If you want to see how effective the patterns are ...just fire one shell.../ then you evaluate the saturation of the pattern area - typically a 30" circle from the center or point of impact.
When you sight in a scope ..or a red dot ...on a rifle or a handgun you are looking for point of impact..( way different than a pattern ) ....so you fire 3 rounds ...to verify the point of impact (vs you flinching, etc). Then you adjust the sight and fire 3 more ...and dial it in.
Patterning and finding or adjusting for point of Impact ...are 2 very different things....
Looking for a Point of Impact on a shotgun ...you'd use a Full choke ...and see where the gun is hitting vs where you are looking ( on a shotgun, your eye is the rear sight ) ... This is the concept of "Fit" ...so you adjust the stock, recoil pad, etc ...so the gun hits - where you look. In this case, I'd fire 3 shells as well ...then adjust my stock or comb ...and fire 3 more and dial it in ( just like if a shotgun had a scope or red dot on it). Once I have the shotgun adjusted so it "Fits" - because it hits where I look ....then I consider "patterning" to check my shells or my chokes....
Patterns - effective size of the pattern size vary by choke ...at a specific range....! A modified choke at 35 yds should give you about a 30" circle with an effective pattern - with no holes in it - and it will vary if you shoot one oz of 8's vs 9's or 7 1/2's because the pellet count is different. A skeet choke will give you an effective pattern or a 30" circle at about 21 yds... / and I would pattern a Full choke at 45 yds... ---- then I would evaluate "the pattern or density" of each 30" circle....seeing if my shot pattern had any holes in it. So when you "pattern" a gun ....you are evaluating the shell you chose - or reload --- and see how its performing ( so it ideally gives you that 30" pattern - at the desired kill range )....and you're also evaluating your chokes ...to see how they perform ...just because the choke says its a Mod...doesn't mean it'll give you a good pattern at 35 yds...it might be tighter than you ideally want or more wide open. So if I had 6 Modified chokes...I might pattern each one of them ....to see which 2 of them, I'd set up for my primary use ...in that gun.
Remember a choke is the amount of difference in the constriction between the diameter of the bore ...and the choke.../ so I have some guns (12ga) that are a little tighter bore than others....and picking the right choke makes a difference. Some guns and choke combinations throw tighter patterns ...because the difference in the constriction is a little tighter. I have a Benelli 12ga semi-auto ...and all of its chokes ...in my gun ...are a little tighter than the label on them indicates..../ so with that gun, I shoot an open Cyclinder for Skeet....and IC for Trap singles ...( where with one of my Brownings...I shoot a Skeet choke for Skeet and a Mod for Trap singles).....that's why you have to pattern a gun / plus to see if my reloads are blowing patterns ...maybe I've got them too fast ...or something...or hulls are wearing out ...or whatever...
So don't mix up the concept of Fit - and Point of Impact .....with Patterning a Choke or patterning a shell and choke combination....