Rolling and Weighting

The previous post was spent establishing the obvious; that recent results provide a good pointer to current ability.  This obviously leads to the idea of the use of a rolling average of results to guess the current ability of a team.  But straightaway, there are two problems that arise.  Firstly, what if a team has had a run of easy matches, against weak opposition, giving rise to a strong sequence of results?  There’s no fully structured league programme in international cricket, no guarantee that each team has an equivalent run of fixtures in a certain period of time.  But even ignoring this, there’s another problem.  Rare events are, by definition, rare: unlikely things happen sometimes, but not usually.  And thus the frequency of random occurrences is predictable in the long term. Thus the results of a team in the long term are most likely an accurate indicator of how well, on average, a team has played over this period.  But the average long term quality of a team is itself a poor guide to current form.  Recent results are more relevant; but there are fewer of them, and thus they are more likely to reflect random happenings than underlying quality.  Thus we have a choice: a good estimate of a quality that is a poor indicator what we want to know, or a poor estimate of a good indicator.  What would really tell us how good a team actually is, right now, is a large number of recent matches; but as test cricket takes five days per match, this is never going to be available.

So one solution to this (and one used, in part, by the ICC ratings), is to use an average that is both rolling and also weighted: use lots of results, but assign more impact to recent results.  The problem with this approach is that the weights are inherently arbitrary: in the ICC system, older games suddenly count for only half as much when an annual update is made.  Is there an alternative way of solving this problem?  In fact, there is, based on the system of Elo I mentioned in a previous post; and moreover, this system also addresses the other problem (that of differentially difficult fixture programmes). And its that system I’ll look at next time.