Mechanical Power (Watts) = Force (Newtons) x Speed (m/s)
Mechanical Power (Watts) = Torque (Nm)/time (s)
Electrical Power (Watts) = Voltage (V) x Current (amps)
Likewise, the Power of Light (Lumens) = Brightness (lux) x Lateral Surface Area of Illumination (square meters).
Thus doubling the surface area of illumination, will actually double the lumen count.
The brightness in lux determines the longitudinal throw.
Remember that we need to increase the lux four times, in order to just double the throw!
Similarly, with hi-fi systems, we need to increase the power eight times, in order to double the decibel volume.
Those old incandescent filaments are tiny in size and surface area, so their surface brightness is naturally high.
Thus, they throw a long way.
Although the brightness in lux is great [for great throw], the surface area of illumination is poor!
The incan's hot spot size is tiny.
Their lateral spill is also very dim.
It's a similar with the old XR-E R2 emitters.
They have the highest surface brightness of the LED's, however the hot spot size is tiny and therefore less practical.
Their lateral spill is also very dim.
A modern day XM-L emitter has a little less surface brightness, but it has a huge surface area of illumination.
Since lumens = lux multiplied by surface area, the slightly reduced lux multiplied by a huge increase in surface area of illumination, still equals a huge lumen count.
Thus, XM-L's have a huge lumen output.
The incans have super brightness in lux, but a tiny surface area of illumination, and therefore only a small lumen output.
Thus, lights aren't just about the brightness in lux or candelas; nor longitudinal throw either.
They are also about the lateral width - the lateral surface area of illumination too.
Unlike a laser, light needs width to be practical.
Double the lateral surface area of illumination, and you double the total lumen count...
In both incan and led's, a reflector and lens acts like a motor car's gearbox, or an electrical transformer; it increases one factor, at the expense of decreasing another factor.
Just as the gearbox increases the torque, at the expense of decreasing the rpm speed.
An electrical transformer will increase the voltage, at the expense of reducing the current.
Likewise, the reflector/lens further increases the brightness in lux, at the expense of decreasing the surface area of illumination.
A gearbox cannot increase the total mechanical power; the total power output stays the same.
An electrical transformer cannot increase the total electrical power in Watts; the total electrical power stays the same.
Likewise, a reflector and lens cannot increase the total lumen count; the total lumen count stays the same.
The reflector/lens can be a conventional reflector only, it can be a hybrid of both - like Surefire's Total Internal Reflection TIR optics, or it can be an aspherical lens only with no reflector at all; in all cases, their principles are similar to a motor car's gearbox, while the incan or led is similar to a motor car's actual engine...