Best Tournament Pairing Systems

Running Chess Tournaments
21

If you are looking for a way to reduce the field to a single perfect score as quickly as possible, there are far better ways than the Swiss.

I’ve posted the following anecdote before, but now maybe the time is right.

Four decades ago, at the height of the Fischer boom, the late Richard Verber organized a 5-round, single-section Swiss for high school players. There were about 300 players, huge for its time. Verber’s chief pairings TD was NTD Tim Redman, who subsequently became USCF president and, later, editor of the 3rd edition rulebook. Tim used straight half-vs-half Swiss pairings, no acceleration.

After three rounds, Verber noticed there were still dozens of perfect 3-0 scores. With just 2 rounds to go, and not wanting the event to finish with a pile of 5-pointers, Verber took over the controls. He paired only a handful of the highest-rated 3-0’s against each other. The remaining lower-rated 3-0’s were paired against high-rated 2.5’s, 2.0’s, and I think even 1.5’s.

The result? After just one more round, only three perfect scores remained. Then, in round 5, two of these three drew each other, while the third (much lower-rated) lost to a lower-scoring but higher-rated opponent. Final standings: zero perfect scores.

Ever since, I’ve wondered how this “system” could be quantified and made into an algorithm. One possibility is along the following lines:

  • In round 1, use 1-vs-2 pairings. (1-vs-2, 3-vs-4, 5-vs-6, etc.) This will produce a lot of high-rated losers and low-rated winners who can be paired against each other in subsequent rounds.
  • In round 2, pair only the highest-rated handful of winners against each other, 1-vs-2 style. Pair the remaining winners, sequentially, against the highest-rated losers. Pair the remaining losers against each other 1-vs-2.
  • In subsequent rounds, continue the same idea (somehow).

To quantify round 2 a bit, the handful of winners paired against each other could consist of, say, only those within 300 points of the top. That should result in about a 300-point difference in each pairing in the big middle group, enough to ensure “upsets” (by score) on most of the boards, and thus an extremely fast reduction in the number of perfect scores, round by round.

I’ll leave it to somebody else to work out the details for rounds 3 and following. Want to try your hand, anybody?

This system sounds ideal for a large single-section tournament. Unfortunately, there aren’t too many of those around anymore. The U.S. Open, maybe?

Bill Smythe

22

How would this system deal with requested byes, no show opponents, withdrawals, late entrants, …?

23

Please correct me if I’m wrong, but I think the outcome Bill Smythe describes could be approximated by dividing each score group into four segments rather than two, and pairing as follows:

HYPOTHETICAL SCORE GROUP - 14 players

1 - 1 vs. 4
2 - 2 vs. 5
3 - 3 vs. 6

4 - see above
5 - see above
6 - see above

7 - 7 vs. 10
8 - 8 vs. 11
9 - 9 vs. 12

10 - see above
11 - see above
12 - see above

13 - pair down
14 - pair down

. . . as opposed to the normal Swiss pairing, which would produce a straightforward 1 vs. 8, 2 vs. 9, 3 vs. 10, 4 vs. 11, 5 vs. 12, 6 vs. 13, 7 vs. 14 lineup.

24

I know what you meant, but I just wanted to point out that what we have come to think of as “normal” Swiss pairing is actually only ratings-based Swiss pairing, and only one particular approach to ratings-based Swiss pairing, at that.

Swiss system tournaments were run for a long time before there was a ratings system, and THVBH pairing with ranks based on ratings is not an inherent feature of the Swiss System. Random pairing within score groups is just as much “a Swiss” as the system the USCF specifies in its rule book.

FIDE offers sets of regulations for several different Swiss System approaches. The one that is the most similar to the USCF Swiss pairing rules is the “Dutch” system. fide.com/component/handbook/ … ew=article . This is a ratings-based Swiss system with THVBH pairing within score groups. There are several significant detailed differences from the USCF rules concerning such things as the selection of the “odd player” in a score group, etc, but it is in essentials similar to the USCF rules.

But FIDE allows other SS pairing systems. First, there is the Burstein system, which does not do THVBH pairings at all but rather uses Sonnenborn-Burger and Buchholz calculations to equalize the strength of opponents within a score group as much as possible. The aim of this system is described as “fairness”. “Normal” ratings-based THVBH pairing is not “fair”, in a sense, because it favors the higher-rated players. The effect of THVBH is to give the highest rated players within a score group the easier opponents, in order to smooth their way towards a perfect score and a big finale between the top-rated players in the last round. In a regular 4-round SS with 16 players, the highest ranked player has to beat Ranks 9, 5, 3, and 2 to emerge with a perfect score and win the tournament. The 8th ranked player has to defeat players 16, 4, 2, and 1. But the 9th ranked player has to defeat Ranks 1,5,3, and 2 to do the same, assuming that in all the other games, the higher-ranked player wins. This is what the Burstein system is trying to address. Ratings do enter into the Burstein, but are given low weight. Here are the FIDE regulations on the Burstein system: fide.com/component/handbook/ … ew=article

Another FIDE system is the Dubov system. Unlike Burstein, pairings are based on ratings, but like Burstein, its aim is that opponent strength is equalized within score groups. Instead of using THVBH, pre-event ratings are used in order to give players within a scoregroup as close to the same Average Opponent Rating as possible. The FIDE regulations for Dubov are here: fide.com/component/handbook/ … ew=article

What we consider the “normal” Swiss pairing system is in fact only one choice.

