Loonerty
TheBrownDog
Hello ladies and gentlemen of the Sweet FA.
For Season 26 I presented a thread looking at the results in a statistical way.
Here is that thread:
www.bigfooty.com
Today, I will present the findings for the Season 27 results.
Histogram of Margins
As we began last time, here is a histogram of every margin from Season 27.
This looks a little less normally distributed than last season, but we can still see a reasonably even shape about 0, the expected mean (actual mean: 0.9, so the average result is approximately a 1 point win for the home team). The blue curve shows a true normal distribution, so we do see that there are more low negative margins than expected if the results were truly normal, but there are fewer mid-range negative margins than expected.
Conducting a Shapiro-Wilk test to test for normality:
The p-value is now above 0.05, so we are able to reject the hypothesis that the margins are normally distributed at the 95% confidence level. Interestingly, this is not the result we obtained last season!
Comparison of Home and Away Scores
We will now compare home and away scores.
First, their distributions.
We see here that away scores have a longer tail towards higher scores, while the home score tail goes further towards lower scores. There are more home scores in the 110-140 range however.
Last season we were able to observe the overlap, as both home scores and away scores were accepted to be normal by the Shapiro-Wilk test. This time however, neither distribution passes the Shapiro-Wilk test, so we are unable to provide an image of their overlap.
We may, however, use a t-test to see whether the true difference in the means of the distributions of home scores and away scores is significantly different from 0.
The p-value here is 0.7732, which is much greater than 0.05. Therefore we cannot reject the hypothesis that the true difference in means is 0.
Once again, applying the Kolmogorov-Smirnov test, we obtain a result of 0.9207 for the p-value - therefore we once again cannot reject the hypothesis that the distributions are the same.
Other Stuff
The average margin in Season 27 was 24 points.
Home sides won 52 games in Season 27, Away sides won 51 games and there were 2 draws.
The median margin in Season 27 was 19 points. The largest margin was 85 points, which was the largest away win. The largest home win was 68 points.
Thank you for reading. I will now take questions.
For Season 26 I presented a thread looking at the results in a statistical way.
Here is that thread:
Media - LoonStats Presents: Actual useful statistics on margins and scores
Hello. I decided to start a new thread because the info in here is actually interesting and useful. There is always a lot of talk about potential biases within the sim, even though it's always alleged and is certainly true that it is completely 50/50. This was shown by BRAB a few seasons ago...
www.bigfooty.com
Today, I will present the findings for the Season 27 results.
Histogram of Margins
As we began last time, here is a histogram of every margin from Season 27.
This looks a little less normally distributed than last season, but we can still see a reasonably even shape about 0, the expected mean (actual mean: 0.9, so the average result is approximately a 1 point win for the home team). The blue curve shows a true normal distribution, so we do see that there are more low negative margins than expected if the results were truly normal, but there are fewer mid-range negative margins than expected.
Conducting a Shapiro-Wilk test to test for normality:
The p-value is now above 0.05, so we are able to reject the hypothesis that the margins are normally distributed at the 95% confidence level. Interestingly, this is not the result we obtained last season!
Comparison of Home and Away Scores
We will now compare home and away scores.
First, their distributions.
We see here that away scores have a longer tail towards higher scores, while the home score tail goes further towards lower scores. There are more home scores in the 110-140 range however.
Last season we were able to observe the overlap, as both home scores and away scores were accepted to be normal by the Shapiro-Wilk test. This time however, neither distribution passes the Shapiro-Wilk test, so we are unable to provide an image of their overlap.
We may, however, use a t-test to see whether the true difference in the means of the distributions of home scores and away scores is significantly different from 0.
The p-value here is 0.7732, which is much greater than 0.05. Therefore we cannot reject the hypothesis that the true difference in means is 0.
Once again, applying the Kolmogorov-Smirnov test, we obtain a result of 0.9207 for the p-value - therefore we once again cannot reject the hypothesis that the distributions are the same.
Other Stuff
The average margin in Season 27 was 24 points.
Home sides won 52 games in Season 27, Away sides won 51 games and there were 2 draws.
The median margin in Season 27 was 19 points. The largest margin was 85 points, which was the largest away win. The largest home win was 68 points.
Thank you for reading. I will now take questions.
