Sure — but the arithmetic mean also captures that case: if you only halve the time, it also will report that change accurately.
What we’re handling is the case where you have split outcomes — and there the arithmetic and geometric mean disagree, so we can ask which better reflects reality.
I’m not saying the geometric mean is always wrong — but it is in this case.
A case where it makes sense is what happens when your stock halves in value then doubles in value?
In general, geometric mean is appropriate where effects are compounding (eg, two price changes to the same stock) but not when we’re combining (requests are handled differently). Two benchmarks is more combining (do task A then task B), rather than compounding.
What we’re handling is the case where you have split outcomes — and there the arithmetic and geometric mean disagree, so we can ask which better reflects reality.
I’m not saying the geometric mean is always wrong — but it is in this case.
A case where it makes sense is what happens when your stock halves in value then doubles in value?
In general, geometric mean is appropriate where effects are compounding (eg, two price changes to the same stock) but not when we’re combining (requests are handled differently). Two benchmarks is more combining (do task A then task B), rather than compounding.