The standard calculation is limited. The assumption about what velocity the gas is accelerated to after the bullet clears the muzzle is usually fixed. SAAMI uses approximations that are multiples of muzzle velocity. But a moment's thought will reveal that the higher the muzzle pressure is, the greater the actual gas velocity will be. It will change with powder quantity and barrel length. This determines "rocket effect" or "after-effect" (meaning after the bullet has got out). It's also the reason a muzzle brake works with a heavy load: it lets the gas pressure release in a direction that is not forward, and thus the recoil portion due to rocket effect is reduced. But when you shoot mild, low pressure loads, the brake doesn't make much apparent difference.
Another factor not considered is that muzzle velocity as measured includes some acceleration of the bullet by muzzle blast for a short distance after it clears the muzzle. Harold Vaughn measured a .270 Winchester picking up 84 fps out of about 2800 fps from muzzle blast. About 3%. I looked at a continuous Doppler radar readout of a 40 S&W fired from a 4" barrel, and it gained about 35 fps out of 1050 fps after clearing the muzzle, so it happens with pistols, too. That part of the bullet's momentum should be discounted in the recoil calculation, but it isn't. And it's another factor that changes with muzzle pressure.
Felt recoil is a whole other animal. Jeff Cooper taught pulling a rifle hard into the shoulder to minimize this, and it works. It causes a portion of the body mass to be tied to the rifle firmly enough that the recoil is accelerating that body mass as well as the rifle mass. Despite the equal and opposite momentum, accelerating that larger total mass reduces the recoil velocity of the rifle, and since recoil energy is proportional to the square of velocity, it reduces the recoil energy as the inverse of the square of that velocity difference. You still feel it just fine, but the energy determines much of what the smack to the body feels like. If you don't believe it, fire a rifle held hard into the shoulder, then again with a little gap to the shoulder. A sixteenth of an inch is enough. Caution: don't try this with a hard recoiling magnum.
Another factor in felt recoil is psychological. A lot of people feel the old 1911 in .45 Auto kicks like a mule. Well, fire a dozen full power rounds of 44 Magnum, then pick up the 1911 and tell me it still feels like it recoils hard. It won't. What most people are really experiencing is a startle response to the muzzle disturbance in conjunction with the noise and suddenness of the event. 1911 equal and opposite momentum is transferred to the wrist first by direct recoil, then by the slide slamming into the frame, and then even more as the slide is pushed forward by the recoil spring. It doesn't stop jumping up until the slide locks the barrel up, at which point it transfers its momentum from the recoil spring pushing the slide forward back into the frame, which actually helps move the sights back down on the target. But how high the sights jump altogether still gives the impression of a lot of recoil when it isn't anything special.
