Say I have this glasses prescription:
OD -2.00 SPH +2.00 add 0.5 p.d. BD
OS -1.00 -0.50 x 180 +2.00 add 0.5 p.d. BU
And this prescription (values are fake):
OD -1.70 SPH +2.00 add 0.5 p.d. BD
OS -1.00 -0.50 x 180 +2.00 add 0.5 p.d. BU
If the len power in the first prescription is a bit too strong and the len power in the second prescription is a bit too weak, could a third description be deduced just based on metrics?
You should not try to self diagnose an eye prescription.
That being said, I'm going to partly disagree with the previous answer based on some technicalities. First, the process you describe is actually close to what real eye doctors use. They use a phoropter (machine with all the lenses) to test one prescription then test another. They keep going until they find a point where one is too strong, and the other too blurry. Then they narrow the increments and check in between. This is an iterative process to get down to the exact prescription - so you definitely need more than 2 data points unless you happen to start with the right 2 points.
Now, phoropter's typically measure in 0.25 diopter increments - so glasses prescriptions would be better represented by a finite subset of natural numbers than the real numbers - they go up and down in finitely sized increments, and there are a finite number of them.
So, if your two test prescriptions happen to be only 2 increments apart, and you are sure that one is too strong and one is too week, then yes, if you average the two you should get the correct prescription.
Note: There are some additional considerations, such as astigmatism, that may need to be accounted for - so you can't even use two pairs of glasses that are close to what you need IF they don't have the correct astigmatism factor or eye spacing. So again, you should always get a proper prescription from an eye-doctor.
By analogy consider US shoe sizes - if I give you a size 9 and it's slightly to small, and then I give you a size 10, and it's slightly to big, then you could gnerally conclude you are a size 9.5 (the average of the two) because shoe sizes go in .5 increments. There is no 9.3, or 9.8, etc. to worry about. However, that wouldn't work if you had abnormally wide feet (such as 9.5EE), or if I gave you too test pairs such as 7 and 10, because you could be anywhere between the two - not necessarily exactly the average.
I have a magic number X. Take a guess what it could be?
Is it 15?
No, 15 is too high.
Is it 12?
No, 12 is too low.
This leaves you with the mathematical average of 13.5, but that doesn’t help you because you don’t know wo how much too high and how much too low your other guesses were. What if we allow real numbers, and not only natural numbers? Then there would be an infinite number of a possible magic number (although you could get quite close with a few iterations).
The same principle applies to your prescription as well. You don’t know how much too strong and how much too low they were. And furthermore, eyes change. Maybe you’re cylinder has changed completely, or you got astigmatism?
Bottom line: The answer is no, you can’t get a meaningful result, but you can try to average-out everything. You might get closer and you might be off worse than with either prescription. Visit an eye-doctor answer let them measure.
