So I thought I would do something a little different with this blog. Currently, I am on crutches and so my Saturday is being spent analysing rugby data, what with it being the world cup and all. I thought I would approach sports statistics from a different angle and treat the teams as agents in a model of dominance hierarchy. Like animal hierarchies, I am only interested in the outcome of an interaction and not the score. Therefore, I am only considering the outcome and not whether it was in a group or knock out stage. The data I am focussing on is all the Rugby World Cup matches from 1999 (the first cup where the game became professional) to 2011 the last cup.
I used Elo ratings to determine the dominance or winning ability of all the teams who have competed in world cups. This rating uses dyadic interactions (aka matches) and assigns a positive score to the winner and a negative score to the loser. In addition to this, this rating system uses the expected outcome of an interactions to give weighting to these scores. So for example, if A always beats B, the expected outcome is that A will beat B in successive interactions. The winning scores for A and the losing scores for B get smaller over repeated interactions. If the outcome of a contest goes against expectation (see Japan vs. South Africa), the expected loser gets large winning points and the expected winning large losing points. I ran this this model on all world cup games to determine what team is the most dominant (see below).
So if we treat world cup games as animal contests (given some rugby players this is an easy comparison), we can see that Australia would be the dominant in the rugby social group.
As this model considers data over time (4 world cups) we can see just how stable this “hierarchy” is, using a stability index. This index is bounded between 0 and 1 where 0 is a completely unstable hierarchy and 1 a stable one. The stability value for the world cups is 0.9996, which suggests that across cups, results are pretty consistent.
