Screen protectors are supposed to protect your devices from nicks and scratches, as well as the stress of impacts which might otherwise lead to cracks or shattering. The fundamental principle behind their operation is that screen-protector glass or plastic "gives easier", in a sense, than the glass on, say, a phone or smartwatch, acting analogously to the "crumple zone" in a car.
It's well-known how screen protectors work (and, indeed, there are several such questions on SE), and its certainly arguable that they must, in fact, provide some protection, but how effective are they, actually?
We reduce the problem to the following:
Consider a phone and smartwatch, with "standard" chemically-strengthened glass or equivalent (Gorilla Glass, e.g.), at something like 0.1-0.3mm thick (I wasn't able to find much data on this, surprisingly)
Obviously, screen protectors aid in preventing nicks and scratches (anything between the screen and the outside world is bound to). So, instead, we focus on the protection they offer from cracking/shattering. Most screen protectors are 0.1-0.3mm thick, and are made of tempered glass or plastic.
I've tried running the numbers, however this involves some science I'm entirely unfamiliar with. I can think of a few complications, as well. Protection certainly depends upon the angle at which impact occurs. Similarly, many phones and smartwatches have curved edges (we can assume that the screen protector covers these), which may be weak-points. Also, phones require cut-outs for speakers, microphones, etc.
Note: originally posted on Physics SE. I received some answers regarding how screen protectors work, but bothing on their effectiveness. For those questions, I was directed here.