Actual Handbook

Handbook | C. General Rules and Recommendations for Tournaments
| 04. FIDE Swiss Rules | 04.1. Swiss System Based on Rating 

04.1. Swiss System Based on Rating

Approved by the 1992, 1997 and 1998 General Assemblies.

A. Introductory Remarks and Definitions 

B. Pairing Criteria 

C. Pairing Procedures 

D. Transposition and Exchange Procedures 

E. Colour Allocation Rules 

F. Final Remarks 

A. Introductory Remarks and Definitions 

A.1 Rating
It is advisable to check all ratings supplied by players. If no
reliable rating is known for a player the arbiters should make an
estimation of it as accurately as possible before the start of the
tournament.
(to convert German Ingo or British BCF use rating = 2840 - 8 x INGO =
600 + 8 x BCF)
A.2 Order
For pairing purposes only, the players are ranked in order of,
respectively
 a. score
 b. rating
 c. FIDE-title (IGM-WGM-IM-WIM-FM-WFM-no title)
 d. alphabetically (unless it has been previously stated that this
    criterion has been replaced by another one)

The order made before the first round (when all scores are obviously
zero) is used to determine the pairing numbers: the highest one gets
#1 etc.
A.3 Score brackets
Players with equal scores constitute a homogeneous score bracket.
Players who remain unpaired after the pairing of a score bracket will
be moved down to the next score bracket, which will therefore be
heterogeneous. When pairing a heterogeneous score bracket these
players moved down are always paired first whenever possible, giving
rise to a remainder score bracket which is always treated as a
homogeneous one.
A heterogeneous score bracket of which at least half of the players
have come from a higher score bracket is also treated as though it was
homogeneous.
A.4 Floats
By pairing a heterogeneous score bracket, players with unequal scores
will be paired. To ensure that this will not happen to the same
players again in the next round this is written down on the pairing
card. The higher ranked player receives a downfloat ( ), the lower one
an upfloat ( ).
A.5 Byes
Should the total number of players be (or become) odd, one player ends
up unpaired. This player receives a bye: no opponent, no colour, 1
point. A bye is considered to be a downfloat.
A.6 Subgroups
To make the pairing, each score bracket will be divided into two
subgroups, to be called S1 and S2.
In a heterogeneous score bracket S1 contains all players moved down
from a higher score bracket.
In a homogeneous score bracket S1 contains the higher half (rounding
downwards) of the number of players in the score bracket.
The number of players in S1 will be indicated by "p", indicating the
number of pairings to be made.
In both cases S2 contains all other players of the score bracket.
In both S1 and S2 players are ordered according to A2.
A.7 Colour differences and colour preferences
The colour difference of a player is the number of games played with
white minus the number of games played with black by this player.
After a round the colour preference can be determined for every
player.
 a. An absolute colour preference occurs when a player's colour
    difference is greater that 1 or less than -1, or when a player
    played with the same colour in the two latest rounds. The
    preference is white when the colour difference is << 0 or when the
    last two games were played with black, otherwise black. In this
    case the (obligatory) colour is already written down on the score
    card. (This rule is not in effect when pairing players with a
    score of over 50% in the last round).
 b. A strong colour preference occurs when a player's colour
    difference is unequal to zero. The preference is white when the
    colour difference is < 0, black otherwise.
 c. A mild colour preference occurs when a player's colour difference
    is zero, the preference being to alternate the colour with respect
    to the previous game. In this case the colour difference is
    written down as +0 or -0 depending on the colour of the previous
    game (white or black respectively).
    Before the first round the colour preference of one player (often
    the highest one) is determined by lot.

A.8 Definition of "x"
The number of pairings which can be made in a score bracket, either
homogeneous or heterogeneous, not fulfilling all colour preferences,
is represented by the symbol x.
x can be calculated as follows:
w = number of players having a colour preference white.
b = number of players having a colour preference black.
q = number of players in the score bracket divided by 2, rounded
upwards.
If b >> w then x = b-q, else x = w-q.
A.9 Transpositions and exchanges
 a. In order to make a sound pairing it is often necessary to change
    the order in S2. The Rules to make such a change, called a
    transposition, are in D1.
 b. In a homogeneous score bracket it may be necessary to exchange
    players from S1 and S2. rules for exchanges are found under D2.
    After each exchange both S1 and S2 are to be ordered according to
    A2.

