A ballistic compression type soft recovery system can stop a free-flying supersonic projectile in a controlled manner. The moment such a projectile enters the System, a normal shock gets created and starts hurtling down, to kick off a train of events involving shock reflections, diaphragm rupture, shock merger, creation of new shocks and contact discontinuities, and expansion wave-shock interactions. A good understanding of these phenomena and sensitivity of the System's performance to changes in design parameters is needed to design an efficient soft recovery system. Unfortunately, not much information is available about this. The present work fills this gap. We have developed a numerical model for the system and conducted sensitivity analyses using four design parameters; pressure, molecular weight, the ratio of specific heats, and temperature of gas used in the system. We show that while there is a strong, positive correlation between the first two parameters and projectile deceleration, the other two parameters are less critical. We conducted experiments to corroborate our conclusions and improve our numerical model. Post such improvements, we found the difference between simulation and experimental data to be acceptable. Experiments also confirmed the findings of our sensitivity studies. Finally, we conducted a two-dimensional finite volume analysis to understand the reasons underlying the residual difference between our numerical and experimental data. We show that such differences are due to pressure-rise at a point once a shock passes by it, and such a rise in pressure is attributable to boundary layer effects.