Vega

C.04.3. The DUBOV Swiss Pairing System (Based on Rating)

Approved by the 1997 General Assembly.

Preface:
The DUBOV Swiss Pairing System is designed to maximise the fair treatment of the players. This means that a player having a higher rating performance than another player during a tournament should have more points as well.

If the average rating of all players is nearly equal, like in a round robin tournament, the goal is reached. As a Swiss System is a more or less statistical system, this goal can only be reached approximately.

The approach is the attempt to equalise the average rating of the opponents of all players of a score group. Therefore the pairing of a round will pair players who have played low rated players before with players having high ratings now.

1. Introductory definitions
"R" is the rating of a player
"ARO" is the average rating of a player?s opponents. ARO must be calculated after each round as basis of the pairings.
The "due colour of a player is white",
- if he has played more games with black than with white before
- if these numbers are equal and he has played black his previous game.
The "due colour of a player is black",
- if he has played more games with white than with black before
- if these numbers are equal and he has played white his previous game.

2. Pairings limitations

2.1 Two players who have played each other shall not be paired again.

2.2 A player who has received a point without playing shall not receive a bye.

2.3 The difference of the number of black and the number of white games shall not be greater than 2 or less than -2.

2.4 A player shall not have the same colour three times in a row.

2.5 Apart from the last round a player cannot be transferred to a higher score group two times running and more than three times (if the tournament has less than 10 rounds) or four times (if the tournament has more than 9 rounds) during one tournament.

2.6 A player shall not be transferred from the subgroup due to a colour to the subgroup due to the other colour if this would violate the limitations 2.3 or 2.4.

3. Colour allocation.
Pairing two players the colour allocation shall regard with descending priority:

- give both players their due colour

- equalise the numbers of black and white games played before

- alternate the colours of both players regarding the first difference of their colour history going back from the previous round to the first round

- assign white to the player with the higher ARO

- assign white to the player with the lower R.

4. Odd number of players at the tournament.

The player from the lowest score group, who has the lowest R will get the bye.

If there are players with the lowest R in both the colour subgroups, then the player to get the bye must be due to the dominating colour and in case there are several players with equal R, the player to get the bye must have the higher ARO.

5. Pairing for the first round.
The player's list calculated before is divided into two equal parts: The players from the upper part of the list are placed on the left and those from the lower part, on the right. The first player from the left-hand list plays the first player from the right-hand list, the second plays the second, etc. After that, the colour of the pieces is determined by drawing lots for one of the pairs, for example, for the first pair. In such a case, all odd-numbered pairs have the same colours as the first pair, whereas all even-numbered pairs have the other colour.

If the number of the players is odd, the last player in the list gets the bye having no colour.

This pairing procedure leads to identical results as the procedures used within the other FIDE Swiss Systems.

6. The standard pairing procedure for the remaining rounds.

6.1 Standard requirement (Special cases see below chapter 7):

The number of players having the same score is even and the number of players with due colour white and black is the same. Each player in the score group has at least one possible opponent in the score group.

6.2 First attempt
The players who should play with the white pieces are arranged in order of increasing ARO , the ARO being the same the player with the lower R is placed higher. If ARO and R coincide completely, the players are to be placed alphabetically.

The players who should play the black pieces are arranged in order of decreasing R, if R is the same, the player with the higher ARO is placed higher. If ARO and R coincide completely, the players are to be placed alphabetically.

Two columns of numbers are written down, thereby arranging the pairs.

For example:
White (ARO) Black (R)
2310.0 2380
2318.4 2365
2322.3 2300
2333.7 2280
2340.5 2260
2344.6 2250

The names of the players are then written down, and only one fact is checked - whether the players have not played their opponents before.

6.3 Improvements
If the players have already played each other, then the "white" player is paired with the first "black" player whom he has not played before, from the lower rows;
If such a coincidence takes place in the last row for a group of players with the same score, then the last but one row is changed.
If a coincidence takes place in a row No. k of a group with the same score and all the "blacks" from the lower group have already played with the "white" No. k, then we change the pairing in row No. k - 1, if this does not work, in row No.k-2, etc.
If the "white" No. k has already played with all the "blacks", we look for an opponent for him, beginning with the "white" No.k+1 down to the end of the column, and then, beginning with the "white" No. k -1 down to the "white" No.1. The colours of the pairings are assigned due to the colour allocation rules.

