Photons are never "lost" until they hit something that's absorbing them, the strength of the wave of light (as light is defined by a wave and it's length) after it left the source, is distance related
When you put your light source further away the light waves are still there but the wave is having more difficulty reaching the plants through the atmosphere in the correct strength to saturate it to full efficiency.
We discussed it at length here and in icmag, got banned for it as LED secrets are like plotonium, you can't touch it without having someone dying haha
But like the gentleman above me said, it's comparing oranges to apples, they both have their distinctive purpose, hps will never veg like LEDs, too hard to beat the amount of light and spread and incident angles etc that LEDs have just because if their design and watt limits
HID or in short, mini sun lamps, as they share the same principles as the sun, can't be beat in resin production, which is what your after when flowering cannabis plants.
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Pic by UnkownProphet, not my bud or grow.
You want to reach this level of trichome and bud integrity and size, anything else your wasting your time.