Swiss Tournament Tie-Breaks

It is relatively easy to split a sum of money equitably between two or more recipients. However, cutting a trophy into halves or thirds only makes a mess. Consequently, chess tournaments use tie-breaks to determine the relative standings of chess players who finish with the same scores.

The Swiss System method for running chess tournaments accommodates a large number of competitors. It was first used in Zurich, Switzerland in 1895, where it was developed by Julius Müller, a founding member of the Swiss Chess Federation (see Edward Winter, Chess Notes 4118, 20 January 2006). Random pairings were used among winners and losers when first used, but the system has developed more sophistication since its first use.

Swiss System tournaments are non-elimination. The basic rules* are simple:

1) No one plays the same opponent twice.
2) In each round, players are paired as nearly as possible against others with the same score.
3) Each player should have approximately the same number of Blacks and Whites.

At the end of an event with a number of players that does not exceed 2 to the power of the number of rounds, there will be no more than one perfect score. It often happens, however, that there is no perfect score. Instead, a group is clustered at the top with one-half or one point below perfect. In such case, who wins first place? Tie-breaks are used to make this determination. Tie-breaks also sort players below first place for additional prizes.

Tie-breaks attempt to determine the first among equals by measuring the quality of each player's opponents. There are several methods for making this determination. Usually more than one is used by tournament directors. Below I describe tie-break methods and display how each sorts the participants in one particular tournament. As will be seen, different methods lead to different results.

In this event, three players shared first place, Lucas, Ernest, and Henry. Each of these three won four games and lost one. Each one's only loss was to another of the three. Lucas beat Ernest, the top rated player, but lost to Henry. Henry lost to Ernest.

Henry might prefer Cumulative, as that puts him on top. Lucas comes out on top with Average Opposition. Ernest prevails via Opposition Performance, Opposition Cumulative, and Solkoff.

U.S. Chess Federation rules prefer a system that employs Modified Median, Solkoff, Cumulative, and Opposition Cumulative in that order. In Washington State scholastic events, the standard tie-break system employed is Solkoff, Cumulative, and Opposition Cumulative.

Average Opposition

Average opposition employs the mean of the opponent's pre-tournament ratings. This system will tend to favor the higher rated player, but that did not occur in our sample tournament.

Standings. Average Opposition

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[A]
1	Lucas Beauchamp	1418	W12	W5	W2	L3	W4	4.0	1128
2	Ernest Thayer	1643	W11	W4	L1	W6	W3	4.0	1123
3	Henry Bird	1448	W14	W10	W8	W1	L2	4.0	1076
4	Flannery O'Connor	1069	W7	L2	W11	W8	L1	3.0	1016
5	David Duncan	unr.	W9	L1	L6	W14	W10	3.0	950.5
6	Gilbert Chesterton	889	L10	W15	W5	L2	W7	3.0	888
7	Robert Zimmerman	419	L4	B---	W13	W9	L6	3.0	761
8	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	732.5
9	Shaun Alexander	934	L5	W12	W10	L7	W15	3.0	645.5
10	Charles B. Brown	unr.	W6	L3	L9	W11	L5	2.0	1022.5
11	Robert Frost	793	L2	W14	L4	L10	W12	2.0	931
12	E Dickinson	432	L1	L9	B---	W13	L11	2.0	824.5
13	Carl Sandburg	unr.	H---	L8	L7	L12	B---	1.5	553
14	Rodney Serling	588	L3	L11	W15	L5	L8	1.0	900.5
15	Stephane Mallarme	unr.	L8	L6	L14	B---	L9	1.0	805

Average Opposition Performance

Rather than using pre-tournament ratings, opposition performance employs performance ratings. Performance rating is determined by opponent's rating + 400 for a win, opponent's rating - 400 for a loss, and opponent's rating for a draw.

