Here is a really really simple example
Person A uses 100s to finish a job
Person B uses 200s
With YOUR equation
200/100 so B is 100% slower than A
100/200 so A is 50% faster than B
Yes, that is exactly correct. When you say "slower than A" that wording explicitly takes the time spent by A to finish the job as the point of reference. Working with percentages, that would then be 100%. Similarly, "faster than B" means the point of reference is B, setting the time spent by B as 100%. The difference is thus relative to the base number, whether that is higher or lower. Whereever you set the baseline, the comparisons follow from that.
Your equation is fundamentally flawed because in your equation, A will NEVER be 100% faster than B becasue it has to be finished with 0 second to do that, in YOUR equation.
... is that a problem? It is literally impossible for something to be infinitely fast, that's just how nature works, so ... yes? Is there some fundamental problem with the impossibility of a 100% increase in a relative percentage measuring towards zero? You can't do the task in zero time, and you can't have a 100% increase, because 100% is then the span between a theoretical zero time expenditure and the real time expenditure. This is literally the only common sense approach of comparing time expenditures trending towards zero - the only method that takes into account that zero will never be reached, and that doesn't exaggerate the difference bewteen minute real-world changes.
I mean, this is even included in your hackneyed reformulation, which tries to avoid this by reformulating the variables in question to "units of work per time" (which might be zero, but only at zero work done) rather than "time spent per one unit of work", which is what the slide here (and nearly all such benchmarks) presents.
You're arguing as if it's
better if a change between, say, 20s and 10s compared to a 200s baseline were presented as "10x faster" and "20x faster", despite the fact that this
grossly exaggerates the difference between the two. You see that, right? Presenting those two as 90% and 95% faster is a far more accurate representation of their absolute time expenditure.
Please, use your common sense.
If a person finish his job in 10s when the other guy needs 200s, he is 20x faster than the other guy, but in YOUR equation, he is just 95% faster.
Even if the first person only needs 1s to finish the job, in YOUR equation he is just 99.5% faster.
In reality he is 200x faster
But all of those are still true. Your "in reality" statements, which seem to be meant as rebuttals, are literally the same ratio.
They're saying the same thing.
And all are equally valid - but which is more useful or appropriate depends on context, of course. And the context is what you're misapplying here. The context is not a question looking for a
rate of work, but a
time till completion of work. And in terms of marketing, the application you're arguing for is one that exaggerates the actual improvements. When you're comparing two things to see how fast they can finish a task, it's the reduction in task completion time that matters, not the fact that a 100% reduction is impossible. That's just how the world works.