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Sub:
Resolving ties in tournaments
Date:
8/23/2004
10:56:15 PM Mountain Daylight Time
From: cpjorge
To:
service@chess-poster.com
Greetings,
I would like to know where can I find any
information about rules for resolving ties in tournaments. I've
heard some like the Swiss, moves number, etc.
Thank you.
chess-poster.com
Dear visitor,
We found the
following at:
http://www.oxfordcroquet.com/manage/ties/index.asp
Resolving Ties in Tournaments
Not surprisingly other sports and
pastimes have well developed systems for resolving ties. The
ones which most closely fit croquet derive from
Chess.
Ties arise in
non-knockout tournaments for a number of reasons, e.g.:
-
When insufficient rounds are played
in a Swiss tournament or within Block Play
-
When players each have the same
number of wins but A beat B, B beat C and C beat A.
-
Ties can also
arise when further events, e.g. the play-offs, or the final
have to be cancelled due to bad weather.
The options
available to a Manager to resolve the winner of a competition
fall into the following categories:
-
Number of
wins
-
Who beat
whom
-
Number of
points
-
Quality
of opponent
-
Subsidiary competitions
It is prudent to
advertise which tie breaking systems will be implemented
and in
which order before a competition is played. This saves later
threats against the Manager's life.
Number
of wins:
This is the obvious one - whoever
has the most wins is declared the winner!
Who beat
whom:
If two people tie by other criteria
then, if one of those players has beaten the other,
he wins.
Number of
points:
The number of points scored in all
games by individual players is summed; the player with the most
points wins. This is to my mind an unsatisfactory method. In
large events one player may have played against really strong
competition whilst another may have had games against
puppies. In a handicap competition good players will probably
have to sacrifice loads of hoops whilst the bisques are consumed
and hence will only win by small margins. This therefore is not
a good method.
Quality of
opponent:
There are a number of methods
whereby an attempt is made to quantify the quality of the people
who have been beaten.
(a)
Buchholz
(also known as Solkoff).
Sum of oppositions' scores.
This attempts to value the quality of opponents by the magnitude
of their wins. Losses are included. For each of the players
who tied, their previous opponents' games against others in that
competition are examined. For each opponent the sum of the
points they won by and lost by are summed. Then all those
summed points are summed to produce a 'quality of opponents'.
The tied player with higher 'quality of opponents' is the
winner.
(b)
Sonneborn-Berger. Oppositions'
weighted scores.
This is calculated as above by adding scores of opponents who
have been beaten but losses are not included.
Subsidiary
competitions:
Some form of
competition such as shooting at the peg, arm wrestling, dueling
pistols...
Example:
Consider the
following results sheet. It illustrates the techniques
discussed above and indicates some of the problems.
| |
A |
B |
C |
D |
E |
F |
Wins |
Hoop
Points |
|
A |
|
10 |
-10 |
4 |
5 |
-6 |
3 |
3 |
|
B |
-10 |
|
10 |
7 |
-8 |
9 |
3 |
8 |
|
C |
10 |
-10 |
|
9 |
12 |
-13 |
3 |
8 |
|
D |
-4 |
-7 |
-9 |
|
17 |
15 |
2 |
12 |
|
E |
-5 |
8 |
-12 |
-17 |
|
16 |
2 |
-10 |
|
F |
6 |
-9 |
13 |
-15 |
-16 |
|
2 |
-21 |
How to read the table. Each row contains the
results for a player, hence player B lost to A by 10 points,
beat C by 10 points, beat D by 7 points, lost to E by 8 points
and beat F by 9 points. The number of wins is the number of
positive (green) values in the row. The number of hoop points is
the addition of all the points won and lost in that row; e.g.
for A: Hoop Points = +10 -10 +4 +5 -6 = +3.
Assume the
decisions are made in the following order:
1). Number of
wins
A, B and C each
have three wins hence this cannot be used to determine a winner.
2). Who beat
whom
A beat B, B beat
C but C beat A. This is circular hence we cannot determine a
winner by who beat whom.
3). Hoop points
B and C have both
got the same number of hoop points (8); hence we cannot
determine a winner by the maximum number of points.
4). Quality of
opponent
a)
Buchholz
system.
A played B,
C, D, E, F; sum of their hoop points = +8 +8 +12 -10 -21 =
-3
B played A,
C, D, E, F; sum of their hoop points = +3 +8 +12 -10 -21 =
-8
C played A,
B, D, E, F; sum of their hoop points = +3 +8 +12 -10 -21 =
-8
'A' has beaten
better quality opponents under the Buchholz system than B or
C. '-3' is a greater (less negative) number than -8.
b)
Sonneborg-Berger
system.
A beat B, D,
E; sum of their hoop points = +8 +12 -10 = 10
B beat C, D,
F; sum of their hoop points = +8 +12 -21 = -1
C beat A, D,
E; sum of their hoop points = +3 +12 -10 = 5
'A' has beaten
better quality opponents under the Sonneborg-Berger system than
B or C. 'B' has beaten better opponents than C.
Fortunately in
this example 'A' is the winner under both 'Quality of opponent'
tests. It is not unusual however for one player to be selected
by a Buchholz test and another under the Sonneborg-Berger.
For the above
example:
Player B
would be declared the winner had the following criteria had been
applied:
-
Number of wins
-
Who beat whom
-
Points (A is
eliminated)
-
Sonneborg-Berger
Player A
would be declared the winner under the following criteria:
-
Number of wins
-
Who beat whom
-
Sonneborg-Berger
Thank you for
visiting us,
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