Who should be given a bye?

[kivi]

In later rounds, the strongest player from the bottom group is the best candidate from a BYE, as again such a player is least likely to unduly bias results at the top.

I understand how having the weakest player as bye for first and second rounds might bias the results, but would the same keep happening after that? it seems that at that point, the best players would be likely to have 1 and two wins, and it would be hard for them to play a player with 0 wins.

As you say, in later rounds you don't have that problem, so it is ok to give bye to the weakest of the bottom group. Or random pick in the bottom group, rather than weakest. Actually, best is to pick random among the local players at the bottom, as it is worse for someone coming from far away to be forced to not play a round.

[Matti]

Byes should be given, IMO, in such a way that they are least likely to influence the outcome at the top of the tournament.

For this reason, they should definitely not be given to the top players, as it might heavily influence the outcome in case of tiebreaks.

Generally, I agree. However, what do you think about the idea to give a bye to the single player having four wins after four rounds? Then all the other players could have been paired without pairing anyone down or up.

On the other hand one should also avoid giving a Bye to the weakest players in the first round, because that player will then (because of the free point), be paired with the top players and could in that way influence the top of the tournament unduly.

The ideal candidate in the first round, IMO, is therefore the weakest player from the top half, i.e. the middle player.

In many cases, yes. But if the top half ios close in strength that any player would have a good chance of winning the tournament, I could consider another, weaker player.

For the same reason, BTW, in the second round the middle player from an odd sized top group should be preferred to be paired down.

In later rounds, the strongest player from the bottom group is the best candidate from a BYE, as again such a player is least likely to unduly bias results at the top.

This is possble, but slightly inconsistent with the first round. I might pick the middle one.

[RobertJasiek]

what do you think about the idea to give a bye to the single player having four wins after four rounds?

Positive: his result is not over-determined. Negative: he is punished by not being allowed to play as many games as he had hoped for.

[Matti]

We could extend the discussion to the question:"Who should be paired down?"

BTW, in the second round the middle player from an odd sized top group should be preferred to be paired down.

I agree that the middle player from an odd sized top group is a good candidate to be paired down, but who should he play against? If we use slide pairing, then the opponents are generally half a group apart (by wins or Mcmahon points) and in fold pairing they are on average half a group apart. Following this logic the player paired down, should be given a player half a group lower, in this case the top player from the next group. However, by symmetry if we were to select a player to be be paired up from a group, also the best choice would be the middle player. Then we would pair middle players from two succesive groups and they would be about one group size apart.