So using an actual empirical measurement is not useful, ....
It would not be useful for me.
I know that I can shoot controlled shots more rapidly with a gun with less recoil.
I do not know
how much more rapidly, but measuring split times would only tell me that
for the specific conditions in the experiment.
In the real world, one's rate of fire will vary, depending upon the distance to the attacker as he closes, and as one tries to balance speed and precision to achieve combat accuracy.
The split times measured somewhere with a timer at a given distance when one fires at the signal will have only academic value when it comes to self defense.
...but I am to trust your word that 9mm is faster on follow ups based on your careful observations?
You have much more than my word to go on.
I simply described how my observations taught me something.
Some individuals will be better served by 9mm as .45 recoil is not easy for them to control and they won't take the time or effort to become proficient. For others, proficient shooting comes much more naturally or they are enthused enough to devote the time to become quite proficient.
Rob Pincus addressed that very well: "Physics dictates that the 9mm is going to be a more manageable round (lower recoil) than the .40 S&W out of any particular firearm. So,
no matter how much you train and how much you practice, everyone should be able to shoot a string of Combat Accurate 9mm rounds faster than they can fire a string of .40." (Emphasis added).
A proficient shooter will notice a strikingly small difference in time between follow up shots between 9mm and 45, should they feel it isnt a waste of time to measure it.
Or should they measure it--it doesn't matter.
John has shown us with a few simple calculations how the "strikingly small" difference can make a difference.
Rob addressed that, too: " Of course, if you consider a 4×8 sheet of plywood your “combat accurate” area, you’re going to have to go to a relatively long string of fire to be able to measure a difference in time, but if you stick with a probable target size (high center chest) at a plausible distance (10-15’), it shouldn’t be hard to see a difference at a reasonable number of rounds (3-6)."