Wow,
You are going to make me have to type a treatise, my apologies to any readers.
The first is "more shots". For me, my shot string is defined by a maximum spread in velocity of less than 2 percent. Even if I get 100 shots, any which are outside of that 2 percent maximum velocity variation are unimportant, as they cause too much variation in pellet strikes at longer distances. Most people want their airguns to be accurate first and foremost. Any shots which are less accurate are simply not as useful for anything other than bragging rights. A properly tuned air rifle will almost always give MORE shots which have less than a 2 percent variation. An unregulated gun can (in some cases) give more total shots, but usually less shots within that magic 2 percent. What does 2 percent mean? As an example, with JSB Exact King .25 caliber 25.39 grain pellets, you will have slightly less than a 1 inch drop variation yards (.64 inches according to Chairgun Pro). This would still be a usable headshot on most small critters, but it is at the edge.
Impedance 1 and Impedance 2, the beauty of Plenum: I beg your forgiveness, I am an Engineer by trade, everything is a math model to me. If you are walking through a crowded store at the mall, people brush up against you, or partially block your way, they are "impeding your flow". Arrive at the store early in the morning when fewer people are there, and you can flow through the store more quickly, you are "impeded less". Impedance is a measure of how much your motion, or flow is slowed down or disturbed. With a non-regulated airgun, you have what I call "impedance 1", it represents the resistance to air flow in the valve, through the port from the valve to the bore, and through the bore to the back of the pellet. All airguns impede air flow to some degree, some are worse than others. Your air pressure tries to overcome that "impedance" in order to do the "work" of accelerating the pellet. Higher flow valves, larger ports and bolts which are shaped to allow easy air flow REDUCE your impedance (which is typically a good thing). Making those changes will increase the maximum velocity your pellet is launched at. Now the dark side of low impedance. A rock in a stream makes less ripples when the water is moving slow, than when the water is moving fast. Anything blocking a flow of a fluid (to include compressed air) has a "non linear" effect. The faster the air is flowing, the more that impedance affects the overall flow. Air moving more slowly is affected less by impedance. This is a good thing with an unregulated air rifle, as it helps keep a more constant pellet velocity, even as pressure is dropping in the air tank. (A well designed balanced valve does this function better). Many air rifles have a air flow restriction device installed in the air path after the valve to increase the impedance, to enhance a more constant velocity in your shot string. Now, Impedance 2, When you add a regulator, you now add a new "restriction" to the air flow. Now we have to add the Resistance to Air Flow from the regulator. The regulator is in between your high pressure tank, and the lower air pressure experienced by your valve. Regulators are SLOW, they may take an entire second to get back to the regulated pressure they are set for. A pellet, once it has started motion, is typically gone in less than 1/1000 of a second. We cannot consider the regulator as a significant source of air, once you pull the trigger.. it is just too slow. However, there is a volume of air between the regulator's back side, and the face of the valve; this is called the "plenum". Your plenum space, which holds a small amount of the regulated air, is what is primarily used to launch your pellet. If a plenum is too small, it will limit the peak velocity a pellet can be launched at. If it is too large, then it subtracts from the total space for high pressure air in the Air Tank/Tube. Plenum space is always a compromise. To get a larger plenum, you are typically trading shot count, A smaller plenum does not eat much shot count, but it also limits you to a lower range of velocities. Bringing it all together. If you start with a high impedance air rifle, then improve the valve, porting and reduce bolt restrictions... and then add a regulator with a properly sized plenum. Usable shot counts and velocity WILL go up... Period, always. But that is more work than just adding a regulator. If you are just dropping in a regulator and want to know the probable results, this will be driven by the impedance of your air rifle, and the plenum size. As a reference, if you are able to hit 40+ FPE (with a .25 caliber 25 grain pellet) when your unregulated air pressure has dropped to 1800 PSI, congratulation, you have a low impedance air rifle.
I am merciful, and will stop here. Hope this helps.
Critical related topics not covered: Balanced valves and their effect on constant velocity. Ideal pressure versus plenum volume, Dump valves and their interactions with regulators, Regulator over-shoot on the first shot in a string, Refill rates of different brands of Regulators, Requirement of vent hole for some Regulators, Pellet weight impact on FPE for a given tuning. Bore diameter and its affect on pellet energy, etc... There is much more to this topic.
