I always associate a shots value with the potential for reward or punishment that it presents (unless the hole doles out those results somewhat arbitrarily). In my mind it means that there is a marked strategic advantage gained by the player that can tailor and execute certain types of shots. The soft flat green with a center hole location and empty surrounds offer little advantage to a player who can shape shots, control spin, control trajectory, etc. The hole is just as easily accessed with any of those shots, and the player need not fret to much about which shot he choses or how well he is able to execute that particular shot, because missing that shot still leads to an easy pitch and putt or easy 2 putt for par. I think we call it shot value, because depending on which shot is selected and how well it is performed, a player can quickly move from a birdie try to a double bogey. That is what makes the shot important or valuable and thus demands our full attention. So I guess in a sense, it is a volatility factor (although one that measure just volatility).
However, when we rate a course for shot values I know I kind of combine this with an assessment of variety. It is possible to build a course with very high shot values where a high, spinning fade yields the greatest probability of success on every shot. However, I normally say that a course has high shot values only if over an entire round, a that course demands that (in order to score well) you carefully and skillfully plan and execute all of the proverbial shots in the bag (shots with different shapes, trajectory, spin, etc.) with all of the clubs in the bag.
It seems to me that one needs to play a course many times to get a sense of aggregate shot values since 1) hole locations are probably the biggest factor and 2) wind and other conditions will have a huge effect on shot values.
Anyway, after all of this ranting I will try a short and sweet mathematical definition: A course presents shigh shot values if modest positive perturbations in the selection and execution of shots over an entire round generally results in a commensurate improvement in scoring.