# Poisson Calculator

The Poisson calculator is used by bettors to find the percentage of the possible outcomes of mainly propositional or “prop” bets. This tool is great for finding and edge on the odds offered.

There are more details below on how to use the tool and when to use it.

The sportsbooks below all offer prop bets that you can use the Poisson calculator with.

**Poisson**Calculator

## Poisson Distribution Calculator

Poisson distribution helps bettors find out the likelihood of an event happening within a particular period of time. It is often used to calculate the chances of a prop bet paying off. This poisson distribution calculator does all the hard work for you, quickly providing you with the probability of an event occurring within a game.

## What is Poisson Distribution?

The concept of poisson distribution can be applied to any walk of life. Retailers can use it to determine the number of customers that might visit a store on a particular day, while meteorologists can use it to predict the chances of a storm hitting an area during a given month. In sports betting, poisson distribution is generally used to calculate the probability of a prop bet paying off in a game or a specific period. It essentially helps bettors predict the probability of certain events happening in a fixed interval, but you need to know the historical average rate of success before using the probability calculator.

## What is the Poisson Distribution Formula?

You can only conduct a poisson probability experiment if you know the average number of times an event occurs within a time interval. This average rate of success number is represented by λ, the Greek letter lambda. You can think of λ as the mean. The desired number of times the that you want the event to occur is symbolized by x. This is known as the Poisson random variable. The poisson probability mass function is: P(X=k)=k!λke−λ, where e is Euler’s number.

You can use this formula to determine the Poisson probability and cumulative probability of a number of events occuring, entering λ based on the historical average and x based on the prop bet being offered. It looks extremely convoluted, and you can trawl through several pages of information to learn more about x e λ, λ x, x x, λ λ, e λ and so on. The formula is broken down into many different variants for specific purposes. Statisticians might enjoy examining probability mass f ( x , λ ) = e − λ λ x Γ ( x + 1 ) ( 2 ) lower cumulative functions, ( x , λ ) = e − λ λ x

Γ ( x + 1 ) ( 2 ), ^3x is e 3 x e 3 x , and e^(3x) is e 3 x e 3 x, λ λ x x ! , x = 1 , 2 , 3 , … P ( X = x ) = e − λ λ x x ! , x = 1 , 2 , 3, P ( X = x ) = e − λ λ x x ! , x = 1 , 2 , 3 , … P ( X = x ) = e − λ λ x and so on, but that sort of thing will not mean much to the average sports bettor.

Fortunately, you do not actually need to have a thorough grasp of those formulae. You can simply use our poisson calculator to work out the number of times an event will occur in a given time interval. It uses simple language that all sports bettors can understand, allowing you to quickly decide whether to place a prop bet from a position of strength, but it is underpinned by advanced statistical calculation methods, ensuring you receive a totally accurate probability result each time.

## How to Use Poisson Calculator

Follow these steps to work out the poisson probability distribution rate using this probability poisson distribution calculator:

• Choose either one variable or two variables.

• Enter the Expected Average. This is λ, the historical average rate at which an event has occurred, such as a basketball team scoring 18.2 points in the second quarter or a soccer team scoring 2.4 goals per game.

• Enter the Proposition. This is x, the random variable, or desired number of times you want the event to occur. For example, if the total points line was set at 37.5 in an NFL game, you would enter 37.5.

• Click on “Calculate”.

The poisson distribution calculator will then tell you the probability of the over or the under paying off, based on the historical average rate. The probability results are divided into three sections: “Odds of”, “Percentage” and “Moneyline”. “Odds of” describes the terms of the bet (over or under). The percentage represents the chances of the over or the under paying off in that time interval, based on the historical probability rate of success. Moneyline tells you the fair odds of the bet, based on zero vig. That allows you to determine whether there is a poisson opportunity for you to capitalize upon.

## An Example

Let’s say a sportsbook is offering a prop bet on the amount of three-point attempts the New York Knicks will make in an NBA game. It has -105 on over 15.5 attempts, and -115 on under 15.5 attempts. You have found that the Knicks average 15.2 three-point attempts per game. You now have the random variable (the prop bet) and the average rate of success, so you can work out the poisson probability (p x) using the poisson distribution calculation tool:

• Select “One Variable”

• Enter 15.2 into “Expected Average” text box

• Enter 15.5 into “Proposition” text box

• Click “Calculate”

You will then see that more than 15.5 has an average percentage of 45.24%, while less than 15.5 has an average percentage of 54.7%. The Moneyline odds with zero vig on over 15.5 would therefore be +121.05, and the true Moneyline odds on under 15.5 would be -121.05. You would then be able to see that -115 is an attractive price on under 15.5, as the true odds should be -121.05 based on the average number of times the event has occurred in the past. This poisson probability distribution analysis helps you make educated betting decisions from a position of strength.

## Who Should Use This Poisson Distribution Calculator

You should use this calculator for poisson distribution probability if you want to bring a more rigorous, mathematical approach to prop betting. It can be used to help you decide whether to bet over or under on total points, yards, goals, attempts, corners, free-kicks, three-pointers and so on. You can use the poisson’s distribution calculator to work out the likely success rate of team and player props, include pre-match wagers, live betting and futures betting. You just need the random variable and the average number of times the event has occurred in order to arrive at the poisson probability, also known as p x.

Anyone can benefit from taking the time to calculate poisson distribution, from novice handicappers to veteran bettors. When used correctly, the poisson’s distribution calculator should help you win more prop bets over the course of the year, because you will be armed with the probability distribution before betting on the random variable. You should therefore bookmark this poisson distribution calculator page and use it on a regular basis to work out the probability of each wager paying off.