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Message: <blockquote data-quote="BryonD" data-source="post: 4201339" data-attributes="member: 957">Lanchester's Square Law is a "perfect" mathematical model.  As long as the conditions apply.  Which is almost never.But it is almost always close enough to be a very useful tool.The size of the engagement does not matter.  Though the larger the engagement, the better your chances that the conditions do not apply.  What that probably means is that not everyone is engaged and your battle is actually a collection of smaller skirmishes, and each skirmish is better modeled by the Square Law than the battle itself.  Reinforcements are also not at all accounted for.  To account for them you would have to run the model forward until the first reinforcement arrived and then stop and reset the battle with new initial conditions and repeat that every time a new reinforcement arrived.  Not easy.Another point is that, being a perfect mathematical model, it assumes that every combatant is perfectly engaged continuously until the battles end.  Obviously that is never going to be true.  However, the formula is square with respect to the number of units and only linear with respect to their fighting capacity.  So if you assume that the inefficiency is fairly constant for both sides, then it doesn't matter, it just changes how long the fight will take.  If one side is better than the other at bringing its units to bear, then you must account for that tactical improvement in terms of a higher fighting capacity parameter.  Which can be hard to quantify.  The bottom line seems to be that it is virtually impossible to find real battles and cleanly model them with the Square Law, but it is easy to show that the influence of this mathematical truth is present, modified by numerous other variables.Taking it back to D&D, it actually works better for D&D than for reality.  That is because in D&D you can quantify fighting capacity.  You can state attack bonuses, and average damage, and you can state precise ACs and HP totals.  So the fighting capacity is pretty well defined in a quantitative manner.  And the expectation that every unit is fully and continuously engaged is “more” true in a typical D&D battle than a real battle.  When you have reinforcements it is still a problem, but that is less common in D&D.Its weaknesses in D&D include initiative order, healing, and odd-ball magic stuff.  If a wizard gets initiative and tosses out a fireball, then the presumption of everyone engaged throughout is out the window.  For the goblins that get blasted their time of engagement is zero.  Healing is pretty much like having reinforcements, though not as bad.  That is because the healer is giving up his attacks to restore someone else.  So if you have one fighter and one cleric healing him, it kinda fits as if you have two fighters.  But not as cleanly.  It certainly isn’t what the math assumes.  But it isn’t going to send you way off into huge error either.  And the magic stuff should be obvious.  If a Finger of Death save is failed, then the fighting capacity of a spellcaster can suddenly skyrocket.  Dimension Door is going to wreck havoc on the engagement assumptions.  You can come up with a list of exceptions here.  But again, it doesn’t do as much harm to the final conclusion as you may think.  It just makes a blur around the edges.  You can not tell exactly how things will end, but who will win will still be the same.  These errors are probably going to be less significant than the time the fighter suddenly can’t roll over a 6.</blockquote>

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