6.4 Floater
The aim of the pairing procedure is to pair all players within a score group.
If that cannot be achieved the remaining unpaired players are transferred to the next lower score group and treated according to chapter 8.
If there is a choice the floaters should be chosen due to these characteristics with decreasing preference:
- the player was not floater from higher score groups and can be paired in the lower score group;
- the player was not floater from higher score groups and cannot be paired in the lower score group;
- the player was floater from higher score groups and can be paired in the lower score group;
- the player was floater from higher score groups and cannot be paired in the lower score group.

7. Transfer of players to meet the requirement of Chapter 6.
If the requirement of the standard pairing procedure is not fully fulfilled the following transfers shall be carried out in the order listed below

7.1 If a player has already played with all the players of his own score group, a player from the next possible lower score group is transferred to the score group to be paired who has not yet played with the player in question and can be paired according to the colour allocation rules.

The player to be transferred should fulfil the following requirements with descending priority:
- the due colour is opposite to the due colour of the player in question;
- if there is a choice, then the player with the highest R is to be transferred;
- if there are more than one players having the same R then the one with the lowest ARO will be transferred.

7.2 If the number of players of the score group odd, a player from the next possible lower score group shall be transferred to the score group to be paired, who has not yet played with at least one of the players of the higher score group and is allowed to be paired according to the colour allocation rules.

This player to be transferred should fulfil the following requirements with descending priority:
- his due colour is opposite to the dominating due colour of the higher score group;
- if there is a choice, then the player with the highest R is to be transferred;
- if there are more than one players having the same R then the one with the lowest ARO will be transferred.

7.3 If the number of players in the score group is even and the number of Whites exceeds the Blacks by 2n, then n "white" players, who have the lowest ARO, are transferred to the black group. If their ARO is equal, the player with the higher R is chosen. Should both (ARO and R) coincide completely, the list of the players is arranged alphabetically, the transfer being made from the upper half.

7.4 If the number of players with the same score is even and the number of Whites is smaller than the number of Blacks by 2n, then n "black" players, who have the highest ARO, are transferred to the white group. If their ARO is equal, the player with the lower R is chosen. Should both (ARO and R) coincide completely, the list of the players is arranged alphabetically, the transfer being made from the upper half.

8. Treatment of floaters

8.1 Priority of floater-pairing
The floaters having due colour white are arranged according to chapter 6.2.
The floaters having due colour black are arranged according to chapter 6.2.
Beginning with the highest "white" floater the floaters are paired one by one going down to the lowest floater alternating between "white" and "black".

8.2 Pairing the floaters
Each of the floaters is paired with the player having the highest R, if possible having the opposite due colour. If there are more than one player with equal R, the player with the lowest ARO is chosen.

9. Final remarks

The list of AROs should be published after each round to make it possible for the players to calculate the pairings on their own.

A situation which cannot be directly resolved by using the given instructions, the referee should proceed wisely and impartially in the spirit of the basic principles outlined above.

Vega and the Dubov System

Let's remind that in the Dubov system the player with a higher ARO will play against a player with a low rating and viceversa. The preliminary tasks done by an arbiter before to produce a pairing using such a system are the following:

1. Calculate the Average Rating Opponent (ARO) of each player;
2. Determine the due color of each player as in chapter 1 of the FDS (FIDE Dubov System);
3. Put each player in a score group according to his score and due color.

With respect the other swiss systems the Dubov system requires more work if the arbiter is not helped by a computer. In contrast the subsequent pairing is much more easy to perform manually than other swiss sytem.

Standard case (chapter 6 FDS)

Let's examine first the standard case, i.e. that for which in a score group the number of white and black players is the same. The next picture shows a simply standard case with 4 players. Each player is in the respective due color subgroup:

The ID of the players are 14, 18 (white subgroup) and 1, 15 (black subgroup). The white subgroup is sorted in increasing ARO, while the black one is sorted in decreasing rating (Rat). The Vega output shows even two very useful flags. The flag 'c' indicates if the player can "change due color": the value 0 means not, and the value 1 means yes. Instead the flag 'u' indicates if the player can "upfloat", that is if he can play with an opponent with a greater score: the value 0 means not, and the value 1 means yes.

