Dubov System Swiss pairings

Running Chess Tournaments
1

I’ve been thinking of ways to improve on the USCF Swiss pairing rules. One problem with the USCF system is that when pairing a round it doesn’t take into consideration the strength of opposition a player has faced in previous rounds. The idea occurred to me that a Swiss pairing program should keep track of the average rating of each player’s opponents, with the goal of equalizing this among the players in each score group. I discovered later that there is a FIDE-approved Swiss pairing system which does this: the Dubov System. Details can be found on fide.com.

In July I directed the 64th New Hampshire Open. I ran into a SwissSys bug when pairing the last round in the Open Section. Details are posted in my replies in the topic Swiss Pairing Question. As discussed in that topic, I modified the SwissSys pairings and paired the round in a way which conforms to USCF rules. However, from a subjective standpoint, I had some sympathy with the pairings produced by SwissSys. To recap what I said in the other topic, here was the situation after four rounds:

2367 3 - W B W
2123 3 W B W -
2113 3 B W B W
2258 2.5 B - W B
2000 2.5 - W B W
2041 2 - B W B
2003 2 W B W B
1928 2 B W W B
1816 2 - B W B
1978 1.5 B W B -
1953 1.5 W - B W
1990 0.5 W B B W

2367 has played 2258, 2041, 1928
2123 has played 2000, 1978, 1928
2113 has played 2258, 2041, 1953, 1816
2258 has played 2367, 2113, 1990
2000 has played 2123, 2003, 1816
2041 has played 2367, 2113, 1953
2003 has played 2000, 1990, 1978, 1928
1928 has played 2367, 2123, 2003, 1953
1816 has played 2113, 2000, 1990
1978 has played 2123, 2003, 1990
1953 has played 2113, 2041, 1928
1990 has played 2258, 2003, 1978, 1816

SwissSys pairings were:

2123 vs. 2367
2113 vs. 2000
2041 vs. 2258
1816 vs. 2003
1978 vs. 1928
1990 vs. 1953

This gives 2123 three Whites and one Black and gives 2258 three Blacks and one White. I changed the pairings to:

2113 vs. 2367
2258 vs. 2123
2041 vs. 2000
1816 vs. 2003
1978 vs. 1928
1990 vs. 1953

I believe my revised pairings are correct under USCF rules, but I’m not entirely happy with them. You see, 2113 and 2123 were rivals for the New Hampshire State Champion title. 2113 had already lost to 2258 while 2123 had ducked that encounter by taking a half point bye. In the corrected pairings, 2113 has to play his second master, while 2123 has to play his first one and 2003, also from New Hampshire, has an easy pairing. 2367, 2258, 2000 were all from Massachusetts. 2041 was in transition but shown as NH on the wallchart. The result was that 2123, 2113 and 2041 all lost while 2003 won, making 2123, 2113 and 2003 New Hampshire co-champions.

In an ideal pairing system, shouldn’t 2113 get credit for having played a master in a previous round? The erroneous SwissSys pairings appeared to do that (although I’m pretty sure it wasn’t by design). 2123 would have had to face a master while 2113 would have had an easier pairing. True, the colors would have been wrong, but arguably it was more important to make sure that players in contention for a prize played the same number of strong opponents than it was to make sure they all had the same number of games with white and black.

The recent discussion about the Lone Pine 1975 Swiss pairing controversy got me thinking about pairing systems again. I looked up the Dubov System on fide.com and used pairing cards to see how that system would have paired the New Hampshire Open Open section. To check my work I downloaded the Vega Swiss pairing program, which supports Dubov System pairings. It’s free as long as it’s used to pair tournaments of fewer than 30 players. I used the New Hampshire Open as a test case.

The result was somewhat disappointing. Given the round 1-4 pairings and results the same as in the actual tournament, it produces almost the same last round pairings as under USCF rules except that it pairs 1928 (2 points) vs. 1990 (0.5 points) in order to equalize colors, skipping over the 1.5 point group.

More interesting was my “fantasy chess” re-pairing of the section using Dubov System pairing rules. My rules for the fantasy chess recreation were: if two players were paired in the actual tournament use their result from the tournament; otherwise, if one player outrates the other by 100 or more points assume that the higher rated player wins; if the players are rated within 99 points of each other assume that the game is drawn.

It turned out that I’d assigned the wrong colors in the 2367 vs. 2258 matchup in round 4, apparently because of a difference between the way USCF and FIDE/Dubov handle color history. 2367’s colors were -BW and 2258’s colors were B-W. I assumed 2367 would get white because the most recent color difference was in round 2. Not so according to FIDE/Dubov: B-W is equivalent to -BW, so the player had the same color history and 2258 got white because he had a higher average rating of opponents.

