You can link it to pressure or velocity because they are intrinsically linked and cannot be separated. An easy way to calculate recoil velocity is conservation of momentum wherein you figure the mass and velocity of the ejecta and divide by the mass of the gun. Momentum can also be converted to impulse which is force*time. While force won't remain constant due to the pressure curve, dividing by dwell time in the barrel will give you an estimate. Pressure times area will also give you an idea of the forces but you also need to estimate the friction force of thr barrel on the bullet which is offering a mild containment effect. It is all linked, the math just goes in circles. It is like folks trying to attribute effects to energy vs momentum, can't have one without the other.