Wether they know or not doesn't really matter. They won't give us that information either way.

I would like to say that we can infer the probability distributions from players experience, just by plotting the number of times an upgrade/refinement has succeded at a certain value as a function of the total number of maximum chances before success.

However, i do not believe (from personal experience) that the probability distribution remains constant at all levels. For example, upgrading anything from lvl 1 or 2 to 2 or 3 usually requires less than 5 tries out of 20 or 30. In other words for the first 2 levels a 20% filled bar will usually result in a successful upgrade/refine. However once you reach lvl 4 or 5 you usually need 80% or more of the bar for a successful upgrade/refine.

Although this only takes into account my experience when lvling up charms/tactics/refinement/battle armor and is not a very big sample, this behavior uis surprisingly consistent. Thus i believe that the probability distribution for the low levels peaks earlier than the distribution for the latter ones. Also this is supported by the fact that i know no one who needed 18+ tries to upgrade from lvl 1 to 2 however i have seen players who needed 65+/70 tries to upgrade at lvl 4.

Also i have noticed that its rare for an upgade/refinment to succeed at the middle values, its usually successful whe the first or last quarter of the bar is full. So i do not believe that the probability can be linear.

Those are my observations, again my sample is only me and what i have seen on the forums from time to time. It only serves to give a tendency and not the full behavior.

Good point. But it also illustrates the fact that the only thing we can do would be to map out the distributions for each level of refine/upgrading.

It's impossible to infer from that the actual formula since we have way too many free parameters and possibly virtually any formula.

Even then our sample with the current forums would be ridiculously small. So we can only specify trends using our observations, such as upgrading/refining does not follow a linear distribution and it gets less likely to succeed with a given percentage of the wish/charm/armor bar full as you lvl up.