B. Pairing Criteria

    Absolute Criteria
(These may not be violated. If necessary players will be moved down to
   a lower score bracket.)
B.1
 a. Two players shall not meet more than once.
 b. A player who has received a point without playing, either through
    a bye or due to an opponent not appearing in time, shall not
    receive a bye.

B.2
 a. No player's colour difference will become >+2 or <-2.
 b. No player will receive the same colour three times in row.

Relative Criteria
(These are in descending priority. They should be fulfilled as much as
possible. To comply with these criteria, transpositions or even
exchanges may be applied, but no player should be moved down to a
lower score bracket).
B.3
The difference of the scores of two players paired against each other
should be as small as possible and ideally zero.
B.4
As many players as possible receive their colour preference. (Whenever
x of a score bracket is unequal to zero this rule will have to be
ignored. x is deducted by one each time a colour preference cannot be
granted.)
B.5
    No player shall receive an identical float in two consecutive rounds.
B.6
No player shall have an identical float as two rounds before.
Note: B2, B5 and B6 do not apply when pairing players with a score of
over 50% in the last round.

C. Pairing Procedures

     Starting with the highest score bracket apply the following
procedures to all score brackets until an acceptable pairing is
obtained. Afterwards the colour allocation rules (E) are used to
   determine which players will play with white.
C.1  If the score bracket contains a player for whom no opponent can be
found within this score bracket without violating B1 or B2 then:
  * if this player was moved down from a higher score bracket apply
    C12.
  * if this score bracket is the lowest one apply C13.
  * in all other cases: move this player down to the next score
       bracket.
C.2  Determine x according to A8.
C.3  Determine p according to A6.
C.4  Put the highest players in S1, all other players in S2.
C.5  Order the players in S1 and S2 according to A2.
C.6  Pair the highest player of S1 against the highest one of S2, the
second highest one of S1 against the second highest one of S2, etc.
If now p pairings are obtained in compliance with B1 and B2 the
pairing of this score bracket is considered complete.
  * in case of a homogeneous score bracket: remaining players are
    moved down to the next score bracket. With this score bracket
    restart at C1.
  * in case of a heterogeneous score bracket: only players moved down
    were paired so far. Start at C2 with the homogeneous remainder
       group.
C.7  Apply a new transposition of S2 according to D1 and restart at C6.
C.8  In case of a homogeneous (remainder) group: apply a new exchange
   between S1 and S2 according to D2. Restart at C5.
C.9  Drop criterion B6 and B5 (in this order) for downfloats and
   restart at C4.
C.10 In case of a homogeneous remainder group: undo the pairing of the
lowest moved down player paired and try to find a different opponent
for this player by restarting at C7.
  * If no alternative pairing for this player exists then drop
       criterion B6 first and then B5 for upfloats and restart at C2.
C.11 As long as x is less than p: increase x by 1. When pairing a
remainder group undo all pairings of players moved down also. Restart
at C3.
C.12 In case of a heterogeneous group: undo the pairing of the
previous score bracket. If in this previous score bracket a pairing
can be made whereby another player will be moved down to the current
one, and this now allows p pairing to be made then this pairing in the
previous score bracket will be accepted.
C.13 In case of the lowest score bracket: the pairing of the
penultimate score bracket is undone. Try to find another pairing in
the penultimate score bracket which will allow a pairing in the lowest
score bracket. If in the penultimate score bracket p becomes zero
(i.e. no pairing can be found which will allow a correct pairing for
the lowest score bracket) then the two lowest score brackets are
joined into a new lowest score bracket. Because now another score
bracket is the penultimate one C13 can be repeated until an acceptable
pairing is obtained.
C.14 Decrease p by 1 (and if the original value of x was greater than
zero decrease x by 1 as well). As long as p is unequal to zero restart
at C4. If p equals zero the entire score bracket is moved down to the
   next one. Restart with this score bracket at C1.