Standings. Opposition Performance

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[P]
1	Ernest Thayer	1643	W11	W4	L2	W5	W3	4.0	1194
2	Lucas Beauchamp	1418	W12	W6	W1	L3	W4	4.0	1182
3	Henry Bird	1448	W14	W10	W7	W2	L1	4.0	1101
4	Flannery O'Connor	1069	W9	L1	W11	W7	L2	3.0	1116.5
5	Gilbert Chesterton	889	L10	W15	W6	L1	W9	3.0	941
6	David Duncan	unr.	W8	L2	L5	W14	W10	3.0	934
7	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	766.5
8	Shaun Alexander	934	L6	W12	W10	L9	W15	3.0	744.5
9	Robert Zimmerman	419	L4	B---	W13	W8	L5	3.0	737
10	Charles B. Brown	unr.	W5	L3	L8	W11	L6	2.0	1014
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	976.5
12	E Dickinson	432	L2	L8	B---	W13	L11	2.0	807
13	Carl Sandburg	unr.	H---	L7	L9	L12	B---	1.5	743
14	Rodney Serling	588	L3	L11	W15	L6	L7	1.0	944
15	Stephane Mallarme	unr.	L7	L5	L14	B---	L8	1.0	783

Cumulative

Cumulative sums the scores round by round. A player losing in early rounds will face weaker opponents than one winning in early rounds.

Standings. Cumulative

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[C]
1	Henry Bird	1448	W14	W10	W5	W2	L3	4.0	14
2	Lucas Beauchamp	1418	W12	W9	W3	L1	W4	4.0	13
3	Ernest Thayer	1643	W11	W4	L2	W7	W1	4.0	12
4	Flannery O'Connor	1069	W8	L3	W11	W5	L2	3.0	10
5	Joanne Rowling	809	W15	W13	L1	L4	W14	3.0	10
6	Shaun Alexander	934	L9	W12	W10	L8	W15	3.0	8
7	Gilbert Chesterton	889	L10	W15	W9	L3	W8	3.0	8
8	Robert Zimmerman	419	L4	B---	W13	W6	L7	3.0	8
9	David Duncan	unr.	W6	L2	L7	W14	W10	3.0	8
10	Charles B. Brown	unr.	W7	L1	L6	W11	L9	2.0	7
11	Robert Frost	793	L3	W14	L4	L10	W12	2.0	5
12	E Dickinson	432	L2	L6	B---	W13	L11	2.0	4
13	Carl Sandburg	unr.	H---	L5	L8	L12	B---	1.5	2
14	Rodney Serling	588	L1	L11	W15	L9	L5	1.0	3
15	Stephane Mallarme	unr.	L5	L7	L14	B---	L6	1.0	1

Opposition Cumulative

Opposition cumulative sums the cumulative scores of each player's opponents.

Standings. Opposition Cumulative

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[O]
1	Ernest Thayer	1643	W11	W4	L2	W6	W3	4.0	50
2	Lucas Beauchamp	1418	W12	W5	W1	L3	W4	4.0	48
3	Henry Bird	1448	W14	W10	W7	W2	L1	4.0	45
4	Flannery O'Connor	1069	W8	L1	W11	W7	L2	3.0	48
5	David Duncan	unr.	W9	L2	L6	W14	W10	3.0	39
6	Gilbert Chesterton	889	L10	W15	W5	L1	W8	3.0	36
7	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	30.5
8	Robert Zimmerman	419	L4	B---	W13	W9	L6	3.0	28.5
9	Shaun Alexander	934	L5	W12	W10	L8	W15	3.0	28
10	Charles B. Brown	unr.	W6	L3	L9	W11	L5	2.0	43
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	36
12	E Dickinson	432	L2	L9	B---	W13	L11	2.0	28.5
13	Carl Sandburg	unr.	H---	L7	L8	L12	B---	1.5	22
14	Rodney Serling	588	L3	L11	W15	L5	L7	1.0	38
15	Stephane Mallarme	unr.	L7	L6	L14	B---	L9	1.0	29

Head-to-Head

When two tied players have played each other, the winner of their game wins head-to-head. If they drew, however, or if more than two share the same score, head-to-head is useless. The scores below give each player 100, then subtract 1 for each loss to another player with the same score. As can be seen, it was effective for determining last place.