25

This is a creative approach. But I don’t think you can put Verber’s solution into widespread practice unless you junk a good deal of the current Swiss pairing rules…especially in the specific situation where he implemented it. :slight_smile:

26

Moderator Mode: Off

Which is the best one?

Tennis uses a bracket system where the top rated players play the lower ones until that last few rounds. In this system, the higher rated players are also given an advantage, as you say the Swiss System gives. For instance, the poor guy who got the first round draw against the 1st rated player in the Australian Open was beaten handily only winning 2 games in the first set and none in the next 2 sets. That #1 did go on to win the whole thing, but his opponent in the first round never had a chance to go any further in the tournament.

The nice thing about the Swiss System is that the players compete throughout the whole event and are not eliminated from play.

In a rating based Swiss, the higher rated players are always at an advantage against the lower rated ones, no matter when they play.

In the other systems, the early rounds might be more balanced as to the ratings of the opponents, but when a higher rated opponent loses early, he will inevitably play a lower rated one anyway giving him the odds against that lower rated player.

At least with the rating based Swiss, the more rating balanced competitions, and therefore the more difficult competitions for the players, no matter what their rating, will come near the end.

27

What about nearest opponent pairings – ranked first by score and then by rating?

Combine this with an elimination of class prizes (replaced with additional place prizes). The lower rated players will be playing similar rated players, so they should compete just fine for the open prizes and many more games should be good contests.

The point of such a system is different than the swiss. It’s less concerned with picking a “winner” than assuring good games, but the top performers will still be rewarded.

28

That sounds like the McMahon pairing system, used in handicap go tournaments. In that context, though, it works because the handicaps ensure an approximately even game regardless of the players’ relative strengths.

29

This is basically “1 vs 2 pairing”, which is mentioned in the USCF rulebook. If players are ranked by score and rating, and then 1 vs 2 pairing is used, you have the “Australian Draw” system, which is popular in Australia for Scrabble. Another feature of the Australian Draw system is that rematches are allowed after some number of intervening games. Usually near the end of the tournament, an Australian Draw tournament goes into “King of the Hill” mode, where rematches are allowed immediately. Sometimes “King of the Hill” is used from round 1.

30

Exactly the same way as the regular Swiss system works, I assume. What makes you think that pairing symmetrically around the median within a score group, rather than top half vs bottom half, would create particular trouble with any of those scenarios?

31

The method you describe would still pair players with equal scores for the most part. Accordingly, it would not reduce the number of perfect scores any faster than straight half-vs-half pairings.

(Well, actually, it might reduce the perfect scores slightly faster, because (a) instead of dropping 0 or 1 players into the next score group, it would drop 0, 1, 2, or 3 players, and (b) by pairing players closer together in rating, it might create a few more draws.)

True. But all of these systems pair players with equal scores whenever possible. This is true of half-vs-half (ratings-based), 1-vs-2 (ratings-based), random (not ratings-based), and all the FIDE variations you describe (Dutch, Burstein, Dubov, etc).

This is nothing more than 1-vs-2 pairings. You are still pairing players with equal scores.

Any system that pairs equal scores, regardless of the details within equal score groups, will reduce the number of perfect scores in each round only to half of what it was in the preceding round. (Well, to slightly less than half, due to draws.)

If you are attempting to drastically reduce the number of perfect scores as quickly as possible, you need a system where players with unequal scores are paired, and where the lower-scoring player is likely to “upset” the higher-scoring. The Verber approach did this, in spades.

Richard Verber was, indeed, a creative person – and no slave to any version of the rulebook. His method was certainly a variation, almost discarding the Swiss altogether. By today’s rules, it probably should have been announced in pre-event publicity. But this was the good old days, when creativity counted for something.

Bill Smythe

32

Of all the Swiss System variations mentioned here, the one that intrigues me the most is the Burstein system, which pairs within a score group based on Sonnenborn-Berger scores and seeks to maximize the fair treatment of players.

Speaking as a player who is usually (in my area) the highest-rated player in a typical weekend Swiss, I don’t like any pairing system that makes me play my closest rival in the very first round! The first round is usually the one in which I am most vulnerable to an upset, because I have not yet “warmed up” or shaken the sleep off, etc. It is the danger round, especially since I am required to press hard for a win. I’d like a round or two to warm up before having my biggest rival thrown at me.

Greg Shahade has argued nicely in favor of random pairings, but I don’t like that it creates the possibility that, by chance, rivals for a prize might end up having played vastly different strengths of players. Complaints about unfairness would be rather common, I should think.

The Burstein system seems the best of both worlds to me. It avoids coddling the higher-rated players, avoids critical matchups in the very first round, but also seeks to equalize the strength of the playing fields that each player faces. That’s good!

