Why can't CRI just be a scale from 0-100 indicating how much color there is (0 being monochromatic and 100 being continuous). I hear LPS lamps have a CRI of ~-40. What does that even mean? I know 100 is based off of sunlight, but what does 0 mean?

Color rendering involves the light source spectrum, reflection spectrum of objects under the light, and our vision

Our vision includes the eye, cone cells of 3 types, brain decoding this information and cross referencing it to colors we expect to see and so on. At this point any precise (or as some here used to call it "objective", "scientific" etc) quantification goes out of the window

CRI aims to provide a scale which would make sense, to effects which are subjective, dont have any way of being quantified in numbers, and open to inconsistent interpretation

The way how i understand the intention, CRI (the number) aims to predict how many different colors out of a sample of 100 (specific ones) you can tell apart under the light. Attention : Not see in true color same as under daylight, just tell apart from each other. In this case, values which would make sense are between 1 (they all look the same) to 100 (all look different)

The way how CRI is measured in practice does not actually involve any color sample cards. A few sample values from the light spectrum are measured and plugged into a formula, which puts out a number which is claimed to be the CRI

This formula is entirely artificial. It was designed with the intention to provide a number (between 1 and 100) which would represent the CRI concept as closely as possible, then once a formula which gives consistently fair enough results was figured out, it was standardized

The formula is optimized to have its best "precision" in the range in which comparing CRI is of the most interest, and small differences will rise the most scrutiny. Which is generally the sub-100 range. At lower CRI levels it is less precise. At the fringe ends (LPS) it just breaks. The -40 in itself is meaningless, it is just an artifact that happens when several of the input variables happen to be 0's

The same happens with e.g. polynomial approximations of functions, trendlines added to raw data (be it photometric, economical, or whatever) etc. They have a range in which they are the most precise. And they have the fringe ends where they will show some value (because if variables are blindly plugged in and +-*/ performed, something will come out in any case), but it is not expected to represent anything correctly

Ahh I see, so LPS is pretty much just zero, or performs identically to one that would be zero?

Yep

@Ash: Isn't the CRI of SOX lamps Ra-44?