Back to 1998 CNSC
1998 CNSC Pairings
Sun Jul 5 17:15:38 EDT 1998
The 1998 CNSC will consist of an 18-game preliminary round followed by
a best-of-five playoff between the top two finalists from the preliminary
round. What follows is a proposal for a pairing system for the
preliminary round, eventually to be implemented in the tournament
pairing software. Please e-mail comments to
The goal of this system is to evaluate as fairly as possible who has
played best in the preliminary round. Since players will be ranked
in the end firstly according to their number of wins, it is important
that players with similar W-L records face have faced opponents of
similar strength. To take an extreme example, we do not want to have
two people with 15 wins, one of whose opponents are all in the lower
half of the field, while the other's opponents are all in the upper half.
- Graeme Thomas points out an earlier inconsistency of terminology.
This document should now use 'round' to refer to either the preliminary
or playoff periods, but not to the individual games of which they
In the first game, the fifty players will be arranged according to
their qualifying ratings (peak from the June to September NSA lists).
Players thus ranked 1-13 will play randomly selected players
ranked 26-38, and players ranked 14-25 will play randomly selected
players ranked 39-50.
- Pairing 1-26, 2-27, etc. was ruled out because it
favours too strongly player 25 over player 26, and might tempt
people to tune their pre-tournament ratings.
- My original idea was to match 1-25 randomly against 26-50;
the current method is due to Graeme Thomas. I prefer his
method because it makes for more balanced pairings.
In subsequent rounds, players will be paired according to a modified
'Swiss' pairing algorithm:
- Sort all players first by number of
wins, then by total opponent wins, then by spread, then
by pretournament rating, going back month by month if necessary
to break ties on that least significant criterion. 'Total
opponent wins' is the total of the number of wins currently
tallied by each person that you have been paired with; if the
people you've played are currently 3-1, 2-2, 0-4 and 0-4, the
TOW is 3+2=5.
- Graeme Thomas points out that TOW is called SOS for Sum of Opponent
Scores in Britain, based on former BCF (British Chess Federation)
and FIDE (Fédération
Internationale des Échecs) usage. I choose to call it TOW here,
because Canadian players do not tend to refer to win-loss records
- Graeme points out further that SOS was used in Britain
as a secondary final ranking criterion instead of spread
(and not for pairings, as reported earlier here), and that it
was disliked for that purpose because instead of being able
to calculate how many points you needed to win a game by
to secure a final position in a tournament, you needed to
hope that your past opponents would all win their games
while your rival's past opponents would all lose theirs.
I agree that TOW/SOS is very poorly suited for use as a
final ranking criterion, but believe that it is still a good
approximation for strength-of-field for Swiss pairing
purposes, and better than spread for that purpose.
I admit to being motivated on this point by a desire to
avoid repeating the WSC97 Graham-Sherman problem.
I will make sure that the TOW values are printed game by game,
so that players that want to double-check the pairing system
can do so themselves.
- Graeme's widely used program pairs secondarily to minimise imbalances
among firsts$ and seconds$ (starts# and replies#), which would seem to me
to be too culturally shocking to players who are used to being able to
draw to see who plays first, and does not to my mind do enough to avoid
the aforementioned WSC97 problem. Besides, the existing NSA rules seem
to me to do enough to balance firsts and seconds; and I am unwilling to
consider a hybrid system where players have to report to me each round
on who played first and who played second, as I can't think of any 100%
reliable in which they can do this.
- Graeme's program does however keep track of floaters, based on
I am investigating FIDE Swiss pairings, and considering revising the
mechanics of the system described here accordingly. Note that FIDE's
current Swiss system uses average opponent rating and not TOW/SOS, but
given the noisiness of Scrabble ratings, I don't consider AOR appropriate
for our use.
- Graeme points out still further that SOS pairings are biased toward
players who win early games rather than later ones. (WSC97
showed how spread pairings are biased the other way.) I will
give this further thought.
Start at the top of the list
and consider everyone who has the same number of wins as the
person on top. Add into consideration the next person on the
list if necessary, to make an even number. Split the list of
people under consideration into upper and lower halves, and pair
the upper half against the corresponding players in the lower
half. (Except as noted below.)
If there are players left unpaired, redo the process
described in this paragraph, with the remaining players.
If a pairing as described in the previous paragraph would lead
to players playing each other too often (see below), then try
pairing the upper player with the player below the ideal opponent
(leaving the sublist if necessary), then the player above, then
the player two below, then the player two above, etc. until a
suitable opponent can be found. If the entire pool of remaining
players is exhausted (as can happen toward the bottom of the list),
back up one step to reassign the previous pairing and try again.
- Graeme Thomas prefers to work from the top and the bottom of
the list alternately, to avoid backtracking. I believe that this
has the effect of pushing up any 'pairing error' into the middle
of the field, instead of letting it all accumulate at the bottom.
I prefer to work straight from the top, backtracking if necessary,
in order to make sure that anyone in contention for prize money
has been paired as well as possible.
In games 2-14, no repeated pairings will be allowed.
In games 15 and 16, players may face each other a second time.
In games 17 and 18, players may face each other a third time.
[These restrictions are somewhat arbitrary, and subject to change
if someone can suggest a good reason to do so.]
- Dave Boys points out that game 18 pairings (and perhaps 17)
should reflect the fact that finishing second is just as good
as finishing first. In particular, if #1 hasn't been clinched
going into game 18, pairing 1-2 should probably be disallowed.
- Joel Wapnick says that in a tournament of this nature, it
would be unfair to the strongest player to allow anyone
pairings to repeat a third time. I am considering therefore
changing the above to read "In games 15-18, players may face
each other a second time. In game 18, players 1 and 2 will
not play each other if [condition to be supplied.]"
If any player has clinched any final position before the end of
the preliminary round, that player will be moved to the bottom of
the pairing list so as to avoid influencing the rest of the rankings.
Finally, I believe that the person who finishes first in the
preliminary round should thereby earn the right to play first
in the odd-numbered games of the playoff round. I base my
belief on the notion that there ought to be some reason for
players to prefer finishing first to second, but am willing
to hear arguments why this might not be a good idea.
 At the (manually spread Swiss paired) 1997 WSC,
Matt Graham reached the
final round after having faced a significantly weaker field
than Joel Sherman, because he lost several early games, and
therefore got to play significantly weaker opponents throughout
the middle of the tournament.