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Message: <blockquote data-quote="mmadsen" data-source="post: 1551583" data-attributes="member: 1645">Actually, the law I cited is know as Lanchester's Square Law; there's also a Lanchester's Linear Law.Lanchester's Square Law models modern aimed-fire combat -- not modern barrage fire or ancient hand-to-hand combat -- where the rate of enemy attrition is proportional to the number of friendly combatants, and the rate of friendly attrition is proportional to the number of enemy combatants; e.g. each combatant has a 10% chance of killing an enemy per round of combat.If a force of 100 combatants faces another force of 100 combatants, and each combatant disables 0.1 enemies per turn, then each force will have 100 combatants, then 90, then 81, and so on, until both have 0 (more or less).  If force A has 200 combatants, and force B has 100, then the losses aren't symmetrical: 200 and 100, then 190 and 80, then 182 and 61, then 176 and 43, then 172 and 25, then 169 and 8, then 168 and 0.A naive linear model would have predicted that 200 vs. 100 would have ended up 100 vs. 0, not 168 vs. 0.  The smaller force loses offensive capabilities faster than the larger force, and this spirals dramatically.Again, this is only for combat where the rate of attrition is proportional to the number of attackers.  Obviously, in melee combat, it's not always the case that every attacker can target a defender.  If Horatio holds the bridge, he fights a series of one-on-one fights.  This follows Lanchester's Linear Law -- 200 vs. 100 does turn into 100 vs. 0 if the battle is just a series of one-on-one combats.In barrage combat, the rate of attrition isn't proportional just to the number of attackers but to the number of defenders too.  If you cram enough defenders into an area, one fireball can kill all of them.</blockquote>

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