries, which can significantly impact the match.

Independence: Goals from one team don’t affect the other.
Constant Rate: Scoring likelihood remains the same.
Random Occurrence: Goals can happen at any time during the match.

By knowing these assumptions, you can better interpret the results and apply them to your betting strategies.

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