33

One of the elements of my pairing program is a “simulator mode”, which allows pairings to be made automatically, makes guesses about the outcome of the games, and compiles statistics on such factors as average ratings differences between players, and deviations in expected versus actual outcomes using a variety of rules variations.

Unfortunately, work heated up, including a lot of travel requirements, so I haven’t had much time for “recreational” programming. When I get back to it, there’s a system I want to try. In the first round, I’ll divide the section into four “quarters”, based on ratings. The top quarter will play each other using top half-bottom half. The bottom quarter will do the same. The two quarters in the middle will play using 1-2, 3-4, pairings. I decided this system would probably strike a good balance with competitive games, but still preserving the “drama” factor by diverting games between the odds on favorites until later in the day.

I haven’t figured out exactly how long to keep that scheme up. After the first round, you can do the same thing within scoregroups, but when the scoregroups get small, it doesn’t make sense. Probably, I’ll go from that scheme, to just plain splitting into two halves with scoregroups between 8 and 16 players, and just plain top half-bottom half for smaller scoregroups. I don’t know how well it will work, but I want to try it. It’s sort of a variation on accelerated pairings, but one that makes a bit more sense to me.

34

The main purpose of accelerated pairings, as described in the rulebook, is to reduce the number of perfect scores more quickly. Your system will not do this, as it still pairs players with similar scores.

Recall that, with “conventional” accelerated pairings, in round 1 top quarter plays second quarter, and third plays fourth. In round 2, top-half winners play each other, as do bottom-half losers. But top-half losers play bottom-half winners.

In general this should mean that the second quarter, who lost to the first quarter in round 1, will be paired against the third quarter, who defeated the fourth quarter in round 1. Thus, 0-pointers will defeat 1-pointers in the second and third quarters.

It’s this “losers will beat the winners” pairing strategy that reduces perfect scores quickly.

It’s also the idea behind the Verber pairings I described. You might say that Verber pairings take accelerated pairings to the extreme.

Bill Smythe

35

Bill,
You appear to be right. Also, after going through a few samples, it doesn’t seem to do what I wanted it to do, either. It tends to throw low rated winners upwards after the first round or two.

But, there’s the germ of an idea in there that I still think I can work with. If I pair the losers from the top quarter Swiss against the winners in the middle section, it should still accomplish the same thing as accelerated pairings, with the “losers beat winners” effect you described, but without seeming so artificial as accelerated pairings, and still keeping more games competitive.

I needs must ponder this more.

36

Isn’t the stupid discontinuity simply changed as you approach the endpoints of the group? There’s a sense in which the rating variance from board to board is less discontinuous in the current method than under the NCAA rules, which is why I always thought the NCAA approach was stupid. The NCAA approach is good for show (it should theoretically increase early upsets since the rating variance is decreased close to the midpoint) but I’m not convinced that its good for fairness from the perspective of the individual player on a board by board basis.

37

A function is continuous if (to use layman terminology) a small change in independent variable X results in only a small change in dependent variable Y.

In this case, the function is “pairings within a score group”, X is the player’s rating, and Y is the opponent’s rating. In the NCAA system, a small change in the player’s rating would result in only a small change in the opponent’s rating. The USCF half-vs-half system, by contrast, has a discontinuity at the middle of the score group, because at that point a small change in the player’s rating can result in a huge change in the opponent’s rating.

The “variance” function is a different function, but it has no discontinuities. Under either the NCAA method or the USCF method, a small change in the player’s rating results in only a small change in the variance (between the rating difference in the player’s pairing and the rating difference in his neighbor’s pairing). When it comes to the “variance” function, the NCAA and USCF methods differ not in whether that function is continuous, but rather in the range of values the function takes on. In the USCF case, the function is nearly constant, while with NCAA, it takes on a much larger range of values.

But that’s all geek-speak, I guess. I would NOT like to see USCF adopt the NCAA method. The discontinuity here is not Stupid, it’s just “you have to draw the line somewhere”. As a player, I often find myself at about the middle of my score group. I enjoy the prospect of facing a strong opponent, and am willing to pay for it by submitting to the (approximately equal) possibility of giving this pleasure to a lower-rated opponent.

Bill Smythe

38

In the 1980s, in Minnesota, Bruce Diesen apparently developed a system similar to Verber’s, but very clearly explained in an issue of the Minnesota state magazine. Then USCF ED Gerry Dullea circulated the article via BINFO, and I found it quite intriguing.

Diesen showed 4 round tournaments with many more than 32 players, and yet only one perfect score (or none, even!), and a much higher proportion of games between players within 100 points of each other, which apparently was one of his goals.

Does anyone recall this, and can a copy of the article be found?

As I recall, in round one, he paired 1 v 2, 3 v 4, and so on, as mentioned in other posts here.

In subsequent rounds, he paired the players in the middle of groups in that manner, but paired lower rated players with high scores against higher rated players with low scores.

Obviously, this is not a Swiss system; I guess it was a Diesen system. His article discussed the satisfaction that resulted among the wide range of players, in his single section open events.