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I can only speak from the experience of my own fictional league, where I have had byes in the play-offs for six seasons now. For the first three years, the top two seeds had a bye and since then only the top seed does.
The first round of the play-offs is exactly as the Division Series in real life - best of five with rest days after games two and four. Added to rest days after the end of the regular season and after the first round of the play-offs, it means the team(s) with a bye might not start the postseason until 10 days after their last regular season game.
Under this format, the championship has been won by a team with a bye four times out of six, and only two times out of nine has a team with a bye lost its first play-off series. It hasn't ever seemed to me that the teams with a bye have been put at any significant disadvantage.
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