The easy answer to your question is that the more you stop the lens down, the deeper the depth of field and your sharpness improves. At a certain point it will start going the other way, there will be a sweet spot that you will get the best IQ out of the lens. At F/11 you may start seeing it decline.

But I am not sure that was the answer you were looking for, were you looking for a relationship formula that would tell you what the optimum F value would be on a given lens? It would be interesting to see if such a calculator or formula existed. Maybe it would be something like (All F values < F/8). Then maybe not.