It tells us that the probability of having 1 goal is 33.47%, which is the highest. Of course as it deviates from the mean, the probability lowers. From our computation, the probability of having 7 goals is 0.08%.

I just used the POISSON()function in OpenOffice so the computation is really not that complicated, you won’t be needing the exponentials and the factorials. However, getting the correct value for the average goal u is crucial, more complicated one!

**Calculating the average goal u**

One way to compute the average goal is by using the goal statistics from the league’s previous season [1]. This can be done in three steps:

- Determine the average number of home and away goals of the whole league.
- Determine the Attack and Defense Strength of each team, from the stats of each team.
- Depending if they are playing away or home, multiply the Defense Strength, Attack Strength and the league’s average goal.

For this article, we will determine the average goal for the 26-Apr-14 game of the Premier League, Southhampton vs Everton game. Let us determine the average goal step-by-step.

*1. Determine the average number of home and away goals of the whole league. *

In the 2012-2013 season, there was 592 home goals and 471 away goals. This is in the span of 38 games (19 away, 19 home) with 20 teams. To determine the League’s average home and away goals (ALG), we use this equation:

ALG HOME = GOALS HOME / # OF TEAMS / # GAMES HOME

ALG AWAY = GOALS AWAY / # OF TEAMS / # GAMES AWAY

From this, ALG HOME = 592/20/19 = 1.558 and ALG AWAY= 471/20/19 = 1.239.

*2. Determine the Attack and Defense Strength of each team, from the stats of each team. *

Since Southhampton will be playing home, we check their home statistics (This is every important! I was confused with this one for a while.). From betexplorer.com, they have 26 goals scored while 24 was conceded from home. We calculate the Attack and Defense strength of Southhampton from home using this formula:

ATTACK STRENGTH = GOALS SCORED AT HOME / # OF GAMES HOME / ALG HOME

DEFENSE STRENGTH = GOALS CONCEDED AT HOME / # OF GAMES HOME / ALG AWAY

Everton will be playing away, so obviously we use their away statistics. Again from betexplorer.com, we know that playing away they have created 22 goals while conceded 23. Conversely, the Attack and Defense strength can be calculated as:

ATTACK STRENGTH = GOALS SCORED AWAY/ # OF GAMES AWAY / ALG AWAY

DEFENSE STRENGTH = GOALS CONCEDED AWAY / # OF GAMES AWAY / ALG HOME

Using these equations, we have calculated the attack and defense strengths of Southhampton (Home) and Everton (Away). Here is the tally: