Sorry to go OFF TOPIC.
Instead of going over this again, I will now just keep referring to this post. Now logged in notepad.
Let me simplify and hopefully I'm done with this
1) User takes measurement at 400 lumens at closest throw...
====Option # A) We use a log function to correct that, but by doing so we ignore his other measurements (because they disagree with the LOG function)...
====Option # B) We use multiple numbers from multiple sources, a percentile averaged measurement that is based upon averaging the "middle" of multiple measurements from MULTIPLE reviewers, and throws out measurements that deviate too far.
How can a log function that STARTS out with 1 of his 3 measurements be more accurate than the average between the three measurements (or rather the percentile average of 3 measurements between 5 people), it cannot, it's impossible (think carefully now). The reason being is because if his last 2 measurements at mid and farthest throw are off,
then his first measurement has more odds of being off then the average between three, therefore the log function has worse odds than averaging the three. Since we NEVER start with a perfect number, and we are ALWAYS trying to average a person's measurements, then we always hit this same problem, a log function can only work if the first measurement is more accurate than an average of multiple. With three measurements at three points we are reducing measurement error, with 1 measurement we are increasing it (your example).
Now why does Option B work better, yes Option B might show in the calculator itself a different depiction of LUMENS change as you move the slider from the baseline, but that is because you are seeing averages of measurements. I admit this concept is somewhat complex, but I have some background in statistics, so now let me re-explain it like this...
We do not BASE the equation on the accuracy of the changing of the lumens between when he moves the slider, we base it on universal averages, because what we care about is the accuracy of the end-result between averaged measurements at a GIVEN THROW, which is based on all 3 points being averaged, not just based on a small sample of data. Even if I average multiple reviewers at a single point, the concept is the same, as the whole it can be off more than the log can correct it. The curve is not based on a LOG because it is based on an average of multiple reviewers at each point, simple.
Your example uses Garbage In, Correct Results out, when it is Garbage In - Garbage Out. You have to fix the garbage, modifying garbage does not = accuracy. The way to fix garbage is by averaging, ok sorry I'm done...