General Vahidi and the Overkill Fallacy
Under the heading of Being Unintentionally Funny While Trying To Be Terrifying, reported from YNet at http://www.ynetnews.com/articles/0,7340,L-4153840,00.html
Iranian Defense Minister General Ahmad Vahidi said Israel would be attacked with 150,000 missiles if it launches any military action against the Islamic Republic, the Iran Independent News Service reported Sunday.
Needless to say, Iran does not HAVE 150 thousand missiles with the range to hit Israel. I'm guessing that Ahmad Vahidi came up with this figure by adding up every single weapon which could be called a "missile," down to the level of anti-tank guided missiles, perhaps even hand-held rocket launchers, which might theoretically be brought to bear against any portion of Israeli territory, even depopulated frontier zones. Assuming that he didn't just pull it out of his ass.
This is, however, a good illustration of the "overkill" fallacy, which is the assumption that having X number of weapons, each of which would be expected to kill Y people or do Z amount of damage under ideal circumstances, means that one can expect to kill XY people or do XZ damage when the weapons are used under combat conditions. By this logic, for instance, any small country has the power to exterminate the whole human race, since even a small country will probably possess 10 billion or more rounds of firearms ammunition, each of which could kill 1 person each if fired directly into the base of his brain. The flaw with this reasoning is easy to see when we talk of bullets to the brain (how do you get each human to stand meekly and let himself be shot in the head?) but often escapes notice when dealing with more formidable military weapons -- with whose usage characteristics nonspecialists are less likely to be familiar.
In general, what is being ignored is the difference between firing a weapon at an exposed, unresisting target and firing that very same weapon at a target which has been hidden, hardened, or protected by active defenses, and under conditions where weapons friendly to the target may be shooting at one's own weapons, trying to take them out before they can engage. There are other aspects of combat (maintenance, organization, etc.) which prevent weapons from performing according to their full theoretical potential, but this will suffice for the present.
Another big part of the overkill fallacy is assuming that weapons area effects, which are generally spherical (or conical for directed-blast weapons) will scale up arithmetically in terms of expected kills or other damage. This ignores the reality that the size and geometry of the explosions will probably not perfectly match the size and geometry of the targets.
For instance, suppose that a missile with a one-ton HE warhead will, if it hits the crowds in downtown of a city at rush hour, is expected to kill 1 thousand people and seriously wound 10 thousand more. Suppose that I am facing a hostile nation whose population is 10 million. Ah, I say with the overkill fallacy running in my mind, if I launch 1000 such missiles I will render every single person in that country a casualty -- with 10 thousand such missiles I could kill every one of them. This of course ignores the reality that most of the population of this country won't be conveniently out in the open at rush-hour densities clustered around my target: indeed, they might respond to my weapons buildup with warning and shelter systems and even deliberate dispersal, such that my missiles will be far less effective.
A subtler version of this comes with scaling yield to effect. Suppose that I instead built missiles with two-ton HE warheads. Might I expect then to kill 2 thousand people and seriously wound 20 thousand per shot? No, because the blast propagates spherically and hence the square-cube law (modified by factors for ground geometry and atmospheric conditions) governs its force. This mistake is often made as applied to nuclear weapons, when disarmament advocates try to rate bombs in "Hiroshimas," with the clear implication that a bomb with ten "Hirsohimas" of yield would kill and wound ten times as many people as were casualties in Hiroshima. This is of course untrue, because most of the extra force of the blast will propogate in directions which do not contain people.
Finally, there is the issue of true overkill, which has to do with available targets in the weapons effect area. A simple World War One water-cooled .30-caliber machine-gun is a fearsome engine of destruction, assuming that it can sweep a target-rich environment. But if the enemy attacks in such a fashion that only a few men are exposed to its fire at any given time, those few men are the maximum that it can kill or wound no matter how many shots the machine-gun can fire.
Suppose that there is a target area containing 10 soldiers and I blindly throw a hand grenade which is expected to kill or wound 4 soldiers per explosion on the first explosion. It does so. As I keep tossing hand grenades, can I expect to kill or wound 4 soldiers on the second toss, then the remaining 2 on the third?
No. First of all, we assumed 10 targets in the target area, which ceases to be the case after the first toss downs 4 soldiers. The second toss is into a target area containing 6 soldiers, the third into one containing 6 minus the number the second toss took out, and so forth. The hand grenades are much less lethal than one would imagine, and this assumes utterly passive soldiers who do nothing to take cover or return fire!
These sorts of considerations are why complex simulation is the best way to think about war and weapons effectiveness. It can't be reduced to a single tractable equation: you need to do step-by-step simulation in order to get meaningful results when attempting to predict the likely outcome of a military engagement.
So thank you, General Vahidi, for making your country look stupid before the world. Thank you, for making me calmer about the likely outcome of a war against Iran (if that was an example of Iranian general-officer-grade military thinking, in any encounter between Iranian forces led by officers who think like Vahidi and American forces led by wargame-savvy commanders, the Iranians won't stand a chance). And thank you, most of all, for offering me the opportunity to discuss one of my favorite topics.