D. Transposition and Exchange Procedures

  Example: S1 contains players 1, 2, 3 and 4 (in this sequence); S2
   contains players 5, 6, 7 and 8 (in this sequence).
D.1 Transpositions within S2 should start with the lowest players,
with descending priority:
 1. 5-6-8-7;
 2. 5-7-6-8;
 3. 5-7-8-6;
 4. 5-8-6-7;
 5. 5-8-7-6;
 6. 6-5-7-8;
 7. 6-5-8-7, etc.

Hint: put all numbers constructable with the digits 5, 6, 7 and 8 in
   ascending order.
D.2 When applying an exchange between S1 and S2 the difference between
the numbers exchanged should be as small as possible. When differences
of various options are equal take the one concerning the lowest player
of S1.
Exchange one player
S1   Exchange two players
S1
  4 3 2 S2   3+4 2+4 2+3
5 a c f 5+6 j l o
6 b e h 5+7 k n q
7 d g i 6+7 m p r

The above matrices contain the sequence in which exchanges should be
applied.
Exchanging one player: a) 4 and 5; b) 4 and 6; c) 3 and 5; etc. until
i) 2 and 7.
Exchanging two players: j) 3+4 with 5+6; k) 3+4 with 5+7; l) 2+4 with
5+6 etc. After each exchange both S1 and S2 should be ordered
according to A2.
Remark: if the number of players in a score bracket is odd, S1
contains one player less than S2. So with 7 players S1 contains
players 1, 2 and 3, S2 4, 5, 6 and 7. The exchanges needed in that
case can be found from the above ones by deducting all numbers in S1
and S2 by 1. The last column of the second matrix has then become
obsolete.

E. Colour Allocation Rules

    For each pairing apply (with descending priority):
E.1 Grant both colour preferences.
E.2 Grant the stronger colour preference.
E.3 Alternate the colours to the most recent round in which they
   played with different colours.
E.4 Grant the colour preference of the higher ranked player.
E.5 In the first round all even numbered players in S1 will receive a
   colour different from all odd numbered players in S1.

F. Final Remarks

F.1  After a pairing is complete sort the pairing before making them
public.

The sorting criteria are (with descending priority)
  * the score of the higher player of the pairing involved;
  * the sum of the scores of both players of the pairing involved;
  * the rank according to A2 of the higher player of the pairing
       involved.
F.2  Byes, and pairing not actually played, or lost by one of the
players due to arriving late or not at all, will not be taken into
account with respect to colour, Such a pairing is not considered to be
   illegal in future rounds.
F.3  A player who after five round has a colour history of BWW-B (i.e.
no valid game in round 4) will be treated as -BWWB with respect to E3.
   So WB-WB will count as -WBWB and BWW-B-W as - - BWWBW.
F.4  Because all players are in one homogeneous score bracket before
the start of round one and are ordered according to A2 the highest
player of S1 will play against the highest player of S2 and if the
   number of players is odd the lowest ranked player will receive a bye.
F.5  Players who withdraw from the tournament will no longer be paired.
Players known in advance not to play in a particular round are not
   paired in that round and score 0.
F.6  A pairing officially made public shall not be changed unless it
   violates the absolute pairing criteria (B1 and B2).
F.7  If either
  * result was written down incorrectly, or
  * a game was played with the wrong colours, or
  * a player's rating has to be corrected, then this will only affect
    pairing yet to be made.

Whether it will affect a pairing already made public but not yet
played should be decided by the arbiter.

   Unless the rules of the tournament state otherwise:
F.8  Players who are absent during a round without notification to the
   arbiter will be considered to have withdrawn themselves.
F.9  Adjourned games are considered draws for pairing purposes only.
F.10 F.10 In order to make the final standings the following criteria
apply (in descending priority):
  * the highest number of points scored; should this be equal for
    several participants prize money should be shared;
  * where it concerns the first place: the best result in games played
    against each other;
  * the highest average rating of the opponents;
  * the drawing of lots.

