Much clearer now - thanks for this!Admittedly I have not looked into Speedboosters but I wonder how they increase stops of lights passing through them? Changing perspective such as what an extender does I get but extenders degrade the amount of light rather than boost it.A teleconverter enlarges the image projected by the lens. This is much like moving a projecter further away from a projector screen - much of the image is missing from the screen, and even though the quantity of light coming out of the projector is no different, what is on the screen is bigger and dimmer.
Do it the other way only works if you're using a lens designed for a larger format. It telecompresses the light into a smaller imaging circle, producing a brighter, smaller image. Same concept as a projector throwing out too big an image for a screen, so you move it closer.
Obviously using a larger projector screen (read: sensor) in the first place would have captured the same quantity of light, even through the intensity per unit area on the screen (sensor) is lower.
Or a different way of looking at it is the focal length has changed due to a teleconverter or telecompressor, but the physical aperture still has the same diameter. Therefore the aperture ratio (f stop) has to change.
A telecompressor is just a way of using a smaller sensor to do most of what a larger sensor would do with that lens natively. Even though numbers all get shifted around (focal length, aperture ratio, ISO, but not physical aperture or shutter speed), the end result should be the same (presuming the telecompresor ratio is that same as the crop factor, and you tweak all the settings to create equivalence).