I had realized that you’ve talked about a full ladder of all teams. My ‘real
life’ (not hypothetical) example shows, in which direction can (or 'will') lead
the application of a system working by swapping the positions. So – if North Korea was
in a ranking No.1 from Nov 2011 until Jan 2013, then that tells us almost
everything about such a ranking system. Then we actually do not need consider other
possible oddities between No. 2 and No. 200.
But number 1 is an irrelevance! I am interested in the middle to lower end.
rankings" are not rankings in the sense of giving correctly all the
relative strengths of teams to each other, but are instead a way of
motivating the fixtures in themselves. It provides an instantaneous
ordering, which oscillates (perhaps quite violently) about the "true"
ranking without converging. Indeed it should not converge otherwise the
fixtures stagnate. But one can then average positions over several
years to fudge a measure of typical ability.
Normally ladders are
used in situations where players/teams are expected to play only those
with a nearby ranking. Minnows are not supposed to challenge the
My point was to emphasize a major bug with any
ranking system for internationals : teams do not play frequently enough
against a wide enough range of opponents to statistically overrule the
fluctuations in time of their own actual instantaneous ability.
Rankings are never a reflection of
current ability, but of recent activity. The
points of measurement (matches) are not sufficiently highly resolved to
detect the variations. But ladders, by contrast, detect every variation, albeit in an exaggerated way.
Also one significant
advantage that a ladder system has over FIFA is that it properly
penalizes a "good" team for losing to a "bad" team.
It is no surprise that Jostein Nygard
obviously used a time-machine. Considering his idea he posted in 2002 I would
think: Those who can develop such ideas must have tremendous skills which are
out of this world.
I'm sure the idea is far
older than 2002. But I don't recall it being published online before
that. And the raw data was much harder to find online at that time...
it seems common practice now that people will not cite sources properly
when they write these gimmicky books. They like to pretend it was