Standings. Head-to-Head

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[H]
1	Ernest Thayer	1643	W11	W4	L3	W5	W2	4.0	99
2	Henry Bird	1448	W14	W10	W6	W3	L1	4.0	99
3	Lucas Beauchamp	1418	W12	W7	W1	L2	W4	4.0	99
4	Flannery O'Connor	1069	W9	L1	W11	W6	L3	3.0	100
5	Gilbert Chesterton	889	L10	W15	W7	L1	W9	3.0	100
6	Joanne Rowling	809	W15	W13	L2	L4	W14	3.0	99
7	David Duncan	unr.	W8	L3	L5	W14	W10	3.0	99
8	Shaun Alexander	934	L7	W12	W10	L9	W15	3.0	98
9	Robert Zimmerman	419	L4	B---	W13	W8	L5	3.0	98
10	Charles B. Brown	unr.	W5	L2	L8	W11	L7	2.0	100
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	99
12	E Dickinson	432	L3	L8	B---	W13	L11	2.0	99
13	Carl Sandburg	unr.	H---	L6	L9	L12	B---	1.5	100
14	Rodney Serling	588	L2	L11	W15	L7	L6	1.0	100
15	Stephane Mallarme	unr.	L6	L5	L14	B---	L8	1.0	99

Kashdan

The Kashdan system rewards aggressive play by awarding 4 points for a win, 2 points for a draw, 1 point for a loss, and 0 for an unplayed game.

Standings. Kashdan

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[K]
1	Ernest Thayer	1643	W10	W4	L3	W6	W2	4.0	17
2	Henry Bird	1448	W14	W11	W7	W3	L1	4.0	17
3	Lucas Beauchamp	1418	W12	W8	W1	L2	W4	4.0	17
4	Flannery O'Connor	1069	W9	L1	W10	W7	L3	3.0	14
5	Shaun Alexander	934	L8	W12	W11	L9	W15	3.0	14
6	Gilbert Chesterton	889	L11	W15	W8	L1	W9	3.0	14
7	Joanne Rowling	809	W15	W13	L2	L4	W14	3.0	14
8	David Duncan	unr.	W5	L3	L6	W14	W11	3.0	14
9	Robert Zimmerman	419	L4	B---	W13	W5	L6	3.0	10
10	Robert Frost	793	L1	W14	L4	L11	W12	2.0	11
11	Charles B. Brown	unr.	W6	L2	L5	W10	L8	2.0	11
12	E Dickinson	432	L3	L5	B---	W13	L10	2.0	7
13	Carl Sandburg	unr.	H---	L7	L9	L12	B---	1.5	3
14	Rodney Serling	588	L2	L10	W15	L8	L7	1.0	8
15	Stephane Mallarme	unr.	L7	L6	L14	B---	L5	1.0	4

Median

The Median system sums the final scores of each player's opponents, discarding the highest and lowest. This system is also known as the Harkness system for its inventor, Kenneth Harkness.

