Formula to generate a score from 1 to 100 based on 2 percentages? I am trying to come up with a formula that will result in a score of 1 to 100 (never anything lower or higher). I have two numbers that I can use to come up with this score, a specific percent and an average percent (from all of the others in the set).
The score would essentially not be able to reach the upper or lower bounds, just get infinitely closer. The idea would be to assign a score of 50 if the specific percent matched the average percent, and scale from there. I know I've done something like this in the past, but I've been racking my brain off and on all day and haven't been able to come up with anything. Any ideas?
Edit: I forgot to mention the most important part. The percentages will for the most part be between 0.01% and 2.0%. So the average could be something like 0.42%, etc.
 A: Won't normally distributing your dataset do this, anyway? Your average percent from the others in the set should be your score of 50. And no one can score any higher or lower than your bounds.
Maybe I'm just not reading you correctly.
Re your edit: The particular percentages don't matter, just fitting them to a normal distribution does. Wiki link.
If your average percentage is 0.42%, 0.42% is $\mu$ (that is, the mean, that is a score of 50) on your normal distribution.
Additional: If you can't examine the data ahead of time, Ross's would likely be the way to go.
A: Do you need to come up with the function before you have the data, or can you look at the whole data set before choosing the function?  If you have all the data, percentiles sound like they do what you want.
If you can't examine the data in advance, it would still help to have some idea of the scale.  For example the specific scores might always stay within +-10% of the average, or they might range by a factor of 1000.  If you choose a function that keeps the ones a factor of 1000 within bounds, the ones within 10% will be very compressed.  One example would be to start with the logistic function $f(t)=\frac{1}{1+\exp(-t)}$, which takes input in $(-\infty,\infty)$ and returns values in $(0,1)$.  If values in (0,100) are acceptable, you could set t=(specific percent-average percent)/scale, then score$=\frac{1}{1+\exp(-t)}$, choosing scale to reflect the range of interest.
Added:  with your edit, maybe setting average percent to 1% and scale to 0.5% or 1% will meet your needs.  You could try some values in a spreadsheet and see what you think.
Added2:  that is why I talked about the scale factor, as your values are so close arithmetically.  If scale$=1, t=0.003-0.0042=-0.0012$ and score$=0.4997$.  But maybe you should use a scale of $0.001$.  Then $t=-1.2$ and score$=23\%$.  An idea how this works using average$=0.0042=0.42\%$, scale$=0.1\%$ is (all amounts in percent-the percent signs ruin the formatting)  $$\begin {array}{c   c} raw & score \\
0.00 & 1.48 \\
0.10 & 3.92 \\
0.20 & 9.98 \\
0.30 & 23.15 \\
0.40 & 45.02 \\
0.50 & 69.00\\
0.60 & 85.81\\
0.70 & 94.27\\
0.80 & 97.81\\
0.90 & 99.18\\
1.00 & 99.70 \end{array}$$
