Comparing Leagues by Year over Year changes in Placings

One of the frameworks I've thought about quantifying the competitiveness of a sports league is by looking at how much the placings of teams tend to vary from one year to the next.

In the Premier League and La Liga 17 of the 20 teams competing in a given year survive relegation to compete the following year. (Conversely, 17 of the 20 were also participants in the previous season).

If we assume that the typical team remains at approximately the same level from one year to the next then we can think of two consecutive seasons as two trials of the same experiment. More or less.

In a perfectly competitive league one might expect the standings of a season to have no significant relationship with that of its predecessor or successor. So I thought I'd look at the transition probabilities of placings in La Liga and the Premier League from the 1992-1993 season to the 2013-2014 season.

So, I got transition probabilities and plotted them below. The colour of a rectangle at location (x,y) reflects the probability of a team that finished in place y would finish in place x the following season. Blue regions represent low or zero probabilities; red regions represent relatively high probabilities.

For both the general shape is along the diagonal meaning that teams generally finish in the vicinity of where they finished in the previous season.

The upper left corner of the La Liga plot is somewhat more diffuse. We can see that that there are multiple instances of the La Liga winner dropping out of the top 3 and even into 6th or 7th place the following season. By contrast, there is only one instance of the Premier League winner dropping out of the top 3 the following season (Thanks, Moyes).

Similarly, it's also more likely for the La Liga winner to be a team that placed outside the top 3 during the prior season. I don't know if it's statistically significant but it's there.

Outside of that region the two plots look the same to me more or less. If anything the La Liga plot looks slightly more spread out to me, but it's touch and go. Looking at the numbers I see that there are less non-zero probabilities in the Premier League history. But not by much.

Then I looked at just the last 10 seasons. The events of the mid-90s probably have very little to do with the state of the leagues today but I still need a decent amount of data to justify calling these things probabilities.

Here it does start to seem as if the La Liga plot is noticeably more diffuse while the Premier League plot adheres to the main diagonal more closely. Seeing that I wasn't able to discern much from the earlier plot I decided to form larger buckets of placings and see if anything would reveal itself then. I group the data into groups as follows:

11st to 4th
25th to 8th
39th to 12th
413th to 17th
518th and lower

And this is what the plot of transition probabilities looks like:

Again, not much to see here. Well, the top left corner does more pronounced for the Premier League, in line with the league's reputation for having a stable group of elite teams. Just as before, we can narrow down the years. For these groupings there's more data points per category of transition so it seems reasonable to zoom in on an even smaller time period. The plot for group transitions over the last 5 years is below.

Again, the La Liga plot looks somewhat more spread out (16 of the available rectangles represent non-zero probabilities as opposed to 14 for the Premier League) but I'm not sure that's of any significance. The top left rectangles - representing the elite teams in the league - look similarly red. I think if you remove the aberration of Villareal following up a 4th-placed finish with relegation then there's not much of a difference to live on.


The thing that stands out for me from this approach is the way that the recent probabilities for the Premier League seem to adhere to the diagonal. My intuition is that this is an indicator that the La Liga is more competitive in some sense. Something for a future weekend.


Data here (on github):
Premier League Historical Data
La Liga Historical Data