Larry; ""READ"" that statement on the bottom of page 70, just one more time.
"Apparently the 28 standard load & the 12-gauge are both balanced loads in terms of the length & weight of shot column relative to bore diameter".
Larry, "THAT AIN"T TALKING ABOUT GUN BALANCE" that's talking about load balance. But they simply do not share a similar balance relative to the points he cites.
As to the 28's position relative to the 20 & the 28, bore dia is not the determing factor here but bor capacity. this is relative to the square of their diameter not to their diameter. This why a 1" pipe will deliver 4 times as much water at the same pressure as a ˝" pipe having half its diameter.
Bore capacity of the 28 is 80% that of the 20 while the .410 has only 55% that of the 28 (or 44% that of the 20). So yes the 28 is "Supposed" to shoot much closer to the 20 thn the 28. Of course considering the standard loads of the three gauges of 7/8oz, 3/4oz & 1/2oz the 28 is loaded heavier relative to its bore than the 20 & the .410 even heavier.
Effectives which might appear even broder than this would indicate can easily be accounted for, that at skeet range the 28 even in skeet boring is within its effective range, while the .410 is not. Increasing the effectiveness of the 28 then would not be expected to show a significant improvement, reducing it would.
How many 28's do you see at handicap trap?? That you see goes beyond the effective range of the 28.
While the Art & Science of Shotgunong was a very appropriate title of this book & I will add Bob did a very good job on the art aspect, the ballistics are the science part, this is where in several instences & this topic in particular is where he fell somewhar short.
This doesn't really take a rocket scientist to understand.