Time zones matter. Or rather playing zones, lol.

Perhaps we could have [6pm GMT .. 12pm GMT] style tournaments which are only open to those whose playing times overlap those hours.

More sensibly, perhaps, some statistics about when and how often a player logs in and makes moves could be gathered. I would show as logging in intermittently throughout the day and making several moves in all of the few games that I play (opponent permitting as Abigail points out). Others might show as making a bunch of moves in a subset of their several hundred once a day, or something like that. Abigail would show as giving her games good attention.

But I reckon that more than a few people would be iffy about having their playing patterns noted, so it's not an idea that's likely to go very far.