Shot loads can be everything from mouse fart loads intended to make a day of busting clays comfortable to fire-breathing screamers designed to hit geese flying high over empty fields or kill turkeys at distances considered well past typical shotgun range. You have to determine what sort of shot you are dealing with. The simple method is to examine payload weight and either the powder charge or velocity. For example:
https://www.federalpremium.com/shots...-GMT113+8.html
This Federal gold medal load intended for shooting sporting clays shoots a 1 ounce payload of #8 shot at 1180 FPS. This would be an exceptionally mild shot load mainly intended for use in break-action shotguns.
https://www.federalpremium.com/shots...PBIX137+3.html
This is a 1 3/8 oz. #3 shot payload at 1450 FPS. This would be a pretty stout load meant to reach out and get birds flying high.
If you look at the weight of the payload and the velocity, you get a good idea of what the recoil will be like. 1 ounce is roughly standard payload for a 12 gauge. 1200-1300 FPS is about standard velocity.
A 7/8 ounce payload at 1,300 FPS will be a mild load.
A 1 ounce load at 1,100 will be a mild load.
A 1 ounce load at 1,600 FPS is about maximum 2 3/4" payload and will be stout.
A 1 1/8 ounce load at 1,200-1,300 will be pretty stout.
A 1 3/8 ounce load at 1,450-1,500 FPS will be magnum territory payload and will be stout.
Etc.
While it's not a formal formula, you can think of it in terms of
Payload x Velocity = Felt Recoil
An ounce of lead being pushed at 1,100 FPS is using less powder than the same ounce of lead being pushed at 1,300 FPS. Meaning the equal and opposite reaction at the other end will be lesser, too.