If there is a fixed percent uncertainty in LASIK reshaping of the cornea, why would you expect those people with the greatest correction to have a poorer chance of normal distant vision after the procedure?

LASIK eye surgery is the most well-known and widely used laser refractive surgery for vision correction. LASIK (laser-assisted in situ keratomileuses) is a procedure that can be used instead of glasses or contact lenses.

A unique form of cutting laser is used during LASIK surgery to accurately alter the shape of the dome-shaped transparent tissue at the front of your eye (cornea) to enhance vision.

Since there is a fixed uncertainty in obtaining the required change in the refractive power of the eye; this implies that when a higher change is required in the refractive power of the eye, a higher deviation from the required change is expected.

For example, if the uncertainty of the LASIK reshaping of the cornea, is 5% , and if the required increase in the refractive power of the eye is for example 9 dioptre, then we expect that the final change in the refractive power to have any values which are defined by the following uncertainty,

$9.00\pm \left(\frac{5.00\times 9.00}{100}\right)$9

This means that the final change can have any values that range from 8.55 dioptre to 9.45 dioptre. Or in another word, a deviation as large as $\pm 0.45$dioptre is expected from the required value.

Where, if the required change in the refractive power of the eye is 1 dioptre, then the final change in the refractive power of the eye after LASIK reshaping can be,

$1.00\pm \left(\frac{5.00\times 1.00}{100}\right)$

This means, that the final value for the refractive change can range from 0.95 dioptre to 1.05 dioptre, or only a deviation as big as $\pm 0.05$dioptre is expected.

Now, this doesn't mean that a deviation of $\pm 0.45$dioptre is expected every time, but instead, it’s a statistical parameter, which tells us how far can things deviate from the expected value, for example, a patient doing a corneal reshaping using LASIK, where he requires a change of 9.00 dioptre in his refractive power, might have a final chance in his eyes refractive power of 9.05 dioptre, another one might have a change of 9.17 , another has a change of 9.33 , the worst-case scenario is that it can deviates as much as 0.45 dioptre.

In general, since the uncertainty of the LASIK corneal reshaping is fixed, then it is known that the higher the required change in the eye's refractive power, then the higher the deviation of the final change in the refractive power of the patient's eyes, and hence would have a less chance of having a normal vision after LASIK.

Therefore, the higher value of the eye’s refractive power and also the deviation of change results in the patient not having normal vision after LASIK.