Re: Tournament Fairness


Robert Jasiek <jasiek@xxxxxxxx> wrote:
[ ... ]

Numerical model
---------------

It is (still?) unclear how different aspects should be weighed
relatively to each other. A model for the global view still needs to
be invented. For the individual view of only one aspect, this model
could be used:

Suppose there are N players. Let N be the amount of available fairness
for all players. Then a considered aspect in the individual view is
"fair" iff each player gets the fraction 1.

Yet further unclarity has to be eliminated by assessing how changes in
the aspect should be represented by fractions different from 1.
Research is just about to start...


An unwieldy assumption. For example: how are players chosen
to receive a "bye" round? If playoff is used for tiebreaker then why
can't everybody have a playoff round? Some tables in a tournament
hall are easier to reach than others. Not all players have equivalent
understanding of the rules. Can "fairness" be an individual notion,
or is it merely an abstract notion for "collective" fairness? Would
equal chances ever imply -individual- equality of merit? We don't
usually find equal opportunity leading to equal results.



Example: Tiebreaker
-------------------

Fairness of a tiebreaker depends on the tournament system because
every tiebreaker works differently in different tournament systems. It
also depends on the purpose of usage. E.g., a tiebreaker might work
reasonably well for the pairing strategy but not work well for the
final results ordering.


You cannot design a rational pairing strategy without knowing
something about tournament rank-order prior to pairing the round.
"Fairness" imputes convergence upon expectation with some
allowance for the possibility of surprise or upset. We would need
explanations when expectation is too often confirmed and also
explanations for surprises and upsets.

Phrase "final results" is misleading: it is merely rank-order
at the conclusion of all rounds scheduled by that tournament.
The workable tiebreaking methods we discuss do not depend
upon number of rounds played. More rounds add significance
to McMahon Score as well as more significance to tiebreakers.
Running random rounds prior to applying the pairing strategy
acknowledges our defects at estimating initial round pairings.



Within the specific scope of application, every feature (examples:
significance, Is the player responsible for it?) of the tiebreaker can
then be analysed in detail.


The individual won't regard it as fair if opponents later perform
poorly in the course of a tournament. Having tiebreakers tends
to encourage players to "educate" each other, perhaps during
post-mortem game analysis or general considerations about play
(talking about the game itself, usually in a room other than the
tournament hall). If opponents can "learn something" amidst a
tournament then their subsequent performance might contribute
more SOS for tiebreaker. So individual standards for "fairness"
are inherently faulty. The whiners and complainers will usually
get more relative attention or publicity because there isn't much
"newsworthyness" among fairness accounts from a great majority.

Not yet discussed is analysis of the SOS patterns. A high
differential between SOS, given the constant McMahon scores,
could indicate something suboptimal about early round pairing,
unless the players involved are excessively stronger than others.
Instead, low differences among SOS might indicate "fairness"
for a pairing group, thereby lend credence to tournament result.
Conclude that LOW difference SOS scores are "more significant."
Here, take sum of differences, or sum of squares of differences.
If SOS differences are "too low" however, then perhaps sharing
the place is more fair than attempting to interpret significance.
Rather than attempting to define an arbitrary threshold, directors
decide from the outset whether they require zero difference SOS,
among two or more players, to share the placement.



- regards
- jb

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