About the World Rugby RankingsTM

The ranking of the world's rugby nations has long been a lively topic of conversation. As my contribution to this discussion, I have written a computer program that uses previous international match results to compute a ranking of the teams.

The basic criterion that I use to rank the teams is very simple: I calculate the ordering of teams that correctly predicts the greatest number of previous international match results. In other words, if you had used these rankings to place even-money bets on each of these previous matches, then no other possible rankings would have given you a better outcome.

These previous match results, however, are weighted, to give recent results more importance than those that occurred several years ago. The weights are calculated as follows:

        weight = 0.4 ** (days_ago/365)
("**" means "to the power of".) "days_ago" is the number of days since the match was played. (However, if the match was part of a test series, then the same "days_ago" - and thus the same weight - is used for all matches in the series.)

This weighting formula is, of course, subjective. The key point to note is that recently-played matches are considered 2.5 (i.e., 1/0.4) times as important as matches played a year ago, and these in turn are considered 2.5 times as important as matches played two years ago, and so on. (The number 0.4 is somewhat arbitrary, but was chosen because it tends to produce accurate results when rankings are computed 'retrospectively' for past years.)

The ranking system also ignores very old matches. Matches more than 4 years old are always ignored (i.e., given a weight of zero). Matches between two teams are also ignored if the total time-weighted number of matches played between these teams is less than 0.1 (which corresponds to roughly 2.5 years ago). Basically, the win-loss record between each pair of teams goes back 4 years (which is usually enough time to include the most recent Rugby World Cup), but if these teams played only once in this time, then that result is ignored after about 2.5 years.

The key thing to note about the ranking system is that the main factor that decides the rankings is weighted head-to-head win/loss results, not points differences.

It is possible, however, for more than one ordering to be 'maximal'. (This frequently happens, for example, if two teams have not played each other in recent years.) In such cases, I then use points differences (from games played against each other, and games played against mutual opponents) to break ties.

For a team to be ranked, it must have played, within the last four years, a total of at least five matches against at least three already-ranked teams. (This means that countries with only a limited record of recent international matches will not be ranked.)

The World Rugby Rankings are recomputed monthly, shortly after the start of the month. They are made available on the World-Wide Web at "http://wrr.live555.com/", and posted to the newsgroup "rec.sport.rugby.union".

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The World Rugby Rankings are ©1996-2016 Ross Finlayson. ("World Rugby Rankings" is a trademark of Live Networks, Inc.)

Readers are free to add links to the rankings (URL: http://wrr.live555.com/), or to quote them in Netnews discussions. Publications (paper or electronic) may also make a "fair use" copy of the rankings - e.g., for commentary - provided that the URL (http://wrr.live555.com/) is also included. However, regular publication of copies of the rankings requires the permission of Ross Finlayson (email: finlayson(at)live555.com).