“If Bayern Munich won 3:1 against FC Barcelona and Borussia Dortmund won 3:0 against Barcelona, then Dortmund will win 6:1 against Munich.” We all did this calculations when we were younger! What we didn’t know back then is that we implicitly assumed a strong transitivity in soccer and therefore a high predictability of results. Because when we know that A beat B and B beat C, than we can be quite sure that A will beat C. But of course we all know that soccer does not work like that. But how transitive is soccer actually. That is, how often can we observe a triplet A beats B, B beats C and A beats C?
This entry will deal with this question and also compare the transitivity of soccer with other sports around the world.
Transitivity in Soccer World Wide
I analysed my dataset with 177 leagues around the world and calculated the percentage of transitive triplets for each leagues. The graph below shows the sorted percentages (without country names).
It seems that there is a high variance in transitivity. However, we can observe a slight clustering of continents. Especially Africa seems to be clustered at the lower end of the graph. Indeed, with 44%, Africa has the lowest average transitivity. It is followed by South America (53%), North America (55%), Asia (57%), Europe (60%) and Australia (69%).
The most/least transitive leagues are the following:
Of course the most interesting leagues are the “Big Four”. Here, Italy is the least transitive (51%), followed by Spain (56%), England (59%) and Germany (63%).
All in all I did not expect such high values for the transitivity. Is soccer more boring than we thought?
Transitivity in different German Leagues
Since I was interested if there is a trend to lower/higher transitivity the lower the league is, I additionally scraped results from Germany up to the “Oberliga” and also the first division of women. The bar chart below shows the transitivity values.
As you can see, there is no real trend to observe. Sad, but well at least i got some new data…
Transitivity in other sports
How does soccer compare to other sports? Again I used my scraping skills and downloaded all results of 2013 in 1. divisions of different sports
Most of the considered sports are more transitive than soccer. Therefore, more boring? I will not judge that!