[Kevin Camin] “for example, if the camera had a base ISO of 800, would shooting at 400 or 100 somehow produce a less noisy image?”
The answer is: it depends.
Noise comes from starving a sensor of light, not merely from the amplification of the sensor. Some cameras handle underexposed areas really well (C300 Mark II, A7S Mark II). Some cameras do not handle underexposed areas well at all (GH4). If you underexpose anything on a GH4, you get noise. Why would you underexpose? Well, some things actually [i]are[/i] dark, and you might want more contrast if you’re shooting to get as close to the final image as possible. This is where a waveform monitor comes in handy because you can actually see if you’re underexposing anything.