I think between 2x and 20x, depending on things like whether you're wearing a long-sleeved shirt, what other stuff you have in your pocket, etc. I can't see how it could ever be 100x and even the 20x end of the range I gave is probably too high.

I suspect you're greatly underestimating how quickly you can check the time with a watch on your wrist. Even if literally no thought were required, human reflexes are on the order of 200ms latency; 100x more than that would be 20 seconds. In reality, there's a conscious element and that always slows things way down. I don't think the actual effective time taken to check the time by any means at all is ever less than about a second, even if it feels faster. Maaaybe half a second if you truly don't need to move anything but your eyeballs.

On the other hand, I find that it usually takes me 3-4s to get my phone out of my pocket and check the time on it.