A very simple illustration is in firing a gun; for even if the skill of one marksman be greater than that of another, it will be unimportant, if the target is so large and so close that even the inferior marksman can hit it at each shot.

The probability of hitting a target--so far as overs and shorts are concerned (or deviations to the left and right)--varies with the fraction _a/y_, where _a_ is the half height (or width) of the target, and _y_ is the mean error.

The greater the size of the target, and the less the mean error, the greater the probability of hitting.

The size of the two targets being fixed, therefore, the smaller the mean error the greater the probability of hitting.

The probability of hitting, however (as can be seen by the formula), does not increase greatly with the decrease of error, except in cases where _a/y_ is small, where the mean error is large relatively to the width or height of the target.