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Thanks to the ingenious works of French Mathematician Simeon Denis Poisson in the 19th century, bookies enthusiasts can calculate the probability of sports betting wagers using the Poisson distribution betting strategy.
Editorial Note
This guide explains how bettors can use the Poisson distribution to estimate the probability of count-based outcomes, such as goals, sacks, or other events occurring within a game. The calculations and betting lines are educational examples only; model accuracy depends on the quality of the data and assumptions used, and no method can guarantee a winning wager.
Quick Answer
The Poisson distribution betting strategy estimates how likely an event is to occur a specific number of times based on its expected average. Bettors can use it to model count-based outcomes, convert the resulting probabilities into fair odds, and compare those odds with sportsbook prices. It works best when events occur independently and at a relatively stable average rate.
What is the Poisson Distribution Betting Strategy?
In simple terms, the above definition connotes that, when bettors know the average number of times an event will happen, they can use the Poisson distribution method to calculate how likely other numbers deviate from that average.
How it Works the Poisson Distribution Betting Strategy?
Like most betting strategies, the Poisson strategy can be tailored for use in nearly any sport of your choosing. The only requirements for this betting method are the league scoring average for both away and home teams, as well as away and home scoring averages for the two teams involved in the game you intend to predict.
Notably, you don’t have to understand all the nitty gritties of Simeon Denis Poisson’s publications to use the method, as the Microsoft Excel application offers a universal formula that easily calculates what you need. The Excel formula is =POISSON(x, mean, cumulative). The breakdown of the formula is:
- X: The number we seek to solve; in this case the numbers are 4.0 and 5.0.
- Mean: Our expectation in the results.
- Cumulative: This simply asks if we are solving for a range of data or an exact outcome.
For this example, we would enter ‘true’ because we’re not looking for an exact outcome.
Example of Using Poisson Distribution in NFL Handicapping
In the example below, we will be using the Poisson method to in trying to predict the number of sacks in an NFL game. Like turnovers, sacks are recorded as a single unit when they happen. Although sacks have a small probability of happening on every play, they have many potential occurrences, making them a commonality in NFL games. That said, let’s get to the example, using the sample data below:
- Pinnacle: o4.0 -110/ u4.0 -110
- Top Bet: o4.0 -107/ u4.0 -107
- 5 Dimes: o5.0 +210 / u5.0 –230
- Bovada: o4.5 +180/ u4.5 -200
Using the =POISSON(x, mean, cumulative) formula, the values in our formula will be as follows:
- X: The numbers here will be 4.0 or 5.0
- Mean: In this case, we will go with an average of 4.0 sacks per game. Note that this number is usually based on historical averages or data, but the 4.0 used here is for purposes of an example
- Cumulative: In this case, we will be entering ‘true’ since we are not looking for an exact outcome
Calculating Poisson Distribution Betting Strategy
Calculating Poisson using 4.0 as the X, then our Excel calculation will be as follows: =POISSON (4.0, 4.0, TRUE), which results in 62.88 percent or 0.628837 as our implied probability. This probability can be easily converted into American odds using an odds converter or using basic mathematics. Through the conversion, we get -169.41, meaning that a fair market value on the OVER or UNDER at 4.0 is approximately -169.
Considering the pricing range of Pinnacle (at -110) and Top Bet (at -107), both odds are eliminated from our breakeven odds of -169, since they both don’t look to offer value on both sides of the bet. Conversely, Bookies (at –230) and MyBookie (at +180) looks to offer great value and +EV betting opportunity.
Calculating Poisson using 5.0 as the X, the corresponding Excel values will be =POISSON (5.0, 4.0, TRUE), which results in 78.51 percent or 0.78513 as the implied probability. Converted to American odds, it comes to approximately -365. This would mean that we’d need +365 / -365 as our breakeven odds, and going by our examples, none of our examples fit the bill to offer value, so we’ll skip it.
Conclusion
Remarkably, the Poisson method is a simple predictive model of sports betting that does not allow for consideration of too many factors like game status and club circumstances, which often have an effect on the game.
But even with its limitations, Poisson can be a valuable starting point to understand the basics of creating your own odds, which you can in turn used to advise your betting endeavors.
Bettors who want to model a wider range of possible outcomes can also explore this introduction to the Monte Carlo method, which explains how repeated simulations can estimate probabilities when several variables and uncertain outcomes are involved.
Its applicability to other sports also makes it a great option. But as an underlining rule, ensure that you choose your sports wisely and follow all the necessary guidelines for recognizing valuable Poisson Distribution opportunities.
MyBookie: Bet On Anything. Anywhere. Anytime.
About the Author
Since 2008, D.S. Williamson has written about sports and sports handicapping. His philosophy is value-based, meaning stats and other handicapping factors are only worth something in comparison to wagering odds. He believes money management and making value-based wagers is the single more important factor that distinguishes successful sports bettors from non-successful sports bettors.
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