Chuck is 100% correct here & both velocity & recoil are dependant on that pressure being applied.
The thing is However neither Velocity nor Recoil can be determined by a comparison of "Peak/Max" chamber pressure.
By using different powders you could load an ounce of shot to 1200 fps @ 10K PSI while you could also load 1Ľ oz to 1300 FPS with only 8K PSI.
Thus there is no direct relation between "Max" pressure & either velocity or recoil, but there definitely is a mathematical relation between pressure & either velocity or recoil.
About all most of us have the means of measuring is the MV. Using that in conjuction with total weight ejected we can then calculate the recoil.