I got lucky on my overnight AA flight from LAX-IAD on Sunday. Plane was pretty much at capacity apart from a couple of middles near the back, one of those being next to me

Seat map on yesterday's BA flight showed loads of space so picked a nice row all to myself. Arrived for boarding and all but 2 seats taken.
Same with my previous flight in Club world / Business. Right up to the time I checked in the seat map showed 3 out of 20 empty seats including my seat mate. Get on the plane and all 20 seats filled - coiuld be op ups, people who have changed flights, moved from a different section etc.

Don't think there's any reall pattern to it. If people don't have status or check-in online, then it's not always apparent that there will be 300 people on a flight when the seat map shows 30.
I've had flights showing as empty and when you board, half the cabin actually is free so a row each.

If you check in online with BA, that locks you into that seat. Might be able to change at the airport or by phoning up though but not online.