The Poisson Distribution betting strategy involves calculating the likelihood of outcomes in sporting events using a mathematical formula. It is mainly used in football betting and is suited to sports with continuous action. It is a data-driven strategy which uses stats from both specific teams and the league to predict results. Read on to find out how to implement the Poisson betting model into your betting strategy.
- 1 What Is the Poisson Distribution Betting Strategy?
- 2 How Does Poisson Distribution Work?
- 3 When to Use the Poisson Distribution Strategy
- 4 Pros & Cons of the Poisson Distribution Approach
- 5 Best Online Bookies to Test the Poisson Distribution Betting Strategy
- 6 Poisson Distribution vs Other Betting Strategies
- 7 Poisson Distribution Calculator or Tools
- 8 Real-World Example of Poisson Distribution in Action
- 9 ThePuntersPage Final Say
- 10 Poisson Distribution FAQs
What Is the Poisson Distribution Betting Strategy?
Poisson Distribution is a probability theory which measures how likely something is to occur in a specific period. It was developed by 19th century French mathematician Siméon Denis Poisson as a method to determine the probability of a number of wrongful convictions which had occurred in specific countries.
This translates to sports betting by using relevant data to predict an outcome. In football betting, it can predict the number of goals scored by one or both teams and, through this, you can predict the result.
How Does Poisson Distribution Work?
Poisson Distribution is often used in football to predict the result based on the probability of a certain number of goals being scored. To do this, you must calculate the average goal expectancy of the league you are betting on along with the attack strength and defence strength for both teams. To get a team’s attack or defence strength, simply divide the number of goals they have scored/conceded by the league’s average.
The Poisson Distribution formula is P (k events in interval) = (λk e –λ) / k!
In this formula:
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P is the probability
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k is the number of occurrences in the interval (number of goals)
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λ is the expected number of goals
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e is Euler's number (e = 2.71828…)
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k! is the factorial of k
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 “Event occurrences”, and the expected average goals score per match in the bottom, in “Expected event occurrences”.
An example could be if you wanted to bet on a match between Manchester City and Brentford. The stats provided the following expected goals (λ):
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Manchester City (Home): λ = 2.4
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Brentford (Away): λ = 0.9
Using the calculator, we can see the probability of each team scoring each number of goals up to five. The table shows that based on the model the most likely outcome is a 2-0 win for Man City.
| Home \ Away | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 0.0907 | 0.0816 | 0.0367 | 0.0110 | 0.0025 | 0.0005 |
| 1 | 0.2177 | 0.1959 | 0.0879 | 0.0263 | 0.0061 | 0.0013 |
| 2 | 0.2613 | 0.2353 | 0.1055 | 0.0316 | 0.0073 | 0.0016 |
| 3 | 0.2090 | 0.1880 | 0.0843 | 0.0252 | 0.0058 | 0.0013 |
| 4 | 0.1254 | 0.1128 | 0.0506 | 0.0151 | 0.0035 | 0.0008 |
| 5 | 0.0602 | 0.0542 | 0.0243 | 0.0072 | 0.0016 | 0.0004 |
If you convert each of these into a percentage, you can then compare them to the bookie’s odds to see if you can find any value bets.
| BRE 0 | BRE 1 | BRE 2 | BRE 3 | BRE 4 | BRE 5 | |
|---|---|---|---|---|---|---|
| MC 0 | 3.69% | 3.32% | 1.49% | 0.45% | 0.10% | 0.02% |
| MC 1 | 8.85% | 7.97% | 3.59% | 1.08% | 0.24% | 0.04% |
| MC 2 | 10.62% | 9.56% | 4.30% | 1.29% | 0.29% | 0.05% |
| MC 3 | 8.50% | 7.65% | 3.44% | 1.03% | 0.23% | 0.04% |
| MC 4 | 5.10% | 4.59% | 2.06% | 0.62% | 0.14% | 0.03% |
| MC 5 | 2.45% | 2.20% | 0.99% | 0.30% | 0.07% | 0.01% |
When to Use the Poisson Distribution Strategy
The Poisson Distribution betting strategy is best used in sports where the number of events is random and infrequent. It is most commonly used for football and hockey. In football, it is used to predict the number of goals scored by each team or in the match as a whole. Therefore, it is an excellent tool when betting on markets such as Over/Under goals or the match result.
