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The Problem
We would like to rate our ability to play Squash (or Badmington,
Table Tennis, Lawn Tennis, ... , or whatever
we have chosen as our proxy for one-on-one combat ) against
the whole player population, placing ourselves on some universal
scale between "best" and "worst". We would like something
like the golf-player's handicap.
Unfortunately the only available evidence is a set of pair-wise
comparisons that provide a fairish guide as to whether one
player is "better" than another, and a poorish guide as to
how much. "Better" (when applied to game-playing skills) is
an ill-behaved comparator.
 "Taller",
by contrast, is a good comparator (of height):
It's unequivocal. If you're taller than me, and I'm taller
than John, then — without any doubt at all — you're taller
than John.
It's measureable. A height ranking can be established without
any measuring tool at all, but equipped with a means of
measuring height differences it is possible to do the job
better and faster. We could generate a height scale rather
than just a ranking. And it would be quicker, because if
you're 3 inches taller than me, and I'm 2 inches shorter
than John, then I know — without the need for any further
measurement — that you're 1 inch taller than John.
The outcome of two-player games obeys neither of these rules.
Establishing an unequivocal ranking, still less an unequivocal
scale, is therefore much more of a problem.
Leagues
The obvious approach is for everybody to play everybody else.
Unfortunately this approach turns out to be either impractical,
or arbitrary. And it doesn't work if games are missed, because
there is no fair way of representing a null match: awarding
a walk-over confuses talent with justice; assuming a draw
is an attractive option for the weaker player.
The main problem however, is the number of matches that full
competition requires. If a typical squash club were to attempt
to match every active player against every other one, then
a club of ~250 would need to organise 30,000+ matches. That's
clearly impractical, so the traditional solution is tiered
leagues and a system of promotion and relegation between them.
At that point it becomes arbitrary. The promoted players or
clubs have not been tested in the leagues to which they are
going, so it might be appropriate to promote more, or less
or further. The more leagues there are, the more arbitrary
the system becomes. Not only is it arbitrary, it is slow.
So slow in fact, that participants can lose their enthusiasm,
their youth, their skill, or even their health, before finding
equilibrium.
 Knock-out
competitions
A knock-out competition is a much faster way of discovering
the best player. But it can eliminate the second best player
in the first round, so as a ranking tool, the knock-out competition
is a non-starter.
Ladders
Challenge-based ladders would seem the most direct method
of establishing club rankings, but in practice they don't
work so well:
- unless the challenge interval is varied, to reflect the
higher density of people of average talent in the middle
of the club, progress can be frustratingly slow
- nothing is gained by accepting a challenge, so it is tempting
to decline them.
- the margin of victory is ignored.
- match schedules cannot be imposed, so it is easy for rankings
to lose their legitimacy.
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