Defeat In Detail

It has long been a principle of military strategy that one must not divide one's force in the face of an equal or superior enemy. A divided force risks defeat in detail, in which each part of the force is engaged by the full force of the enemy in turn and easily defeated.

By the 1900s mathematicians had worked out formal models for combat, and these yielded the square law of combat effectiveness. According to this law, the combat power of a force is equal to the square of the number of the units in the force, all other factors being equal. If a force x fights to tbe death with a smaller force y, then when the smaller force is annihilated, the larger force will be left with a strength of (x²-y²)^1/2.

If equal forces are engaged and fight to the death, both are annihilated. But if the second force is divided in half, and the first force engages the two halves of the second force one at a time, then at the end of the first engagement the first force will still have 87% of its original strength. After the second engagement, the first force will still have 71% of its original strength. It will have annihilated an equal enemy with 71% of its own strength intact solely because it remained concentrated while the enemy force was divided.

This mathematical model of defeat in detail describes continuous fire of a large number of guns on each side against the other. It does not take into account differences in force quality, the possibility of surprise, the confusion of battle, and other factors that might affect the outcome. The model also breaks down when firepower takes the form of a small number of highly destructive attacks, such as air strikes or torpedo attacks. However, the general principle that one should not divide one's forces in the face of the enemy continues to hold in most situations.

References

Hughes (1986)

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