Best Betting Scenarios
Poisson Distribution: Useful for pre-match betting on goals and results
Chris Sampson: This betting strategy is best used pre-match on low-scoring sports. In football, it is extremely useful when researching goal markets such as under/over and BTTS, 1X2 and exact scorelines. It is also useful to work out the probability of different results and compare them to the bookie’s odds to see if you are getting value.
While it uses real life stats, you have to be aware that it doesn’t take into account how goals and other events can change games or shift momentum, or a team’s motivation levels. No system is foolproof, and you know that with Poisson distribution that it is based on data.
It is useful to use this strategy alongside a bankroll management system, such as Kelly Criterion, in order to keep your betting finances in control.
Pros & Cons of the Poisson Distribution Approach
Like all betting strategies, there are advantages and disadvantages to the Poisson Distribution method. We have listed them below.
- Great for low scoring sports: Goals in football are relatively rare and are distinct values.
- Gives probabilities for exact scores: This means that bettors can use the data for goals totals, BTTS, match result and exact scoreline markets.
- Gives an understanding on how odds are set: Odds are based on probabilities. Using this method helps you understand the process the bookies will go through.
- You can find value in odds: By using this formula you can compare your odds to the bookie. Where you see a greater probability of an event occurring than the bookie you can find some great value bets.
- Mathematical backing: Poisson Distribution is based on facts and data. It removes bias and allows you to make your picks on historical stats.
- Long term profitability: You may not get many big wins, but if you base your bets on this much data, you have a better chance of making informed choices, which could lead to profit over a long period of time.
- Assumes independence: Technically, goals are independent events, but the model ignores the fact that goals change the momentum of games and the tactical approach of teams. It also assumes goals will occur at a constant rate, ignoring different phases of the game.
- Less effective in high scoring sports: The model does not work as well in sports where scoring is more frequent.
- Underestimates draws: The probability of draws is underestimated, mainly due to home and away not being considered.
Best Online Bookies to Test the Poisson Distribution Betting Strategy
Check out our list of the best UK bookmakers to test out the Poisson Distribution betting strategy.
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Founded:
2000
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
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Bet £10 & Get £30 18+. Min deposit requirement. Free Bets are paid as Bet Credits and are available for use upon settlement of qualifying bets. Min odds, bet and payment method exclusions apply. Returns exclude Bet Credits stake. Time limits and Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Founded:
1997
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
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Bet £10 Get £40 in Bonuses 18+ New GB customers only. Min £10 debit card deposit. Place a £10+ bet at Evens (2.0)+ on Sports within 7 days. Opt in for £20 in free bets and £20 Casino Bonus. Valid for 7 days. Geographical restrictions. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Min. stake: £0.01
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Founded:
1967
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
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Bet £10 Get £50 in Free Bets 18+ New customers only. Register with BETFRED50. Deposit £10+ via Debit Card and place first bet £10+ at Evens (2.0)+ on Sports within 7 days to get 3 x £10 in Sports Free Bets & 2 x £10 in Acca Free Bets within 10 hours of settlement. 7-day expiry. Eligibility & payment exclusions apply. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Min. stake: £0.10
Max. withdrawal: £20,000
Min. deposit: £5
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Founded:
1886
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
Payment methods(9):
Bet £5 Get £20 in Free Bets 18+ New UK+IRE Customers only. Certain deposit methods & bet types excl. Min first 5 bet within 14 days of account reg at min odds 1/2 = 4x 5 free bets. Free bets valid for 7 days, stake not returned. No cashout, restrictions + Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Min. stake: £0.01
