Football Stats Query - Maths Types, Step This Way

[Furtho]

I want to find a simple, statistical way of comparing leagues on the basis of their (let's call it) competitiveness, by which I mean the degree of parity achieved by all the participating teams in a given league.

For example, one method I came up with was of counting the number of teams in a division that across the course of a season gained more than two points per game or fewer than a single point per game, adding them together and dividing by the total number of teams. The Premier League, say, consists of twenty teams playing 38 matches. Manchester United, Liverpool and Chelsea won more than (38 x 2 =) 76pts and Sunderland, Hull, Newcastle, Middlesbrough and West Brom all got fewer than 38pts. Therefore a total of eight out of twenty teams fell outside my parameters, or 40%. The equivalent figure for the Championship in the season just finished is only 8.5%.

But somehow I feel that this way of looking at things doesn't express any sense of the extent to which one or more teams might skew the figures, by being really really good or absolutely terrible. I can't explain very well what I'm hoping to achieve here, but has anyone got any suggestions as to a formula that's straightforward to execute and would enable comparisons of divisions to be made?

[Bored Of Education]

Football Stats Query - Maths Types, Step This Way

Here are the UEFA co-efficients if they help

I am doing a presentation on hypothesis testing in Maths next week and want to use my A & B teams's results this season where they played the corresponding teams of other clubs to see if there is an association between the results.

I wanted to use goal differences in each match but I don't think I am going to find a test that takes into account the positives and negatives so am just going to have to award 0, 1 or 2 points instead.

Hello? Anyone out there? They love this sort of shit in "world"

[Bored Of Education]

Football Stats Query - Maths Types, Step This Way

Sassafrassarassum double posts

[Furtho]

Football Stats Query - Maths Types, Step This Way

Bumpumpadum.

[Banana Banana]

Football Stats Query - Maths Types, Step This Way

I think you could do a chi-square test based on a norm that a league with completely equal teams would always draw each other.

If you give two points for a win and 0 for a draw you can then calculate the absolute difference between the norm.

[Bored Of Education]

Football Stats Query - Maths Types, Step This Way

Interesting idea but I have just finished my hypothesis testing exam so I will give my brain a couple of days to clear

[Oldelpaso]

Football Stats Query - Maths Types, Step This Way

I guess the answer in both cases depends greatly at what sort of level of maths you are comfortable with. A way of measuring the parity of a league would be to find the standard deviation of the number of points earned per game across the league as a whole.

For Bored's hypothesis test, the weakness in using goal differences between corresponding results is that the difference between a 4 goal win and a 5 goal win would be the same as the difference between a one goal win and a draw. In the respect, win, lose and draw is a more robust measure anyway.

[Bored Of Education]

Football Stats Query - Maths Types, Step This Way

My main worry was that there was no test that would keep the, for want of a better word, integrity of negatives and positives through to the conclusion e.g. a 1-0 win as a 1-0 loss

My only worry about the 2 points for a win, 1 for a draw and 0 for a loss was that the B team only lost one game so the conclusion would be obvious from the start.

Having said that though, every one of the five test questions today had stats that you would be able to judge just by looking at them anyway.

I am not going to be studying hypothesis testing again