First off, I'm not as concerned about "momentum" as I am changing the focus from winning to not winning a game, which is different than enjoying an actual bye week. This analysis doesn't touch on statistical data for teams that tank games heading into the playoffs vs. those that don't.
Secondly, comparing regular season home team winning percentage to playoff home team winning percentage without controlling at all for quality of opponents in the regular season sample is fraught with noise and distortion.
In the regular season good teams win on the road vs.bad teams a lot. In the playoffs, the home team is almost always the team that proved to be better than its opponent during regular season. So you'd expect the home team, which is almost always the better team, to have a higher winning percentage in the playoffs. And, of course, the teams that earn the bye week are the cream of the conference crop, so of course they're going to win at home against decidedly underdog opponents in the playoffs at a much higher rate than the rest of the population, bye week or no bye week. When you get to the conference championship, those are typically two very evenly matched teams. The best two teams in the conference. Yep, you'd expect any "bye week advantage" to be erased at that point since, again, it's the quality of competition gap that has closed, not the rest and relaxation gap.
