-- even a perfect torque spec with all new parts has ± 30% load variation (95% confidence or two sigma) under lab conditions.
This is something I've long since assumed and wondered the real world implications.
Everything compounds to add more variation. The bolts themselves won't be 100% identical, there will be some metallurgical differences, even if they are 99.99% identical, they aren't 100%. The shape of the bolts won't be 100% correct, they might be 99.9% the same.
A single particle of grit might be on the bolt face. A single drop of oil might get on the threads.
The tool itself is only 2% accurate at best. Where do you grip your hand on the tool, is it exactly dead center? Or are you off by 1/4"?
If the torque wrench is 15" OAL then 1/4" variation in the grip is 0.25/15 = another 2% variation in torque.
Even if you grip exactly dead center of the handle, are your forearm muscles acting equally across the width of your grip or are they asymmetrically acting more towards the thumb?
So if the fastener is supposed to be 20 foot pounds, at what point is too high that you'll strip it? 25 foot pounds? 30 foot pounds?
If it's supposed to be 20 pounds at what point is too low that it won't hold? 15 foot pounds? 10?
I assume there's a distribution curve where anything within a certain range, perhaps 16 to 24 foot pounds is acceptable. Though what makes it interesting is there's a binary outcome. Either you over torque it and strip the bolt, or you over torque it and do not strip the bolt. So then you add in statistical analysis and say at 24 foot pounds there's a 95% chance you dont strip the bolt. At 30 foot pounds there's a 50% chance you strip the bolt. At 35 foot pounds there's an 80% chance you strip the bolt.
Undertorqueing seems to have more variability. In the case of a water pump, if you under torque by a lot, it might immediately leak. If it you under torque by a little, it might have a very very slow leak that is inperceivable. Except over a long period of time when you measure coolant levels and it's low.
It's also possible undertorquing is fine, until it isn't. That the fastener works its way off due to vibrations over time. But over what time? Maybe 15 foot pounds on a 20 foot pound fastener is fine for the first 1,000 miles of driving, or even 10,000 miles, but will start to work itself off.
My point to all of this is that the 30% variation in acceptability seems reasonable and about what I would have estimated as the acceptable range. That doesnt mean it's fine to not use a torque wrench, because there's a lot of factors outside of the torque wrench that impact the tightness of the fastener that are alot harder to control for. So control for the ones you can control.