It would be tiresome to recount all the battles both on sea and land, in which smaller forces defeated forces numerically greater; but it may not be possible by any other means to force the fact on the attention—even sometimes of naval officers—that material vessels, guns, etc., are merely instruments, and that the work gotten out of any instrument depends not only on the instrument itself, but on the skill with which it is employed. Usually, when thinking or speaking of the power of any instrument (or means or method or organization) we mean the power of which it is capable; that is, the result which it can produce, if used with 100 per cent of skill. Possibly, we are subconsciously aware that we assume perfect skill; but whether we are or not, we have become so accustomed to the tacit acceptance of the phrase, "other things being equal," that we have come to forget that other things may not be equal at all; and that they certainly will not be on the day of trial, if we forget or undervalue those other things, while our antagonist does not.

Let us always remember, then, that the effective work gotten out of any means or instrument is the product of the maximum capability of the means or instrument and the skill with which it is used; that, for instance, if two fleets fight, which are numerically equal in material and personnel, but in which the skill of the personnel of the A fleet is twice as great as the skill of the personnel of the B fleet, the A fleet will be twice as powerful as the B fleet.

It may be objected that it would be absurd to assume the skill of the personnel in one fleet as twice as great as that of the personnel in the other fleet, but it can easily be shown that even so great a disproportion is not impossible, provided the skill in one fleet is very great. The value of superior skill naturally becomes important where the difficulties are great. 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. For instance, if a/y is .1 in one case, and .2 in another case, the probability is practically double in the second case; whereas, if a/y is 1 in one case, and 2 in another, the probability increases only 55 per cent; while if it is 2 in one case and 4 in the other, the probability of hitting increases only 12 per cent.

This means that if two antagonists engage, the more skilful should, and doubtless will, engage under difficult conditions, where y is considerable relatively to a; for instance, at long range. Suppose that he engages at such a range that he can make 10 per cent of hits—that is, make 90 per cent of misses; and that his misses relatively to the enemy's is as 90 to 95—so that the enemy makes 95 per cent of misses. This does not seem to be (in fact it is not) an extreme case: and yet A will hit B twice as often as B will hit A. In other words, the effective skill of A will be twice that of B.

This illustrates the effect of training—because all that training in handling any instrument can do is to attain as closely as possible to the maximum output of the instrument; and as the maximum output is attained only when the instrument is handled exactly as it should be handled, and as every departure is therefore an error in handling, we see that the effect of training is merely to diminish errors.

That this illustration, drawn from gunnery, is applicable in general terms to strategy seems clear, for the reason that in every strategical situation, no matter how simple or how complex, there is, and can be only one best thing to do; so that the statement of any strategic situation, if followed by a question as to what is the best thing to do, becomes a problem, to which the answer is—the best thing to do. Of course, in most strategic problems, there are so many factors almost unknown, and so many factors only imperfectly known, that we can rarely ascertain mathematically what is the best thing to do. Nevertheless, there must be a best thing to do, even if we never ascertain exactly what it is. Now in arriving at the decision as to the best thing to do, one estimates the weight of each factor and its bearing on the whole. If one estimates each factor correctly, that is, if he makes no errors in any estimate, and if he makes no error in summing up, he will make an absolutely correct decision; and any departure from correctness in decision can result from no other cause than from errors in his various estimates and in their final summation. In other words, skill in strategy is to be attained by the same process as is skill in other arts: by eliminating errors.

So, when we take the decisions of the game-board and the war problem, we must not allow ourselves to forget that there has been a tacit assumption that the numbers and the skill of the personnel have been equal on the two sides; and we must supplement our decision as to the best material to be employed by another decision as to how we shall see to it that the assumption of equality of personnel shall be realized in fact—or rather that it shall be realized in fact that our personnel shall get the maximum of effectiveness out of the material.

In designing the machine, therefore, we are confronted with the curious fact that, in general, we must design the various material parts before designing the personnel parts that are to operate them.

The most obvious characteristic of the personnel parts is that the number of personnel parts shall be sufficient to operate the material parts.

To ascertain the number of personnel parts, the only means is actual trial; though naturally, if we have previously ascertained the number of men needed to operate any kind of mechanism, say a certain kind and size of gun, we can estimate quite accurately the number needed to operate a similar gun, even if it differ somewhat from the other gun. After the gun is tried, however, we may have to change our original estimate, not only because the estimate may have been in error, but because the requirement of operating the gun may have changed. For instance, the requirements of fire-control have within very recent years compelled the addition of a considerable number of men to the complements of battleships.