I'm pretty sure you've defined all of the terms as statistic deviations away from the group average.
Post your complete theory in one place, just for clarity.
No, the distinction between saving and hoarding does not rely on statistic deviations away from the group average under the definition I proposed.
It has to do with deviations away from the historical price averages.
A hoarder accumulates because they expect price to increase significantly.
A saver does not accumulate because they expect price to increase significantly over time. Rather, a saver saves to preserve an asset for future use, and possibly to benefit from appreciation in the asset (but again, does not expect significant price increases, as defined statistically).
Another element of hoarding (but one that does not necessarily distinguish it from saving) is that the hoarder accumulates a significant amount of the asset. You can argue that this definition relies on personal preference but this is not the case. You do not have to have a preference for the asset in order to hoard, you merely need to accumulate a significant amount of it, and do so because you expect that the price will increase significantly. Measuring the deviation from the mean also does not mean the definition relies on society's collective preferences, society's average level of acquisition could be based on factors other than the collective preference of individuals for the asset, people could be accumulating ugly smelly icky pond goo, because they believe that it is a store of value. One person could be accumulating a significant amount of ugly smelly icky pond goo, expecting that it will not merely be a store of value in the future, but actually increase in value significantly, i.e., the person could be hoarding.
Personal preferences for an asset be correlated with the level of accumulation, but they are different measures. The definition's reliance on level of accumulation is entirely agnostic as to people's preferences for the asset (or society's).
The definition distinguishes saving from hoarding in an objective manner that does not rely on personal preference. It looks at two objective measures that can both be analyzed using statistical tools (price increase expectation and level of accumulation).
I hope people don't find this discussion too insanely technical or boring, I actually think it's pretty interesting, I had never thought about the distinctions between hoarding, speculating, and saving until today. I do think, though, that I have met the task set forth. Although I definitely would like to hear if anyone has any other arguments against what I proposed?