In my previous post i compared the least squares rating of football teams to the ordinary three points for a win rating. In this post I will look closer at how these two systems rank teams differently. I briefly touched upon the subject in the last post, were we saw that the two systems generally ranked the teams in the same order, with a few exceptions. We saw that Sunderland and Newcastle were the two teams in the 2011-2012 Premier League season who differed most in their ranking in the two systems. The reason for this was of course because the least squares approach is based on goal difference, while the points system is based only on match outcome. This means that teams who win a match by many goals will benefit more on the least squares ranking than on the points system. For example, a 3-0 win will count more than a 2-1 win when we use goal difference, but they will give the same number of points based on match outcome. This also holds if wee look at the loosing team; a 2-1 loss is better than a 3-0 loss.
It seems more intuitive to rank teams on a system based on goal difference (using least squares or some other method) than the tree points for a win system, especially when we remind ourself that it lacks any theoretical justification. Awarding three points for a win instead of two was not used before the 1980’s and were not used in the World Cup until 1994. The reason for introducing the three points system was to give the teams more incentive to win. Also, as far as I know, even the two points for a win lacks a theoretical basis as a way to measure teams strength. But even if the points system lack an underlying mathematical theory, it still could be a better system than a system based on goal difference for deciding the true strength of a team. A paper titled Fitness, chance, and myths: an objective view on soccer results by the two German physicists A. Hauer and O. Rubner compares the two systems using data from the German Bundesliga. They looked at each team in each season from the late 1980’s and calculated how much the teams goal difference and points correlated between the first and second half of a season. A higher correlation means that there is less chance involved in how the measure reflects a teams real strength. What they found was that goal difference was more correlated between the half-seasons than the 3- and 2 points for a win system.
However, this does not mean that goal difference is the best way to measure team strength. I would like to see if there are some other measures that correlate better between season halves. What first comes to mind is to look at ball possession or shots at target.
As a last note, even if goal difference has a better theoretical foundation as a measure of “who is the best”, I do not think that leagues and tournaments should quit the points system. It may very well be that the points system makes a football competition more interesting since it adds more chance to it.