I don't want to get to, to, pushy or technical.
There is a lot of difference between soft tissue (your hands) and a machine rest and 'sand bagging' is some place in the middle. Every change in stress/pressure will impact the dynamics of the recoil and harmonics of each weapon when fired.
With this said. What I would do:
Start with a full break down of the weapon, clean everything. Lube where needed and put a protective coating as needed as the weapon is put back together. Check the barrel channel for contact between the metal and the stock. Check the connection points between the receiver and the stock (some are pillars, some are cuts in the stock {if the latter and the stock is wood, think about glass bedding}, some are other means). Some receivers do better with tightening in a set sequence. Check with the manufacture on this if there is any question. The receiver must be held tight and stress free.
Moving on to the scope/sights. Check (degrease if appropriate) fit and tightness.
I use a pant leg from an old pare of jeans, sewn closed to hold a double zip lock bag of plain old rice that is packed tight with no ballooning with air. This bag set on my shooting box that is on top of a table. My hand is between the rice bag and the fore-end of the rifle. I don't hold on, just cradle. The butt-stock is pulled into my shoulder with my hand in place. Constancy is the desire.
I start with a box with a grid target taped to it at 35 yards. This is close enough I don't have to walk a lot (old broken fat men don't like to walk a lot, I also check my blood sugar to see it is in the right range, told you I was broken). This range is easy to get the sights in line with the desired condition.
I have found very few weapons that I was a better shot than the weapon could shoot.
I have always found it strange where some shooter goes out hunting and uses a mono-pod or by-pod and then free hand shoots. Then complains that there is something wrong with the weapon. I have though of tiring to get them all wound up so I could buy that no good hunk of junk for a song. It is just a thought
Hope I haven't bored you or irritated you. Just tiring to help.
To you question. All depends.. on the weapon, load, how it is all held.
Load with care,
OSOK