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A knockout system should not be used to decide second or third places, they are entirely dependent on the pairings. A knockout system can find the winner only.
A generalised knockout system will give all the players a place in the results, but the order is decided mostly by randomness and not by the relative playing strengths of the players.
Here's an example: Suppose you have 5 players, names A, B, C, D, and E, each of them with the same rank, say 5 dan. To make things interesting, they are from different countries, and of different ages, so that their actual playing strengths are such, that the player earlier in the alphabet always wins.
Now let's assume that we cannot magically predict their actual relative strengths, and we run the tournament starting from the assumption that every player is as likely to win as the other.
For the first round we use the pairing rules on the parent page, and the list comes out as (of course, my random number generator chose the worst case scenario):
E gets a bye, A wins B and C wins D, so for the next round we get:
C gets bye, A wins E, B wins D
before the final round, the list looks like this:
finally A wins C, (the others needn't play anymore) so the final results are
The strongest player was placed first, as the knockout system is guaranteed to do, and the second strongest player was placed after the weakest one, as the knockout system is known to do from time to time.
So, unless you can reliably predict the results of unplayed games (you need this ability to make the magical pairings which would in theory fix this flaw of the knockout system), then you should not use the knockout system to decide anything but the first place.
Or to sum it up, the generalised knockout system guarantees a unique score for all the participants, but except for the first place those scores are not meaningful.
-Bass
Agree, better results will be achieved with either double/triple knockout, or with a variant of Swiss where any player that has reached a unique score is fixed in place (and stops playing).
The argument has some weaknesses.
Here's what happens assuming A>B>C>D>E (/=bye)
| ID | score | R1 | score | R2 | score | R3 | score |
| A | 0 | / | 1 | C+ | 3 | B+ | 7 |
| B | 0 | D+ | 1 | / | 3 | A- | 6 |
| C | 0 | E+ | 1 | A- | 2 | / | 5 |
| D | 0 | B- | 0 | E+ | 1 | / | 3 |
| E | 0 | C- | 0 | D- | 0 | / | 1 |
I think that the more general objection to the system is:
Any player that loses in the first round, is automatically precluded from finishing in the top half.
So if you do not have a reliable prior order for the players, and are thus forced to pair randomly, this system is almost guaranteed not to find the 2nd, 3rd, 4th best players reliably (as the group of players gets larger, it becomes more and more unlikely that the second/3rd/4th place finishers are actually the 2nd/3rd/4th best players).
Right....because its a single elimination, one loss and you are out of the running for the top places with early losses have more severe results (first round loss, you're in the bottom half; second round loss, you're in the bottom 3/4ths, etc), there is significant pressure to use slaughter pairings (best against weakest) or the best approximation of slaughter pairings. So there is little point in playing unless you are among the strongest players...and for the strongest there is little point in playing till the last rounds when they will have interesting games.
This is the reason for McMahon Pairing with its assigned bands which simulate the result of early slaughter rounds, thereby allowing interesting games from the beginning.
Known good prior ordering of players by playing strength required for McMahon.
Yes, this is a weakness that McMahon shares with this system. If you have no reliable prior ordering of the players, it doesn't work (because there is no way to assign bands). In which case Swiss is a good choice.
Any player that loses in the first round, is automatically precluded from finishing in the top half.
Exactly. This is inherent, and that's what makes this form what I call "brutal". But the pairing takes that into account, to avoid strong players stranding in the second half (or any second half at any stage).
But the nice thing about this system is that it behaves the same for winner and loser (it is at the same time a knockout to determine the "total loser"), it keeps all participants busy and works the same way in every round: it is totally symmetrical, one has to fight in each round.
No, in single knockouts the best players do not have to fight at all in the first round, unless paired against each other, but this is very rare....usually slaughter pairings are used. The weakest players are without the ability to fight against the top players. All the top and bottom players play games that have nearly predetermined outcomes and no way to change the outcome but for the stronger player to decide to throw the game and self-eliminate.
Only in later rounds, when relatively equal strength players are matched against each other does the fighting begin.
All the top and bottom players play games that have nearly predetermined outcomes and no way to change the outcome but for the stronger player to decide to throw the game and self-eliminate.
With correct handicaps (e.g. not such a thing as H-2) and komi, each game in each round requires full attention of both players.
Haven't ever seen a knockout tournament with handicaps. How do you set the handicap if you dont know the playing strength order of the players and the strength differences so that handicaps can be assigned?
The ordering by playing strength is the very information the knockout is to provide do us, yet in order to set up knockout correctly, we must know the ordering beforehand.
What am I missing here?
Without such strength information more tournament types cannot function properly: see eg Mc Mahon Example.
Agreed....this is the reason that round robin tournaments are inherently better; they do not assume the very information that the tournament is meant to provide. The only downside is the number of games to be played. As a result of being unable to play the number of games required for a round robin, we resort to Swiss, McMahon, and the various knockouts.
Perhaps this is the reason that Japan uses/used? a round robin tournament to determine who becomes a professional. Round robin is also used to determine the challenger for a number of top Japanese titles...such as Honinbo, Kisei, Meijin, etc.
Round Robin is generally fairest, but Swiss also functions very well without prior information about the strength of the players (unlike McMahon, which need it to set bands)
Yes, I chose the worst case scenario to point out the problem, and I specifically chose a semiplausible real life situation where we cannot gain any "magic information" about the players' real strength from their ranks alone.
According to the pairing rules on the parent page, E gets the first round bye, (all players start equal, so any order is possible) but if I made a mistake, please modify the scenario accordingly.
There is an error in axd 's example He wrongly gives the bye to B but in real games the second round bye would go to one of the first round losers (D or E) And the other would be ranked against A (I suppose)
Therefore more realistic scenario's would be
1) (A playing E in second round, D getting a bye)
id s0 R1 s1 R2 S3 R3 S4 A 0 / 1 E+ 3 B+ 7 B 0 D+ 1 C+ 3 A- 6 C 0 E+ 1 B- 2 D+ 3 D 0 B- 0 / 1 C- 2 E 0 D- 0 A- 0 / 1
or
(A playing D in the second round, E getting a bye)
id s0 R1 s1 R2 S3 R3 S4 A 0 / 1 D+ 3 B+ 7 B 0 D+ 1 C+ 3 A- 6 C 0 E+ 1 B- 2 E+ 3 D 0 B- 0 A- 0 / 1 E 0 D- 0 / 1 C- 2
An other maybe a bit less realistic examples would be that A plays B
id s0 R1 s1 R2 S3 R3 S4 A 0 / 1 B+ 3 C+ 7 B 0 D+ 1 A- 2 E+ 5 C 0 E+ 1 D+ 3 A- 6 D 0 B- 0 C- 0 / 1 E 0 D- 0 / 1 B- 2
or A plays C
id s0 R1 s1 R2 S3 R3 S4 A 0 / 1 C+ 3 B+ 7 B 0 D+ 1 D+ 3 A- 6 C 0 E+ 1 A- 2 E+ 5 D 0 B- 0 B- 0 / 1 E 0 D- 0 / 1 C- 2
It is okay to use examples but lets try to keep them a bit in according with the rules. ( a bye goes to a [player with the least wins that had not a bye before)
The bye should be used in all cases where there is an odd number of participants.
In (my) example, when round 1 has completed, there are three players A,B,C that have to compete against each other in round 2.
Because A has had a bye, the bye must be allocated to B or C. In this case, B, being the strongest.