Using the correct Dubov pairings with 2258 white in round 4, 2123 would have played 2367 in the last round. More interesting are the last round pairings if 2367 had had white in round 4. Standings would have been:

2367 3.5 -BWW

2258 2.5 B-WB
2123 2.5 WBW-
2113 2.5 BWBW
1953 2.5 W-BB
1928 2.5 BWBW

2367 has played 2258, 1928
2258 has played 2367, 2113
2123 has played 2113
2113 has played 2258, 2123, 1953
1953 has played 2113, 1928
1928 has played 2367, 1953

USCF pairings for round 5 would have been:

2113 vs. 2367
2258 vs. 1928
1953 vs. 2123

Dubov pairings would have been:

1953 vs. 2367
2258 vs. 2123
2113 vs. 1928

At first glance the Dubov pairings did exactly what I hoped they’d do: equalize the strength of opposition between 2123 and 2113 by making 2123 play the master who 2113 has already played, while giving 2113 an easier opponent. Looking at the system more closely, though, 2113 didn’t avoid the pairing with 2367 because of the strength of his earlier opponents but because both 2113 and 2367 are due for Black. In USCF pairings 2113 is paired against 2367 because the difference in rating between 2113 and 1953 is more than 80 points (switch for alternation). In Dubov pairings the difference in ratings doesn’t matter. That brings up another issue: is it really fair to the other players for 2367 to get such an easy last round opponent?

In conclusion, I’m sticking with USCF pairings, at least for now.

2

I’ve looked at Dubov, but decided that it would be difficult to apply in a USCF setting (or almost anything other than a really big Swiss with everyone having ratings). The big problem is that it relies very heavily on the fact that you can, right off the bat, partition a score group into those seeking White and those seeking Black. Those due White are paired completely differently from those due Black (due Black are passively moved around in an attempt to equalize, to the extent possible, the average opposition for those due White). This probably can work fine if you have a score group with 20 players. But the real problem for pairing software (and TD’s) isn’t pairing score groups with 20 players; it’s pairing the 3 followed by 2 followed by 2 when some players that have already met. When you get in a situation where color (should) take a back seat to simply finding pairings that work, then a pairing system which relies heavily on color will have problems.

3

Tom,
There are events that have very large score groups where the Dubov system might increase “fairness”, scholastic nationals. In the Open sections of these events the higher rated players have an advantage in that in the score groups near an even score, they will be paired down much more frequently that lower rated players. One can just look at the average rating of opposition for the final 3.5 score group and you’ll find a strong anti-correlation with rating. For teams, this leads to a large advantage for the higher rated teams. I’m pretty sure that this is an unintended consequence but I may be wrong.
Mike Regan

4

Pairing systems, even those in other sports, seem to give advantages to the higher ranked, leading ideally to a 1 vs. 2 matchup in the final round. The object is to find a winner. The “fairness” of individuals matchups every round is a lesser consideration. For example, in tennis there are seedings in brackets that heavily favor the #1 and to a lesser extent, the #2 player. It is not uncommon to see the top ranked player playing the lowest ranked or a qualifier in the first round. He may not play any contenders until the round of 16 or quarterfinals. In the meantime, his rivals might play up and coming young players, other contenders, and dangerous unseeded players whose ranking may have slipped for a variety of reasons. The Swiss System also does that, too, to a degree, but is a “fairer” system as it pairs players within score groups, with score trumping rating.

When we did not have databases to explore the performance of White and Black, or ratings to order players for pairing, color was not as much of a consideration when doing pairings. The most important rule was that players may not play again. Players compete within score groups. Attempts were made to alternate color and to equalize color, but this was not as big of a concern. In a five round event, everyone ends up with unequal colors. Often players with the same number of Whites and Blacks determined their own pairing color in the last round by flipping a coin rather being assigned by a TD. That was part of the Harkness method. Players considered that to be “fairer” rather than being assigned a color based on higher rank, rating, or TD determination. Today, we are very much more color conscious because the databases show a significant advantage statistically for White. The use of pairing programs arbitrarily assign colors based on rules for assignment. How “fair” as to equality of each pairing by rating difference can be done, but is probably too messy and can lead to even more ties for first at the top at the end of the tournament. Then you end up using tiebreak schemes, which are fair or unfair, depending on your perspective, rather than ending up with a single winner base on actual play. This makes me wonder what the Dubov system is really trying to achieve. In Europe, their prize systems are more spread out. In the US, ours are more all or nothing with class prizes sprinkled in. It is really first place or no place in many American tournaments.

5

Actually, in standard tennis procedure, all the seeds have exactly the same probability of facing any particular non-seeded player in the first round. (On occasion #1 has had to face the highest ranked non-seeded player. That would be described as a tough draw.) And seeds are (in effect) interchangeably 1-2, 3-4, 5-8, 9-16, 17-32.

6

One other problem with applying it in the USCF realm is that the word “unrated” appears nowhere in the pairing spec. I assume the idea is that a FIDE unrated would be treated as whatever is the default rating for calculating norms, but USCF doesn’t really have anything analogous to that.

Re applying it to Nationals, teammate and state pairing preferences might make it quite a bit more difficult to implement in practice.

7

For my scholastics I double the USCF rating points recommendations for alternation and equalization in my Syswiss. Seems to give fewer odd pairings in the final round