" - okay, I think there is something there, I just need to nail it down. More precise claims point at smaller bits of reality. It takes more twos to point to smaller bits of reality. A theory that makes a more precise prediction is much more valuable, if it's right, it hit a smaller target. A theory that makes a more precise prediction is more easily wrong, which is just another way of saying what I just said - it couldn't be more valuable if it was right unless it was more easily wrong. You have to have a much better understanding of reality to make more precise predictions and have them still be correct.
And your claim is only as precise as - if my measurement can't tell the difference between two claims, then I don't get any of the benefits of having made one rather than the other, a claim is only usefully precise if it's precise about what you're going to see, so, what your measurement is."