Max. withdrawal: £250,000
Min. deposit: £5
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Founded:
1946
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
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Bet £10 & Get £30 in Football Free Bets 18+ New customers only. Opt in, bet £10 or more on any football market at minimum 1/1 odds within 7 days of registration. No cash out. Get £30 in Free Football Bets, selected markets. Free Bets expire in 7 days. Full T&Cs apply. Please gamble responsibly. GambleAware.org #ad
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Min. stake: £0.05
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Min. deposit: £5
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Founded:
2023
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
Bet £10 Get £40 in Free Bets 18+ New customers only. 7 days to place qualifying bet of £10 at Evens (1/1) or above to receive 4 x £10 Free Bets: 1 x £10 football, 1 x £10 horse racing & 2 x £10 Bet Builders. Free Bets cannot be used on e-sports and non-UK/IE horse racing. EW bets min £20. 7 day expiry. Exclusions apply. Stake not returned. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad |
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Founded:
1999
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
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Bet £10, Get up to £60 in Free Bets 18+ Spread betting losses can exceed deposit. 18+ www.gambleaware.org. Place a £10 fixed odds single or £10 each-way bet at minimum odds of 1/2 and get 3 x £10 free fixed odds bets, 3 x £5 Total Goals football spread bets and 3 x £5 Winning Favourites spread bets and a £1 racing Race Index spread bet. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Min. stake: £1.00
Max. withdrawal: £25,000
Min. deposit: £1
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Founded:
1989
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
Payment methods(7):
Bet £10 Get £20 in Free Bets 18+ New UK customers (Excluding NI) only. Mobile exclusive. Min Deposit £10. Min stake £10. Min odds Evs. Free bet applied on 1st settlement of any qualifying bet. 30 days to qualify. Free bets expire in 7 days. Cashed out/Free Bets won't apply. Account & Payment method restrictions apply. 1 Free Bet offer per customer, household & IP Address only. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
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Min. stake: £0.01
Max. withdrawal: £50,000
Min. deposit: £5
24/7 Customer Support:
Mobile-App:
Android
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Founded:
1992
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
Payment methods(3):
Bet £10 Get £60 in Free Bets 18+. Bet £10, Get £60 in Free Bets: Available to new customers only, aged 18 or over, residing in Great Britain. The promotion will run from 11th March 2025 until discontinued by Sporting Index Ltd. using its reasonable discretion, ("Promotion Period"). Offer can only be used once per customer. Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
Good to know:
Min. stake: £0.01
Max. withdrawal: £20,000
Min. deposit: £1
24/7 Customer Support:
Mobile-App:
Android
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Founded:
1926
UK Gambling Commission
This bookmaker is licensed by the UK Gambling Commission (UKGC), ensuring compliance with strict regulations designed to promote fairness, transparency, and the safety of players. The UKGC license is a mark of trust, safeguarding your funds and personal information while encouraging responsible gambling. Learn more about the UKGC here
Payment methods(8):
Bet £5 Get £20 18+ New Customers only. Certain deposit methods & bet types excl. Min first £/€5 bet within 14 days of account reg at min odds 1/2 to get 4 x £5 free bets. Free bet available to use on selected sportsbook markets only. Free bets valid for 7 days, stake not returned. Restrictions + Full T&Cs apply. Bet Responsibly. GambleAware.org #ad
Good to know:
Min. stake: £0.01
Max. withdrawal: £250,000
Min. deposit: £5
24/7 Customer Support:
Mobile-App:
Android
iOS
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Poisson Distribution vs Other Betting Strategies
We have compared the Poisson Distribution strategy to some other betting strategies and system and presented our findings in a table.
