As far as I am aware, a normal distribution over a non-linear scale is not possible because by its very definition, a normal distribution is an absolutely continuous probability distribution. Meaning every point between the minimum and maximum values will be included in the graph.

To put it simply, since the bell curve is drawn without lifting the pencil from the paper, the range of values on the x-axis needs to be continuous.


The levels have nothing to do with the bell curve. Whether you want to say each level is 5 units above the other, or 5% above the previous one, the point remains that the mean value would be equal to half the maximum value.

Further, if you want each point in the X-axis to be a percentage value above the one before, then you have to somehow prove to me that the values in between cannot be true. Meaning if level 1 is strength 10, and level 2 is 20% above, meaning strength 12, then you need to show that no one can be of strength 11, which is ridiculous.

Further, even if this were true, the graph would not be a bell curve because between 10 and 12, no value in the Y-axis will correspond to the values on the X-axis. So you'd have to lift your pencil, making it not a bell curve.