Typical chilled/magnum lead shot runs 8-13 Bhn with most testing at 9-11 Bhn. Cu plating adds very little to no hardness, Ni plating is just slightly better because the plating is very thin. If you're not going any further than loading from the as-purchased shot bag, either Cu or Ni plated are of benefit more-so for penetration depth than patterning. The primary benefit of the Cu/Ni plated pellets is the reduced friction losses caused by drag on feathers/fur/hide thus increasing penetration depth in a trade-off of a slightly smaller wound channel.
Plated shot is sized the same as non-plated and the lighter Ni/Cu plating alloy and a harder base lead alloy do create a slight loss of mass so it is proper to increase by one pellet size when going to a so-called magnum or plated shot. For example, a typical #7.5 shot pellet of 9 Bhn all Pb alloy will have a mass of about 1.25gr while the same size pellet in Ni plated 12 Bhn alloy is about 1.09gr or roughly the same mass as a typical all Pb #8 pellet of about 1.07gr.
As Harry said, any additional hardness will help with pattern maintenance simply by helping to reduce damage on firing but a suitable wad column with cushion is a must and often times buffering material helps too but the biggest benefit will come from using a shot sleeve or cup to keep the pellets off the bore. Spin on the pellets that's imparted from contact with the bore is the biggest pattern killer and even more-so than deformed pellets. Aside from using a sleeve/cup, the next easiest pattern improving method is duplexing the shot sizes such as #5/7; #4/6 or #3/5 and it is done 60/40 by mass, not volume with 60% being of the larger size pellets. Best to use a clear plastic container like from peanut butter, add the weighed shot and turn end over end gently so as not to dimple the pellets until they are evenly mixed. A square, or nearly so, payload loading combined with sufficient wad cushioning will give higher velocity reducing the downrange drop while increasing the available momentum via mass at velocity. The primary goal is to keep the SSL as low as possible in order to keep the PPD as high as possible. It never ceased to amaze me at how the modern suppository gun and ammo mfg's have corrupted the basics purely for sales hype - rifle bullets are getting lighter & faster while shotgun loads are getting heavier and slower ... the exact opposite of what works best on both accounts. Still doesn't make sense to me how anyone can justify a "MAGNUM" load that kicks like a mule yet only produces 1115 fps at the muzzle resulting in 16" of drop in 55yds, an average PPD of just 1.3% thanks partly to the 20'+ SSL and not to mention the greatly reduced impact energy levels.... Perhaps it's just me but a 6" drop with a 6% PPD sure seems to work a whole lot better in the field than the so-called "MAGNUM's".
Commercial magnum shot alloy is 4-6% Sb (antimony) with a 0.5-1.0% As (arsenic) but it's quenched, not heat treated which is why the Bhn is low but the alloy typically used will only result in about 18 Bhn when heat treated. The hardest shot is obtained by using WW alloy and heat treating which results in producing shot upwards of 27-30 Bhn thus eliminating the need for plating. Heat treating shot isn't as easy as doing larger bullets/balls, the oven must have excellent temperature control obtained by using a combination of thermal barriers or convection control combined with tight temperature control via a fast response thermocouple and digital pyrometer. Typical bi-metallic t-stat controlled ovens will result in either failure to obtain/maintain critical temperature, a pile of discs as opposed to pellets or puddle of what used to be pellets. Both heat & hold as well as the quenching operation must be tightly controlled as if you allow the pellets to air-quench prior to hitting the water bath, the resultant Bhn will be lower.