| Staking Strategy | Purpose | Best Scenario to Use It | Limitations |
|---|---|---|---|
| Poisson Distribution | Predicts frequency of an event | Football, low scoring sports | Doesn’t consider context of game |
| Standard Deviation and Variance | Helps assess consistency and risk | In markets with fluctuating odds | Does not predict specific results |
| Kelly Creterion | Calculates how much to bet when you have an edge | To manage your bankroll | Can’t be used to predict results |
| Hedge Betting | Lock in profit and reduces risk by betting on all outcomes | Live betting and other variable markets | Limits potential profit and requires significant capital |
| Value Betting | To wager only when the true odds are better than the bookie | All sports when you have identified a bet where the true probability is higher than the bookie’s assessment | Can be risky without careful bankroll management |
| Fibonacci Betting | Staking/money management | Recover losses systematically | Like other negative progression systems, such as the Martingale and the Labouchere it is high risk. |
Poisson Distribution Calculator or Tools
There are a number of Poisson Distribution calculators available online. You simply enter your data, and the calculations are carried out for you.
Real-World Example of Poisson Distribution in Action
We used the Poisson Distribution formula to predict the match between Newcastle United and Everton on the final day of the 2024/25 season. We were able to use data from 37 matches of a 38-match season. The key stats were as follows.
| Newcastle United | Everton | |
|---|---|---|
| Goals Scored per Match | 1.79 | 1.11 |
| Goals Conceded per Match | 1.24 | 1.16 |
| Goals Scored per Match Home/Away | 2.11 (Home) | 0.84 (Away) |
| Goals Conceded per Match Home/Away | 1.05 (Home) | 1.29 (Away) |
League Average is 1.4 goals per team per match.
Based on these stats, the model predicted that the most likely scoreline was a 1-0 win for Newcastle, followed by a 2-1 win for the home side. Everton’s greatest chance of picking up points were in a low scoring draw.
| Goals | Newcastle Probability | Everton Probability |
|---|---|---|
| 0 | 22.4% | 36.7% |
| 1 | 33.4% | 36.3% |
| 2 | 24.9% | 18.0% |
| 3 | 12.4% | 5.9% |
| 4+ | 6.9% | 3.1% |
| Scoreline | Probability |
|---|---|
| 1-0 Newcastle | 12.2% |
| 2-1 Newcastle | 9.0% |
| 1-1 Draw | 12.2% |
| 2-0 Newcastle | 8.4% |
| 0-0 Draw | 8.2% |
| Newcastle win | 55% |
| Draw | 25% |
| Everton win | 20% |
The outcome was somewhat different. Newcastle needed a win to guarantee Champions League qualification and produced a nervy, disjointed performance. Everton, who had one of the league’s meanest defences in the second half of the season were very well organised and, while the home side missed some chances, they were largely frustrated. Everton broke away to take the lead and it finished 1-0 to the visitors.
This is a good example of Poisson Distribution’s strengths and weaknesses. The predicted scoreline looked very plausible and would on several occasions have been proved right. But while the prediction was on sound statistical ground, it failed to take into account other variables, including the occasion and team changes due to injuries.
ThePuntersPage Final Say
The Poisson Distribution betting strategy is a proven model, based on statistics. It uses real life, relevant data and can be incredibly useful when betting pre-match on Under/Over goals, BTTS, 1X2 and exact scorelines. The downside is that it doesn’t take into account changes and shifts in momentum as it classes goals as independent events. Like all betting systems it is not a guaranteed path to success, but it is a betting strategy that can help you make more informed choices. It can work well when combined with value betting and a bankroll management system. You can read up on other systems on our betting strategies page.
Poisson Distribution FAQs
There is no system guaranteed to make a profit. However, Poisson Distribution is based on mathematical facts and can be a powerful indicator in pre-match football betting.
Yes, you can use Poisson Distribution to research your bets on bet365.
Poisson Distribution works best in low scoring sports. Football is where it is most commonly used.
Poisson Distribution is not banned by bookmakers.
While Poisson Distribution can be used when betting in-play, it is more suited to pre-match betting. It does not take into account shifts in momentum and tactical changes, therefore while your research can be used as a guide when betting live, it is much more suited to placing bets ahead of the game.