Life In 19x19

Hi,

for this question please only consider involuntary odd man byes, not "I want to go sightseeing" byes. I will be referring to a split and slip (eg. 1-5, 2-6, 3-7, 4-8) paired swiss seeded using pre-tournament rating with a fairly small number of participants (eg. 7, 9, 11)

There seems to be two different approaches to awarding byes. The first is to consider bye as a player with the smallest possible rating and using the usual split and slip to do the pairing of N+1 players. In this case, the median player (in latter rounds: of the weakest score group) gets the bye. The second approach is for the weakest player to get the bye and remaining N-1 players to be paired in standard fashion. Both approaches have their logic. The first one doesn't move the weakest player into a stronger group for the subsequent round and seems more consistent. The second approach awards the bye to the player least likely to be in the top X (where standings matter the most) and maximizes the number of games between top position contenders.

Are there any studies or statistical papers regarding this? Or does anyone have any knowledge they could share about he impact on tiebreakers etc.?

The second part of my question is about compensating byes in terms of tiebreakers. Sometimes players do not get any SOS for a bye, but sometimes they get some defined increase of SOS. Eg. MacMahon software by default awards (player's-final-score - 1) SOS-points per bye. Some people suggest awarding SOS equal to the rounded average score of real opponents.

Do you know any articles about this or do you have any explanations for some of the compensation formulas and their consequences?

Thanks for any info you might have
tiger314

Chess usually has a good description, try

http://www.tournamentdirector.co.uk/ecf ... rules.html

The question has been discussed at: http://lifein19x19.com/forum/viewtopic.php?f=45&t=6803.

The basic choices the give a bye (at the first round) are: the lowest player, the middle player and the top player. The basic choices to score a bye are 0, ½ or 1 point (win). Suppose we prefer top players to play more games compared to bottom players and we like to have fair pairings. The first criteria excludes the top player from having a bye.

The ideal result at the end of the tournament would be that the players with byes are all at the bottom of the result list. One way to achieve this is to give bye always to the weakest player, who yet haven't had a bye. However, if the weakest player gets a point after the first round from a bye, the pairings for the next round would be slightly unfair or suboptimal. In this case giving zero points works better. However getting a bye and no points might feel like a double punishment to players.

A better way could be to choose the middle player for a bye at the first round. You did not specify how many rounds are played in the tournament. If the number of players is no more than double compared to the number of rounds, this works well. The middle player and all below him would have received byes by the end of the tournament. If we had 11 players and 4 or 5 rounds, I might select the player at the 3rd quartile, the 8th for a bye. He would be low enought to deserve a bye, but high enough to get a fair pairing after the second round.

On subsequent rounds I would give the bye to a player near the middle of the lowest score group, who still hasn't got a bye.

The common and simple way the count the SOS is the use the players own score for bye round(s). Of course one could develop a statistical model to make a better estimate, butt maybe it is an overkill.