Recently I've found a formula relating mean average deviation (MAD) SNR to root mean square (RMS) SNR:
$$\text{SNR}_\text{MAD} = \sqrt{\frac{2}{\pi}} \text{SNR}_\text{RMS} $$
which assumes Gaussian statistics. This is for a definition of MAD something like
$$ \text{MovingAverage}[\ |x - \text{MovingAverage}[x]|\ ]$$
for some signal $x$ measured in the time domain. My question is where does the above SNR formula come from? I'm pretty new to signal processing so maybe there's a very basic reference that describes this. Is there some intuition for why MAD SNR is smaller than RMS SNR?