I am trying to "scale" one set of data to another set based on minimum, maximum, and means of the latter set. So hey guys, I'm the guild master of an MMO guild that uses a point system for determining the order that loot is handed out. We are merging into another guild with a different point system. One of my goals during this merger is to merge our point system into theirs.
I'm looking at this in terms of bell curves on a shared coordinate plane. I want to transform our data to fit theirs. Let's say hypothetically my data has the minimum value at 10 and the maximum value at 180, with the majority of the items sitting around 45-65. Their system hypothetically has the minimum value around 50 and the maximum value around 600, with averages around 250.
I would like to be able to take some representation of their system, and then apply a transform on mine that would stretch and skew and otherwise transform our set of data to more closely match theirs. In this idea, my highest entries would be boosted the 400-something to match their highest, our lowest would be boosted the 40 or so, and the middle values would be accordingly "scooched" up by an appropriate amount to match their distribution.
Obviously, the increase at the low end could potentially be much smaller than the increase at the top end, so simply adding a fixed amount wouldn't work well. Is there a formula, algorithm, general approach, or even terms for what I am trying to do? I am not opposed to googling and developing my own approach for this, but with such a significant lack of terminology knowledge, I find myself getting a bunch of pretty useless google results.
Any help would be immensely appreciated!
 A: Let's refer to to your two sets of values as G1 and G2 ("G" for guild). If they have similar distributions (especially if they both are approximately normally distributed), a good approach is "matching $z$ values". Here's how you do it:
For both sets calculate the mean ($\mu_1$ and $\mu_2$ respectively - (that's the Greek letter "mu") and standard deviation ($s_1$ and $s_2$, respectively) -- you should be able to google those terms and find formulas for them pretty easily. Then if $x_1$ is a value from G1 you calculate its $z$ score:
$$z = \dfrac{x_1 - \mu_1}{s_1}$$
and then you turn that same $z$ value into a G2 value using the $\mu$ and $s$ from G2:
$$ z_2 = s_2 \cdot z + \mu_2$$
Roughly speaking, dividing and multiplying by the $s$'s fixes up the spread of the data, and subtracting and adding the $\mu$'s matches up the centers.
If this doesn't work the next thing I'd try would be "matching percentiles", though this is a bit harder to understand and implement, so give this "$z$ values" approach a try and see if the converted values you get make sense.

Addendum: Re-reading your question I've realized that you identified that you want to adjust both the center and spread of your data, but you proposed using the min and max to measure the spread. In statistics, min and max are really unreliable and unstable measures of the spread of a set of data, while the standard deviation is very good (at least for approximately normally distributed data). So that's why we prefer this matching $z$ scores approach - it uses standard deviations.
