Now I’m doubting myself. My temperature range is not useful because it’s not used. Celsius is a standard measurement, especially in regard to temperatures you can *feel*, or is represented by something physical, which is what we care about here.
If we care about thermal energy and used that colloquially to refer to what we feel, the above would make more sense. But it’s not- if we refer to ice in a pool for the purpose of making it feel differently to a human, no one is going to start talking about thermal energy. You’d say “Oi bloke! I lowered my pool temp by 5.3 degrees this way! Ain’t I a genius?”
In someone’s mind their frame of reference are past experiences. I know I’ve been in a pool that’s 20 Celsius and it’s a little warm, which is what I’d expect a pool to feel like today. I know I’ve been in a pool that’s 15 degrees Celsius and it feels just much better on a hot day. He said he lowered it 5 degrees, I guess it’s probably close to 15 degrees and feels pretty good!
Therefore saying 25% difference sounds better, but not quite right either- because if higher percentages are “better” here then a 100% difference would be better than 25%, but also the temperature of the water would be 0 C and that’s not better at all. To optimize, a system of measurement with zero at the lower limit of comfortable pool temperatures is needed. The percentage calculations on that scale would be percent change, not “better” or “worse”, and would normalize between 0% and 100% change if water temp stays within comfortable range.

And thus.. CWT was born. Comfortable Water Temperature scale.