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.:
The options available to a Manager to resolve the winner of a competition fall into the following categories:
It is prudent to advertise which tie breaking systems will be implemented in which order before a competition is played. This saves later threats against the Manager's life.
This is the obvious one - whoever has the most wins is declared the winner!
If two people tie by other criteria then, if one of those players has beaten the other, they win.
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.
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.
(b) Sonneborn-Berger. Oppositions'
Some form of competition such as shooting at the peg, arm wrestling, duelling pistols...
Consider the following results sheet. It illustrates the techniques discussed above and indicates some of the problems.
Assume the decisons 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
1) Buchholz system.
'A' has beaten better quality opponents under the Buchholz system than B or C. '-3' is a greater (less negative) number than -8.
2) Sonneborn-Berger system
'A' has beaten better quality opponents under the Sonneborn-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 Sonneborn-Berger.
For the above Example:
Player B would be declared the winner had the following criteria had been applied:
Player A would be declared the winner under the following criteria:
Martin Murray adds in 2014:
Many thanks Luc, especially for the reference to the Oxford croquet web site page. I checked out both the Buchholz and Sonneborn-Berger systems, and they are both systems for resolving tie-breaks in Swiss tournaments, typically for chess. They both operate of NUMBER of wins (and draws), neither mention MAGNITUDE of wins, unsurprisingly, since in chess there is no such concept. To replace "number" by "magnitude", and then apply this to a (complete) American block, where all have played all, is totally inappropriate. It is also illogical, since if the scores make certain players better than others (the basis of the system the Oxford site proposes), surely C's win over A (by 26) is a better win than B's or C's.
The sooner the page on the Oxford site is corrected the better. Otherwise other managers will be misguided by it.
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