How to assess and quantify system improvement and changes?

In one of the currently popular threads, a number of members (all of whom I respect) have made significant claims regarding system improvement.

For example: A recent post mentions "a double or triple improvement in my system." A conversation a few days ago with two audio buddies had them quantifying a DAC change as a 10% improvement by one and 30% by another.

This, by virtue of our pursuit, occurs throughout our discussions in the various threads.

Starting this thread to see if we can mine the collective and come up with guidelines and outcomes that are reproducible, relevant and reliable for comparisons and discussions between audiophiles.

Thanks!