# Poisson Distribution & how to use it to handicap Goal scoring props in Soccer

Poisson Distribution & how to use it to handicap Goal scoring props in Soccer – Goal scoring props are some of the most manageable soccer propositions to handicap.

### intro

This is especially true for the markets will both teams score, will there be a draw and which team will score first. In this article, I will take the time to talk about the rarely discussed math required to calculate the fair odds and probabilities on these markets. I will also touch on how to handicap correct scoring markets.

Prerequisite: It is imperative you first understand the information covered in my article on over/under betting, which shows how to handicap the number of goals each team will score in a match. Pulling the exact example from that article, there was an EPL match where I handicapped Southampton was expected to score 1.27 goals, and Everton was to score 1.70 goals. I’ll use this to show the handicapping for several markets.

### Poisson distribution – Handicapping on if Both Teams Score

For this, we’re going to run the Poisson distribution on each team’s chance of scoring 0 goals. As a reminder from other articles, in Microsoft Excel, we enter =POISSON(solve-for, expected, false) when solving for an exact score. So:

Everton: =POISSON(0, 1.7,false). Enter this in Excel, click the tab, and see 18.27% of the time they score 0 goals, which means 81.73% of the time, they will score a goal.

Southampton: =POISSON(0, 1.27, false). Enter this in Excel, click the tab, and see 28.08% of the time they score 0 goals, which means 71.92% of the time, they will score a goal.

The chance that both teams score is 0.8173*0.7192=58.78%. If you Google search for an odds converter that has an implied probability field, enter that, and you’ll see that 58.78% in American odds is -143. Therefore the fair odds with no vig on if will both teams to score is Yes -143 / No +143.

Now that you have the fair odds calculated, the final step is shopping multiple online sportsbooks ( see SBS Rating for all that are reputable) and betting yes at any offering better than -143 and betting no at any offering better than +143.

### Poisson distribution on Will There be a Draw?

For this, we can use the same math calculated earlier. We know Everton will fail to score 18.27% of the time, and Southampton will fail to score 28.08% of the time. The probability the game finishes a 0-0 tie is 0.1827*0.2808, which equals 5.13%. Again using an odds converter, we can see in American odds this is a correct score of 0-0 at +1849.

### Poisson distribution on Which Team Will Score First?

In most sports, the base formula for which team to score first is -100(Favorite/Dog)=Favorite odds to score first in American Odds format. This would typically mean if we are expecting Everton to score 1.7 and Southampton 1.27, the math is -100(1.7/1.27)=-133 as Everton’s no-vig odds of scoring the first goal. The problem here is this formula does not work for soccer as there are more ties in soccer than in other sports.

To adjust, we first use the formula risk/return=implied-probability (which is a fancy term for break-even percentage). -133 is risk \$133 to win \$100 the return is \$233 (\$133 stake + \$100 win). Therefore the math is \$133/\$233=57.08% chance Everton scores first. This leaves a 42.92% chance that Southampton scores first. The problem is that just earlier, we calculated there is a 5.13% chance neither team scores.

What we need to do is remove 57.08% of 5.13% from Everton’s chances. This is 0.5708-(0.5708*0.0513)=54.15% that Everton scores first. As we already know, neither team scores 5.13% of the time, by process of elimination that leaves Southampton scoring the first 40.72% of the time. If I place these into an odds converter, I can see the fair no-vig prices on the first score are Everton -118, Southampton +146, and No Score +1849.

A small tip is this method I just gave is a shorthand. It will be slightly off by mere fractions on 96% of the games you handicap. The direction it will be off is that it will slightly overstate the favorite’s chances (we’re talking by rounding error type fractions). If you were handicapping a game where the favorite was 60+% likely to score, it would become off by a noticeable fraction, and you’ll need to find a more significant edge when betting the favorite to score first.

### Handicapping Correct Score

The math I just showed can be used to calculate any correct score. Let’s say we’re calculating the odds of a correct score of Everton 2-1 and are still working with the predicted score of Everton 1.7 and Southampton 1.27. I’m going to just run a Poisson distribution for each.

Everton: =POISSON(2, 1.7, false). Enter this in Excel, click the tab, and see there is a 26.4% chance Everton scores exactly two goals.

Southampton: =POISSON(1, 1.27, false). Enter this in Excel, click the tab, and see there is a 35.67% chance Southampton scores exactly one goal.

The probability the exact score is Everton 2-1 is 0.264*0.3567=9.42%. An odds converter will show this +962 in American no-vig odds.

### Poisson Distribution Calculator

Important disclaimer
Poisson distributions are not exact for a reason scoring is not an independent (totally random) occurrence. In games with no score, the pace is slower once the first goal scores the pace increases. If an equalizer is scored, it slows again.

What most handicappers accept is that Poisson slightly over forecasts scores of 0-1 and 1-0 and slight under forecasts scores of 0-0 and 1-1. Depending on which way you are betting, you’ll need to either find a more significant edge than Poisson reflects or can bet with a slight negative edge based on what Poisson predicts.

The fact Poisson is not entirely accurate does make it challenging to use Poisson to calculate the chances of a draw. This is because Poisson over forecasts 0-0 and 1-1, which are the most common draws.

If you’re an advanced handicapper, this can be solved by learning about Bivariate Poisson, which is a more accurate distribution model. Again, for all but advanced handicappers, standard Poisson remains the method most used. You just need to remember there is a slight over the forecast of 0-1 and 1-0 scores and the minor under the estimates of 0-0 and 1-1 scores.