Standings. Median

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[B]
1	Ernest Thayer	1643	W11	W4	L2	W6	W3	4.0	10
2	Lucas Beauchamp	1418	W12	W5	W1	L3	W4	4.0	10
3	Henry Bird	1448	W14	W10	W9	W2	L1	4.0	9
4	Flannery O'Connor	1069	W7	L1	W11	W9	L2	3.0	9.5
5	David Duncan	unr.	W8	L2	L6	W14	W10	3.0	8
6	Gilbert Chesterton	889	L10	W15	W5	L1	W7	3.0	7.5
7	Robert Zimmerman	419	L4	B---	W13	W8	L6	3.0	7
8	Shaun Alexander	934	L5	W12	W10	L7	W15	3.0	6
9	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	5
10	Charles B. Brown	unr.	W6	L3	L8	W11	L5	2.0	9
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	6.5
12	E Dickinson	432	L2	L8	B---	W13	L11	2.0	6
13	Carl Sandburg	unr.	H---	L9	L7	L12	B---	1.5	4
14	Rodney Serling	588	L3	L11	W15	L5	L9	1.0	8
15	Stephane Mallarme	unr.	L9	L6	L14	B---	L8	1.0	7

Modified Median

Modified median treats players with even scores (i.e. 2.5 in a five-round event) the same as the Median. Players with plus scores discard only the lowest scoring opponent's score. Players with minus scores discard the highest scoring opponent's score.

Standings. Modified Median

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[M]
1	Ernest Thayer	1643	W11	W4	L2	W6	W3	4.0	14
2	Lucas Beauchamp	1418	W12	W5	W1	L3	W4	4.0	14
3	Henry Bird	1448	W14	W10	W9	W2	L1	4.0	13
4	Flannery O'Connor	1069	W7	L1	W11	W9	L2	3.0	13.5
5	David Duncan	unr.	W8	L2	L6	W14	W10	3.0	12
6	Gilbert Chesterton	889	L10	W15	W5	L1	W7	3.0	11.5
7	Robert Zimmerman	419	L4	B---	W13	W8	L6	3.0	10
8	Shaun Alexander	934	L5	W12	W10	L7	W15	3.0	9
9	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	9
10	Charles B. Brown	unr.	W6	L3	L8	W11	L5	2.0	11
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	7.5
12	E Dickinson	432	L2	L8	B---	W13	L11	2.0	6
13	Carl Sandburg	unr.	H---	L9	L7	L12	B---	1.5	4
14	Rodney Serling	588	L3	L11	W15	L5	L9	1.0	8.5
15	Stephane Mallarme	unr.	L9	L6	L14	B---	L8	1.0	7

Solkoff

The Solkoff tie-break method sums the final scores of the opponents. No scores are discarded.

Standings. Solkoff

#	Name	Rtng	Rd 1	Rd 2	Rd 3	Rd 4	Rd 5	Tot	TBrk[S]
1	Ernest Thayer	1643	W11	W4	L2	W6	W3	4.0	16
2	Lucas Beauchamp	1418	W12	W5	W1	L3	W4	4.0	15.5
3	Henry Bird	1448	W14	W10	W9	W2	L1	4.0	14
4	Flannery O'Connor	1069	W7	L1	W11	W9	L2	3.0	15.5
5	David Duncan	unr.	W8	L2	L6	W14	W10	3.0	13
6	Gilbert Chesterton	889	L10	W15	W5	L1	W7	3.0	12
7	Robert Zimmerman	419	L4	B---	W13	W8	L6	3.0	10
8	Shaun Alexander	934	L5	W12	W10	L7	W15	3.0	9.5
9	Joanne Rowling	809	W15	W13	L3	L4	W14	3.0	9.5
10	Charles B. Brown	unr.	W6	L3	L8	W11	L5	2.0	15
11	Robert Frost	793	L1	W14	L4	L10	W12	2.0	11.5
12	E Dickinson	432	L2	L8	B---	W13	L11	2.0	10
13	Carl Sandburg	unr.	H---	L9	L7	L12	B---	1.5	7
14	Rodney Serling	588	L3	L11	W15	L5	L9	1.0	12.5
15	Stephane Mallarme	unr.	L9	L6	L14	B---	L8	1.0	10

*The United States Chess Federation Official Rules of Chess, 6th ed (2014) list these three as priorities 1, 2, and 4, respectively. Number 3 is upper half versus lower half. The USCF rules also list a 5th priority: alternating colors.