What most people forget/ignore is the fact that there are at least 3 degree of HQ: +1, +2 and +3. HQ +1 does not require a minimum Quality, however +2 and +3 do and in my own experience you need a minimum 100+ Quality for +2 and 200+ Quality for +3. Yes it is better if we can see more of the correlation between Quality and HQ, but don't forget part of it is already there.