Poisson Distribution: Part 2 – Calculating Goal Expectancy

Part 1 offered a brief introduction to the world of Poisson Distribution. In this article, we look into the practice of finding Goal Expectancy, or the number of goals we can expect in a match.

The process involves:

• Using historical results to determine the average goals for and against for both teams.
• Comparing these figures to the league average.
• Creating values for each team’s attacking and defensive strength.
• Turning this data into Goal Expectancy figures that we can use.
• Putting Goal Expectancy into a Poisson Distribution formula which calculates the probability of each result when a pair of teams face one another.

In part 3, we’ll show you how to create an odds tissue and compare it to what the bookmakers offer. This enables you to determine whether a specific bet offers ‘value.’

However, today, we look at how to calculate Goal Expectancy.

Gather Your Data

This is the most time-consuming aspect. Let’s look at the Everton vs. Liverpool Merseyside Derby match played on October 17, 2020. We created this article before the match, but the game will have been completed by the time you read this.

You can take a snapshot of a league table as it stands. This is probably the best option in the middle of a season. However, most European leagues, at least, have only started. Therefore, to get a reasonable data size, you should use last season’s table. The issue here, of course, is the significant differences in teams now compared to last year.

In general, you would need to find the average home and away goals scored and conceded by each team last season. Create a spreadsheet and include the data for all 20 sides in the English Premier League.

However, we are only going to use the league average when analysing this one game. Here is a quick overview of the 2019/2020 English Premier League season.

• Goals Scored at Home Overall: 576 in 380 games – League Average = 1.51
• Goals Scored Away Overall: 458 in 380 games – League Average = 1.20

Next, we need to determine Everton’s home goals scored average and average goals conceded per game at home. We also require Liverpool’s away goals scored average, and average goals conceded on the road:

• Everton Home Goal Average For: 1.26
• Everton Home Goal Average Against: 1.11
• Liverpool Away Goal Average For: 1.74
• Liverpool Away Goal Average Against: 0.89

What is Each Team’s Attack Strength?

We get this figure by getting a team’s average and dividing it by the league average.

• Everton: 1.26 / 1.51 = 0.83
• Liverpool: 1.74 / 1.20 = 1.45

What is Each Team’s Defence Strength?

Once again, we get each side’s average and divide it by the league average for goals conceded.

• Everton: 1.11 / 1.20 = 0.93
• Liverpool: 0.89 / 1.51 = 0.59

Finally! We Calculate Goal Expectancy

We get Everton’s Goal Expectancy by multiplying their Attack Strength by the Defence Strength of Liverpool AND the average number of league goals scored at home.

0.83 x 0.59 x 1.51 = 0.74

We calculate Liverpool’s Goal Expectancy by multiplying their Attack Strength by the Defence Strength of Everton and the average number of league goals scored by away teams.

1.45 x 0.93 x 1.20 = 1.62

According to this data, the average goals likely scored in the match for each team is as follows:

• Everton: 0.74
• Liverpool: 1.62

Last season, the game finished 0-0, and the stats above suggested a tight game. It usually is between these two teams at Goodison in recent times. However, we are not yet finished.

Using Poisson Distribution

This step involves determining the likelihood of each possible scoreline. This means using the Poisson Formula:

P (k events in interval) = (λ^k e ^–λ) / k!

In case you were wondering, the various symbols in the formula mean the following:

• P: Probability.
• k: In the Poisson formula, it officially means ‘the number of occurrences in the interval.’
• λ: Expected goals.
• e: 2.71828, which is known as Euler’s number
• k!: The factorial of k. The function says to multiply all the whole numbers from the chosen number down to 1. Therefore, 5! = 5 x 4 x 3 x 2 x 1 = 120. 2! = 2 x 1 =2, and so on.

As we mentioned in part 1, Excel can work it out for you. There are also loads of online calculators. In many cases, you only need to include the home and away goal average.

After finally finding a calculator that suited our needs, we could come up with useful data. Here is a look at the most likely scores and the percentage chance of it happening:

• 1-0 Liverpool: 15.29%
• 2-0 Liverpool: 12.39%
• 1-1 Draw: 11.32%
• 0-0 Draw: 9.44%
• 2-1 Liverpool: 9.16%
• 1-0 Everton: 6.89%

Here are the percentage likelihoods of other outcomes:

• Over 0.5 Goals: 90.91%
• Over 1.5 Goals: 68.49%
• Over 2.5 Goals: 42.01%
• Over 3.5 Goals: 21.27%
• Over 4.5 Goals: 9.09%
• Everton Clean Sheet: 19.8%
• Liverpool Clean Sheet: 47.62%
• Both Team to Score: 42.01%
• Everton Win: 16.91%
• Liverpool Win: 58.44%
• Draw: 24.64%

Of course, the above is based on last season’s data. This season in the English Premier League has seen a massive increase in the number of goals scored. Will the Merseyside Derby be the usual cagey affair at Goodison in recent times, or will we see one of the classics the teams used to serve up?

Final Thoughts on Goal Expectancy

In general, Poisson works best when trying to see if a home or away win or draw is overpriced. It is potentially useful for over 2.5 goal bets too. However, please remember that it is based on historical data. In our example above, Everton fans will point out that this season’s team is better. However, we are only a small part of the way through the season, so one shouldn’t make assumptions based on tiny data sizes. Given the unusual start to this season in England, perhaps it is worth waiting another couple of months to see how things pan out.

The only way you will know whether there are possible value bets is by converting your Poisson findings into odds. This is what we look at in Part 3.