A single number needed for an estimate of grayness

Question

I'm playing around with images of projector screen fabrics and want a single number that indicates how close to being neutral the image is. What I do is select a small portion of the image, average the selection, and use Photoshop to tell me the colour numbers. Let's just say the Lab numbers (L, a, b) for three fabrics are:
A: 80, -2, -6
B: 85, 7, -1
C: 83, -4, -4
The L gives me the luminance (how bright the screen is), and I think the "a" and "b" should be zero for a true neutral. But if they are not zero, what is the best way to indicate how far the colour is from gray?
Use an absolute average? In which case the single number, call it "grayness" (with 0 being true gray), would be 4 for all samples, indicating that the fabrics are equally gray.
Use Pythagoras to calculate the distance from the a,b origin (assuming "a" and "b" can be treated as perpendicular axces)? In which case the "grayness" value would be: A = 6.3, B = 7.1, C = 5.7, indicating that C was the closest to gray.
Other method.
Any suggestions most appreciated.

Answer 1

Thanks for the suggestions. I want to try for a limited understanding of this.
Saturation, under HSB in Photoshop (thanks Noel and Conroy), looks easy to use, and that may be the way to go, but when I looked it up (under HSL and HSV) on Wikipedia, I'd have no hope of understanding how it is calculated. So I checked out Color Difference on Wikipedia (thanks Chris), and Delta E is something I could probably get a grip on. However, something in Wikipedia's explanation doesn't make sense. They state:
The values L, a, and b (like used in the equations below) are usually double precision values scaled between (-1,1).
And then give the formula, in L, a and b:
DeltaE(ab) = SQRT[(L2-L1)^2 + ...]
It then says that a DeltaE of ~2.3 means a "just noticeable difference", which might be useful for me. If I want to use the DeltaE formula, what values of L, a and b should I use? Those that Photoshop indicates? The reason I ask is that Photoshop gives values of these that range larger than one, but Wikipedia says they are scaled (-1, 1).
Assuming two colours, A and B, as in my example, is the following calculation correct?
DeltaE = SQRT [(80-85)^2 + (-2-7)^2 + (-6+1)^2] = 11.45
Which would indicate a clearly noticeable difference. Also, shouldn't Wikipedia's formula read DeltaE(12), the difference between readings 1 and 2, not DeltaE(ab)?