Iranian Defense Minister General Ahmad Vahidi said Israel would be attacked with 150,000 missiles if it launches any military action against the Islamic Republic, the Iran Independent News Service reported Sunday.
Needless to say, Iran does not HAVE 150 thousand missiles with the range to hit Israel. I'm guessing that Ahmad Vahidi came up with this figure by adding up every single weapon which could be called a "missile," down to the level of anti-tank guided missiles, perhaps even hand-held rocket launchers, which might theoretically be brought to bear against any portion of Israeli territory, even depopulated frontier zones. Assuming that he didn't just pull it out of his ass.
This is, however, a good illustration of the "overkill" fallacy, which is the assumption that having X number of weapons, each of which would be expected to kill Y people or do Z amount of damage under ideal circumstances, means that one can expect to kill XY people or do XZ damage when the weapons are used under combat conditions. By this logic, for instance, any small country has the power to exterminate the whole human race, since even a small country will probably possess 10 billion or more rounds of firearms ammunition, each of which could kill 1 person each if fired directly into the base of his brain. The flaw with this reasoning is easy to see when we talk of bullets to the brain (how do you get each human to stand meekly and let himself be shot in the head?) but often escapes notice when dealing with more formidable military weapons -- with whose usage characteristics nonspecialists are less likely to be familiar.
In general, what is being ignored is the difference between firing a weapon at an exposed, unresisting target and firing that very same weapon at a target which has been hidden, hardened, or protected by active defenses, and under conditions where weapons friendly to the target may be shooting at one's own weapons, trying to take them out before they can engage. There are other aspects of combat (maintenance, organization, etc.) which prevent weapons from performing according to their full theoretical potential, but this will suffice for the present.
Another big part of the overkill fallacy is assuming that weapons area effects, which are generally spherical (or conical for directed-blast weapons) will scale up arithmetically in terms of expected kills or other damage. This ignores the reality that the size and geometry of the explosions will probably not perfectly match the size and geometry of the targets.
For instance, suppose that a missile with a one-ton HE warhead will, if it hits the crowds in downtown of a city at rush hour, is expected to kill 1 thousand people and seriously wound 10 thousand more. Suppose that I am facing a hostile nation whose population is 10 million. Ah, I say with the overkill fallacy running in my mind, if I launch 1000 such missiles I will render every single person in that country a casualty -- with 10 thousand such missiles I could kill every one of them. This of course ignores the reality that most of the population of this country won't be conveniently out in the open at rush-hour densities clustered around my target: indeed, they might respond to my weapons buildup with warning and shelter systems and even deliberate dispersal, such that my missiles will be far less effective.
A subtler version of this comes with scaling yield to effect. Suppose that I instead built missiles with two-ton HE warheads. Might I expect then to kill 2 thousand people and seriously wound 20 thousand per shot? No, because the blast propagates spherically and hence the square-cube law (modified by factors for ground geometry and atmospheric conditions) governs its force. This mistake is often made as applied to nuclear weapons, when disarmament advocates try to rate bombs in "Hiroshimas," with the clear implication that a bomb with ten "Hirsohimas" of yield would kill and wound ten times as many people as were casualties in Hiroshima. This is of course untrue, because most of the extra force of the blast will propogate in directions which do not contain people.
Finally, there is the issue of true overkill, which has to do with available targets in the weapons effect area. A simple World War One water-cooled .30-caliber machine-gun is a fearsome engine of destruction, assuming that it can sweep a target-rich environment. But if the enemy attacks in such a fashion that only a few men are exposed to its fire at any given time, those few men are the maximum that it can kill or wound no matter how many shots the machine-gun can fire.
Suppose that there is a target area containing 10 soldiers and I blindly throw a hand grenade which is expected to kill or wound 4 soldiers per explosion on the first explosion. It does so. As I keep tossing hand grenades, can I expect to kill or wound 4 soldiers on the second toss, then the remaining 2 on the third?
No. First of all, we assumed 10 targets in the target area, which ceases to be the case after the first toss downs 4 soldiers. The second toss is into a target area containing 6 soldiers, the third into one containing 6 minus the number the second toss took out, and so forth. The hand grenades are much less lethal than one would imagine, and this assumes utterly passive soldiers who do nothing to take cover or return fire!
These sorts of considerations are why complex simulation is the best way to think about war and weapons effectiveness. It can't be reduced to a single tractable equation: you need to do step-by-step simulation in order to get meaningful results when attempting to predict the likely outcome of a military engagement.
So thank you, General Vahidi, for making your country look stupid before the world. Thank you, for making me calmer about the likely outcome of a war against Iran (if that was an example of Iranian general-officer-grade military thinking, in any encounter between Iranian forces led by officers who think like Vahidi and American forces led by wargame-savvy commanders, the Iranians won't stand a chance). And thank you, most of all, for offering me the opportunity to discuss one of my favorite topics.