Using Poisson Distribution in Your Sports Betting Strategy

August 9, 2023

In sports betting, sharp bettors have long relied on statistical analysis to gain an edge over sportsbooks. One powerful tool in their arsenal is the Poisson distribution, a probability theory developed by Siméon Denis Poisson in the 19th century. This distribution allows bettors to leverage historical sports data to predict the most likely outcome of a sports event. 

While not foolproof, understanding and applying the Poisson distribution can be critical to a successful betting strategy, especially for sports where scoring occurs in small increments, such as soccer, hockey, and certain NFL props wagering.

What is a Poisson Distribution? 

At its core, the Poisson distribution calculates the probability of unrelated events occurring within a specific period, assuming the expected number of events is known. For sports betting, this means using historical game results to estimate the likelihood of various potential scores in a future event.

How the Poisson Distribution Enhances Sports Betting Predictions

The Poisson distribution is a valuable tool in sports betting that helps predict a sports event’s most likely final score. 

To illustrate its application, consider a hypothetical soccer match between Arsenal FC and Chelsea FC, using historical scoring data from the 2017-2018 English Premier League season.

First, we gather relevant data from the season:

Goals scored at home by all EPL teams Goals Scored on the road by all EPL teams Goals scored at home by Arsenal Goals allowed at home by Arsenal Goals scored on the road by Chelsea Goals allowed on the road by Chelsea
Goals 582 436 54 20 32
Matches 380 380 19 19 19
Goals/Matches: Average 1.532 1.147 2.842 1.053 1.684


Attack Strength and Defense Strength

Next, we calculate the “Attack Strength” and “Defense Strength” for each team:

  • Arsenal Attack Strength: 2.842 / 1.532 = 1.855 
  • Chelsea Attack Strength: 1.684 / 1.147 = 1.468 
  • Arsenal Defense Strength: 1.053 / 1.147 = 0.918 
  • Chelsea Defense Strength: 1.158 / 1.532 = 0.756

Predicting Scores Using Poisson Betting Strategy

Now, we can predict the likely number of goals each team will score in the matchup:

  • Likely goals scored by Arsenal = 1.855 x 0.756 x 1.532 = 2.148 
  • Likely goals scored by Chelsea = 1.468 x 0.918 x 1.147 = 1.546

Based on these calculations, the expected average goals scored in the match would be:

  • Arsenal: 2.148 
  • Chelsea: 1.546

Poisson Distribution Calculators to Determine Multiple Outcomes

The next step is to use Poisson distribution calculators available online to determine the probability of a range of scoring results for each team.


Goals 0 1 2 3 4 5
Arsenal 11.67% 25.07% 26.93% 19.28% 10.35% 4.45%
Chelsea 21.31% 32.95% 25.47% 13.12% 5.07% 1.57%


While the Poisson distribution provides valuable insights into scoring probabilities, it is essential to consider certain limitations. 

Factors like injuries, locker room dynamics, weather conditions, and unexpected player performances can significantly impact the outcome of a sports event, making predictions based solely on statistical data less reliable.

Limitations of the Poisson Distribution in Sports Betting

Despite its usefulness, the Poisson distribution has limitations. It does not account for human factors like injuries, locker room dynamics, or unexpected individual performances. 

Weather conditions and external factors can also affect the outcome of a game. As a result, while the Poisson distribution can offer valuable insights, it is not a guarantee of success in sports betting.

Sharpening your statistical skills can help you make more informed wages and improve your chances of finding value in the odds board. Remember, sports betting involves inherent risks; no strategy can guarantee consistent winnings.

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