The Nebbish
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- Feb 13, 2015
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This problem has a real life, Premier League football aspect to it. The question I would like to answer is:
What is the probability that Arsenal finish the season with the highest number of goals?
So far Chelsea have 55, Manchester City have 51 and Arsenal have 47 goals. There are 13 matches left in the season.
I will assume that the total number of goals for each team follows the Poisson distribution. Further I will assume that each team is expected to score 28 more goals in the remaining 13 games. (You could assume that teams will continue to score in the ratio that they already have for the remainder of the season but I'm NOT going to do that. I'm actually going to assume that they score the SAME number of goals from now on. I've reasons for thinking this but they aren't as important as the method for working out the answer. We can always change the numbers later.) Also, we are ignoring all the other teams, which isn't totally realistic, but I can live with that.
So the three variables follow a poisson distribution with Chels (28) Arsenal (28) and Man City (28). Means = variance = 28 for each variable.
Mathematically, the question is: what is the P(Arsenal Goals > both Man city and Chelsea goals) at the end of the season.
This is where I get stuck!
I can easily work out the probability that a particular team score a particular number, or I could use the cumulative poisson function to work out whether a team would score more than say 73, or 80 goals. But to answer the specific question: what is the probability Arsenal score the most goals by the end of the season?
I just don't know.
What is the probability that Arsenal finish the season with the highest number of goals?
So far Chelsea have 55, Manchester City have 51 and Arsenal have 47 goals. There are 13 matches left in the season.
I will assume that the total number of goals for each team follows the Poisson distribution. Further I will assume that each team is expected to score 28 more goals in the remaining 13 games. (You could assume that teams will continue to score in the ratio that they already have for the remainder of the season but I'm NOT going to do that. I'm actually going to assume that they score the SAME number of goals from now on. I've reasons for thinking this but they aren't as important as the method for working out the answer. We can always change the numbers later.) Also, we are ignoring all the other teams, which isn't totally realistic, but I can live with that.
So the three variables follow a poisson distribution with Chels (28) Arsenal (28) and Man City (28). Means = variance = 28 for each variable.
Mathematically, the question is: what is the P(Arsenal Goals > both Man city and Chelsea goals) at the end of the season.
This is where I get stuck!
I can easily work out the probability that a particular team score a particular number, or I could use the cumulative poisson function to work out whether a team would score more than say 73, or 80 goals. But to answer the specific question: what is the probability Arsenal score the most goals by the end of the season?
I just don't know.
