Every TD knows that when pairing a tournament in the Swiss System, you separate by score group, and then pair that score group.
Within a score group, however, the ranking of the group (in which you split into top half and bottom half) is done by rating.
Why? What’s the theory behind it?
A score a player has obtained is an achievement within the tournament. That’s how the groups are created.
Wouldn’t it make more sense to rank the group by another achievement (like a tiebreak score), rather than a non-tournament-achievement (like pre-tournament rating)?
It’s a form of seeding, as in bracketed seeding. A Swiss is essentially a non-elimination bracketed tournament. Rather than use the type of seeding used in brackets like the NCAA, where some teams have very close seeding in a bracket round while others have a distant seeding (say 1 vs. 16 aand 8 vs. 9, where the differences are 15 and 1 respectively); the Swiss uses seeding where players have very ROUGHLY the same sort of seeding (1 vs 9 and 8 vs 16 - everyone’s seed varies by 8 - the same difference). In high level theory this provides a reasonably fair seeding to ALL players, whereas the NCAA type seeding is focused more on elimination until only a few teams are left. Since the Swiss is not eliminating players, this approach makes sense.
I didn’t make myself clear… I know all about Swiss pairings, as I TDed my first tournament 30 years ago, and while I haven’t TDed much at all since then, I still follow it with much interest.
FYI, everyone does not necessarily have the same tiebreak score after the first round; it depends on the tiebreak system used (e.g., “wins with black” as the main tiebreaker).
Yes, it isn’t an elimination; it is fair seeding that is key. Score groups are the first cut at seeding in second and subsequent rounds.
My point is that if you’re going to use a Swiss, and you are going to use a tournament performance measurement (i.e., score) as your first criterion for seeding (i.e., score groups), then why not use another tournament performance measurement (i.e., some sort of tiebreak calculation) as your second, and subsequent, criterion for seeding.
Has there ever been a journal article (or something similar) on the theory behind the Swiss System?
You might want to contact Mark Glickman. He has written several papers on ratings system theory. I don’t know if he’s written any on the Swiss System itself, but he will have more knowledge about the literature in the field than most of us do.
Why would you call dividing into score groups “seeding”? Seeding is, almost by definition, done based upon information before things start. Grouping players by score is to help determine placement at the end of the tournament.
You’re right, of course; seeding is the wrong word. Perhaps “ranking” is better?
For what it is worth – I just communicated with Mark Glickman who does not know of direct references on the underpinning of the Swiss System.
Yes, the orthodoxy is to accept “rating” as the way to rank people within a score group, but without any theoretical or practical justification for it, why not question the orthodoxy?
What is really needed is a pairing program with the ability to take inputs and produce outputs from text files, so that one can run thousands of simulated tournaments and come up with some answers to the most basic questions about the Swiss… What is the main goal of a Swiss System? What is considered a “fair” pairing? What criteria should we try to maximize or minimize?
I believe the standard Swiss pairing system in use today (top half against bottom half) came from Kenneth Harkness in the mid-20th century. He had a couple of books on chess rules and such; it’s possible you might find something there about the reasoning behind it.
Simulations won’t answer those questions. You have to decide up front what the main goal of the tournament is—simulations then might tell you what (of several proposed methods) is most effective in accomplishing that. The usual assumption is that the job of the Swiss is to pick a worthy winner from a large number of players while eliminating no one. If you are running a tournament where you mainly want everyone to have a good time and play as many games with people of skill level similar to theirs, run quads, or 1-2, 3-4 pairings, not a Swiss.
Ken Harkness’s book “The Chess Player’s Handbook” traces the Swiss System back to the late 1800’s but gives George Koltanowski credit for having popularized its use in the USA.
It does not really give any mathematical theory behind the Swiss System.
On a related subject, here’s another question that could be address using simulated tournaments.
Suppose we had a 6 round Swiss, with 64 players in it. There was a 1260 point gap between the top rated player and the bottom rated player, and each player was exactly 20 points different between the player above and the player below (suppose the range was 2260 to 1000). Each player’s playing strength was equivalent to their rating. Yeah, yeah, I know; perfect world, unrealistic… fine. Just pretend.
If this tournament were conducted 1 million times, (1) would the average score achieved by each player in the tournament correlate to that player’s rating? (2) Would the standard deviation of the average scores of each player be roughly equivalent?
If (1) were not true, then the Swiss System pairings are inherently flawed, as you would hope that the system does not bias the results depending on a player’s starting rank.
However, if (2) were not true, it means that the starting rank of a player affects the variability of the player’s expected results. I expect this would not be the case in a perfectly linear distribution of players and ratings as I suggested above (i.e., the SDs would be the same), but in a case where the distribution of players and ratings is normally distributed, or skewed in one direction or another, I suspect the SDs would differ significantly depending on the starting rank. (I hypothesize that people near a 2^n ranking would have smaller SDs than those not near a 2^n starting rank (where n is a positive whole number less than the number of rounds.)
Anyway, such questions could be explored with simulation if the standard pairing programs were able to input and output delimited text files of pairing and results. Alas, my current understanding is that this isn’t possible.
Yes, creating a simplistic pairing program that does this wouldn’t be too hard to do, I agree (foregoing, as you said, color swaps, 200-point difference issues, etc.). I was hoping to use a standard pairing program, and then call it as a service
I have created an probability distribution of outcomes – based off of the USCF ratings expected win formula – and estimates draw percentage as a function of rating difference… works pretty well, I think.
Such a simulation might just bring up inconsistencies between the ratings formula and the win-draw-loss probability function, not a problem with the Swiss pairings.