Let's stick to the intake theory for now.
So an NA engine only pulls so much air at say 20% throttle right? So wouldn't a stock filter/intake be able to supply more then enough air at 20% throttle? Or are you saying at 20% throttle with an aftermarket intake will somehow allow an engine to draw more air in at the same throttle percentage?
It's not only the amount but the speed at which it travels thru the intake.
The valves open and close on an engine over a known amount of time.
If the air/fuel speed is slowed by a restrictive filter and/or restrictive intake manifold you will have less air/fuel in the cylinder.
If the intake is less restrictive, then the air/fuel speed is faster. Moving faster, more gets into the cylinder creating more power even though the throttle is at the same position.
The term is "
Volumetric Efficeincy". Typically most stock N/A vehicles run around 75 to 85% If you get that percentage up to 90-95%, you will increase power and efficeincy.
The formula for this is: CFM = CID x RPM x VE ÷ 3456
So say you had a 350 V8
At 20% throttle you are at 2000 rpm
Your factory intake has 80% VE
Your engine is flowing 162 cubic feet per minute (cfm) of air.
Now you go down to your favorite speed shop and they install a different intake manifold that increases the VE to 90%.
The same engine at the same throttle/RPM is now flowing 182 cfm of air.
That is a 20 cfm increase.
More flow = more power same RPM/throttle position.
Now you have to reduce the throttle/RPM to provide the same power to maintain the same speed. Less RPM = Less fuel flow rate = higher MPG.
(The forced induction (turbo/SC) engines have a VE over 100% because of the pressure differential. You can still increase the VE of a turbo engine by getting a better flowing intake or by increasing pressure.)
Cold air intakes (CAI) work slightly different. As air gets colder the molecules become more dense (smaller in size).
(which is why your tire pressure decreases in the winter)
So you can fit more molecules in the same volume.
If the engine is flowing 162cfm, there are more molicules per cubic foot if they are at 50* than at 80*.
More molecules per cubic foot = increased power.
A CAI does not increase flow just because the air is cooler. The flow rate stays the same, Just more molecules per cubic foot.
It only increases it if it has a less restrictive flow rate than the stock filter
and the intake has the ability to flow the slight increase.