Quantifying the symmetry of a signal You did it using the norm of the function(signal).

I want to measure this symmetry by subtracting each point of my signal from the flipped one. My question is about the way to normalize this difference. Can standard deviation of the signal be a good option? ( I do not want to divide it by the value of max).
A signal can be decomposed into the sum of an even (symmetric) signal plus an odd (anti-symmetric) signal.  One measure of symmetry of the signal might be the ratio between of the energy in the even decomposition to the energy of the total signal.