In this case the pairing proceede doing the pairs 14-1 and 18-15, provviding that these players are never played before each other. Otherwise we must perform other pairs as in the usual swiss system (section 6.3 FDS). Then the color allocation are done as in section 3.

If the pairing cannot be done, the remaining unpaired players are transferred to the next lower score group and treated according to chapter 8. When this case occur the number of floaters is even because of the fact that the number of players in a standard score group is even. The manner to pair the floaters is a generalization of the case of the "island" (see forward) and will not be covered here.

The Dubov System works on the premise of the standard case. When this not occur the score group has to be patched stepwise as follows:

1. to each player who cannot play any opponent in his score group find a suitable opponent due to chapter 7.1 in the next lower score group;

2. if the number of players in a score group is odd (after step 1 has been done) find a suitable additional player due to chapter 7.2 in the next lower score group;

3. equalize the number of players with due colour white and black (chapters 7.3 and 7.4).

The great benefit of the Dubov system is to handle these cases in the score group where they appear. The other swiss systems pull the difficult players down and hope that the problem will be solved in the next groups. But I like this system espencially fot the fair treatment of the players (see the concept of ARO), and for the better distribution of the colors.

Now let's examine some examples of non standard case.

"Island" case (chapter 7.1 FDS)

The "island" is the player that in its own scoregroup as already played with all other players. In a score group we can have n islands. In the case of 1 island his opponent is looked for in the next lower score group with the following priority:

1. opposite due color
2. highest rating
3. lowest ARO
4. same due color
5. highest rating
6. lowest ARO

For example in the following situation

Because player 9 has already played with 17 and 21. Then Vega found for player 9 the opponent 22, being players 12, 19 and 20 already previously paired with 9. The message of Vega in the verbose.txt file is the following (in red are reported additional comments):

================================
Pairing group 10
================================
[Ch 7.1] ISLANDs: they are: 1 (it is signaled the case)
9 (The player's ID)
> moving player 9 from [W G10] to floater group 10

(The "floater" group is a logical space in which are parked the "islands" and the floaters before to pair them with an appropriate opponent)

> moving player 22 from [B G11] to opponent group 10

(Found the opponent 22. The "opponent" group is a logical space in which are parked the "opponents" of the islands or floaters)

Standard pairing with 1 White e 1 Black
21 - 17

(In the score group 10 now are remained the players 21 and 17 that can be paired)

Total pairs in the group 10 (summary)
***** 9 - 22
***** 21 - 17

Odd score group case (chapter 7.2 FDS)

When the number of players in a score group is odd a suitable player must be found in the next lower score group. This player, of course, must not be an island in the score group where he is going to be transfered. Moreover he must be found with the following priority:

1. opposite due color of the dominant due color of the higher score group;
2. highest rating;
3. lowest ARO;
4. same due color of the dominant due color of the higher score group;
5. highest rating;
6. lowest ARO.

Unequal numbers of players with due color white and black (chapter 7.3 and 7.4 FDS)

This is the last step to be done after the previous case 7.1 and 7.2 if necessary. In this case simply we must equalise the colors. Let's consider the following case in which we are treating the score group 11:

Because the group 11 is odd first we must add a player (chapter 7.2). Vega find the player 11. In fact the players 4 and 8 cannot upfloat because they floated previously (see their u flag set to 0) and for 2.5 cannot upfloat two times running. However the player 11 has due color black and after his transfer the group 11 has 0 white and 4 black players. So we must transfer 2 black player to the white subgroup according to chapter 7.4. The following is the Vega output for the whole treatment of group 11:

================================
Pairing group 11
================================
[Ch 7.2] Group odd! 0 White e 3 Black
> moving player 11 from [B G 15] to [B G 11]
[Ch 7.3 7.4] Colors not equal 0 White e 4 Black
> moving player 19 from [B G 11] to [W G 11]
> moving player 12 from [B G 11] to [W G 11]

Standard pairing with 2 White e 2 Black
12 - 20
19 - 11

Total pairs in the group 11
***** 12 - 20
***** 19 - 11