Johm: There is no ideal depth to diameter ratio. Indeed having a very deep reflector won’t increase throw, but it won’t decrease it either.
djozz: Telescope mirrors and typical flashlight reflectors differ in one way: Telescopic mirrors have a quote long focal length compared to their diameter - for a reason. That way, all parts of the mirror have nearly the same distance to the focal point, thus nearly the same focal length. With those flashlight reflectors it’s different, they are sort of built around the focal point. Every part of the reflector has to have the same focal point of course, but since the different parts have different distances to that focal point, and the distance to the focal point is the focal length, they have different focal lengths and thus cast images of different sizes. This is what makes the corona around the hotspot core. I suggest an experiment: Take a light with a quit big reflector. Take a piece of cardboard and punch a hole into it and put it in front of your light. Move the hole around: When at the edge of the reflector, only light from an outer part of the reflector gets through, and you get a small image of the LED. Move the hole inwards, and the image gets bigger.
Rockspider: “Luminance is the surface brightness, right?” Yes. “So also the brightness is lesser when viewed from the side, isn’t it?” No: The apparent area of the LED seen from the side gets smaller, and that smaller area multiplied with the same luminance gives the lesser luminous intensity to the side. Throw however depends on luminance, not on that apparent area.
The eye is fooled quite easily; it especially is sensitive to contrast. Less corona gives a sharper shape to the spot and thus more contrast, so it looks more distinct and seems brighter. But actually you loose light that would otherwise be directed into the hotspot, too, so throw decreases.
It may only really have increased throw if the LED was misaligned before and you also shifted the LED relative to the reflector into a better spot.