Such anger! I would suggest you crunch the numbers yourself, as your conception of how powers can be moved across a quotient (and how that affects rank order) and the concept of a dimension such as liters (or cubic mm or any unit of volume) being weighed out of proportion "because its cubic" are shaky. In your second edit using volume directly is fine, but should not be miscontrued as "already having a cubic power". The individual dimension (L, W, H) are cubed, but the resulting volume is used. Ahh, I see someone has crunched the numbers for you to show that rank order is easily affected by different powers being used! So not equivalent eitherI think you should read more carefully. I didn't say the formulas are equal. I said, and I quote "rankings are equivalent". That means both formulas would produce the same "ranking" of systems.
I'm not sure what you think is incorrect in what I wrote... I said to use directly Volume (measured in liters, as you know I hope?) and not any power of it. [Edit: My second edit in my previous post was not in for some reason. I fixed that now. There I was offering to use Volume directly]
And I hope you understand what a liter is?
1 Liter = 1000000 mm^3
So, yeah, liter is not a distance measure, it is a measure of volume.
Thank you for illustrating your formulas! The OP of the thread may consider the new formulas in a new round or something, as it might be too complicated to change everything now.Yes. I was wrong by ignoring the power on volume thinking it didn't matter but it does have a very major impact.
Geometric mean for 2 terms = (a * b)^0.5
Current: CPU*GPU / Volume ^0.5
Correct: Geometric Mean / Volume
Incorrect: Geometric Mean / Volume ^ 1.5
Simple: CPU * GPU / Volume ^ 2
Ranking wise they are nowhere equivalent. I only looked at the top 5 but there's a very large difference in how systems are ranked based on the equation used. I was wrong to ignore the power on volume. Like you said, we're measuring performance per liter and putting a power other than 1 on volume makes a drastic difference. My initial suggestion was wrong by ignoring the power on volume. The correct method is to use the geometric over volume with a power of one. Or as you said, the simpler and equivalent equation would be cpu*gpu over volume with a power of 2. The equation in this format may seem like we're giving volume more weight but mathematically speaking.. what's actually happening is we're getting the geometric mean of the cpu and gpu benchmarks.
In conclusion, what we want to measure is performance per liter. If we want to respect that, we have to use either the equations (Geometric Mean/Volume) or (CPU*GPU/Volume^2)
Edit: I think it best to avoid derailing the topic further; this is kind of off topic.