I am not an engineer but like most scientists I like to try to quantify qualitative elements. I agree that something like resistance to deflection would be one way to measure 'pop.' I tried to figure out the 'pop' of an old pair of k2 x15's. I measured the deflection of the ski when loaded with a 31.8kg weight at its midpoint.
I used the deflection of a beam formula: deflection=(W*L^3)/48EI.
Since calculating I would be hard, at least for me, and since I was being less than scientific, I used EI as my unit of 'pop' (P).
where:
defleciton=.06m
W=downward force/load=312N
L=length=1.86m
E=modulus of elasticity
I=moment of inertia
.06=(312*1.90^3)/48EI
in this case EI=P=743
When I did the same test to a flexier pair of skis that I built I got P=637. It should be noted that I eyeballed a tape measure for all my measurements and did a lot of rounding to make things simple. But it was clear that the softer ski had less pop on the snow and deflected much more under weight. If anyone else has a way to calculate 'pop' stiffness, etc I would be interested in hearing it.
This said, I think there is a lot more that goes into the feel of poppyness than the physical ski itself. The technique, strength, and mass of the rider have as much or more to do with how a ski behaves than the ski's parameters. Flex of a ski is also dynamic since one can flex a ski in many different ways: leaning back, stomping with the heal, etc. Not to mention that the shape of the tail will change how the ski compresses. Even if a rockered tail is stiff as a board you will have to lean much farther back to get it to load than a flat tail.
Just some thoughts.
"Powder days? Everyone loves powder days. You can ski powder days the rest of your life. I prefer ice, its faster." -Glen Plake