At my club there has been some discussion as to how to avoid the “wasted” first round which tends to be full of mismatches. The problem is that the tournaments are open, so you never know who is going to play from one week to the next. I guess I need to say that the tournaments are more or less monthly, with one game each week. It seems unlikely that sections would work well, because if a large number of high- (or low-) rated players stay away one week, then there could be significant pairing issues.
An idea that has been discussed is accelerated pairings. This would, of course, pair the top half against itself and similarly the bottom half in week one, and then the top quarter, middle half, and bottom quarter in week two, but how would we handle the players who join in week two with a half point bye from week one? There is significant potential for players to be shifted from the top half to the bottom half, or vice versa, by new entries.
Accelerated pairings are good for reducing the number of perfect scores, but not as good for avoiding mismatches in the middle (we’ve tried it at some of our club events and it didn’t work as well as we hoped). If your goal is to reduce the mismatches on the very top and very bottom boards then acceleration is useful. However, if your goal is to reduce mismatches in general then you may be very disappointed.
If there are no upsets then in round three you have the middle six eighths playing each other, which still has a lot of mismatches, and in round four you have the second through eighth sixteenths playing each other and the ninth through fifteenth sixteenths playing each other (looks a LOT like a normal round two).
So, in the middle, round one looks like a standard round two, round two looks like a standard round three, round three looks close to a standard round one, round four looks close to a standard round two and round five ends up looking a lot like a standard round four. The net effect for the middle is to replace the standard rounds one and five with a slightly less one-sided round one (in round three) and a slightly more one-sided round two (in round four).
I didn’t bother addressing the half-point bye issue because I didn’t think it was that significant. There will be some skewing, but you get similar skewing if two players drew in round one (though maybe not as much if the byes are skewed more to one side of the cutoff).