That gauge pressure at 4000' altitude works out to a DCR at cranking speed of approximately 8.3.
There IS a relationship between cranking pressure and DCR. You can take the DCR and multiply it by local atmospheirc pressure that has been 'modified'. Then you subtract out actual atmospheric pressure to get the actual gauge reading.
This 'modification' accounts for the fact that pressure rises more than the mathematical DCR number. When compressed, air gets hot which in turn raises the pressure even more; this is expressed in what is known as an adiabatic relationship. Anyone who has felt a compressor tank get hot as it fills with compressed air knows this. There are also modifying effects from ring sealing, etc. The 'modified atmospheric pressure' is just the actual atmospheric pressure raised to a numerical power, typically taken as between 1.15 and 1.2 for cold engine computations, and typically ends up being in the range of 20 to 22 psi for common elevations for cold engines.