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The Quadratic Problem—Speculations on 4e
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<blockquote data-quote="Wulf Ratbane" data-source="post: 3793938" data-attributes="member: 94"><p>Although I do tend to agree with you that we <em>can</em> drill down and try to define what makes up <em>quality</em>, for the purposes of applying Lanchester's above, I did not do so.</p><p></p><p>But whether we use your assumptions (which admittedly, farther upthread, are also my assumptions), or use the more abstract model (that I am using directly above), we can clearly agree that a brute is 4x the quality of a mook. </p><p></p><p></p><p></p><p>It strikes me that this might create a problem. Lanchester's assumes that the effectiveness of a unit is based on its kill rate. Dealing only 1 hp of damage per round, you have given your creatures a fractional kill rate.</p><p></p><p>Alternately, we can change the base time unit to mean "As much time as it takes to kill one opposing creature."</p><p></p><p>Again, in either case, the brute has 4x the quality of the mook.</p><p></p><p></p><p></p><p>(Just to make sure we are on the same page, the brutes kill him in 2.5 rounds, and receive 2.5 damage in return, which is 1/64 of their 160 hit points.)</p><p></p><p>I believe we're looking right at Lanchester's square model there. (Although, again, I think you're dangerously substituting "hit points" for "units" here. DPS <> kill rate.)</p><p></p><p>Lanchester's square model is the unit's quality, or effectiveness, times the square of their numbers.</p><p></p><p>The mook has a quality of 1. Now please note, this number "1" is not drawn from their DPS-- I am not using 1 because they do 1 damage/round. Their quality is 1 because they are the baseline. In comparison, the brute has a quality of 4.</p><p></p><p>So by Lanchester's, mooks perform at a rate = (1)(8^2), and brutes perform at a rate (4)(4^2). In both cases, 64.</p><p></p><p></p><p></p><p>Two brutes and four mooks have 120 hit points-- 40+40+(10x4). </p><p></p><p>This puts the rate (using your method) at 1/72, which is confirmed by Lanchester's square law that I performed above.</p><p></p><p>I just eyeballed the figures and deduced that average quality was the only way for the equation to work out-- I wasn't certain when I did it that it was the proper way to calculate mixed groups. However, as it turns out, the paper I linked above confirms this (3.3 Mixed Forces, page 4).</p><p></p><p>EDIT: Just a placeholder edit-- remind me to revisit "Drilling Down on Quality."</p><p>EDIT2: Lancaster? Fixed. I blame my buddy Lasater who's been emailing me all day.</p></blockquote><p></p>
[QUOTE="Wulf Ratbane, post: 3793938, member: 94"] Although I do tend to agree with you that we [i]can[/i] drill down and try to define what makes up [i]quality[/i], for the purposes of applying Lanchester's above, I did not do so. But whether we use your assumptions (which admittedly, farther upthread, are also my assumptions), or use the more abstract model (that I am using directly above), we can clearly agree that a brute is 4x the quality of a mook. It strikes me that this might create a problem. Lanchester's assumes that the effectiveness of a unit is based on its kill rate. Dealing only 1 hp of damage per round, you have given your creatures a fractional kill rate. Alternately, we can change the base time unit to mean "As much time as it takes to kill one opposing creature." Again, in either case, the brute has 4x the quality of the mook. (Just to make sure we are on the same page, the brutes kill him in 2.5 rounds, and receive 2.5 damage in return, which is 1/64 of their 160 hit points.) I believe we're looking right at Lanchester's square model there. (Although, again, I think you're dangerously substituting "hit points" for "units" here. DPS <> kill rate.) Lanchester's square model is the unit's quality, or effectiveness, times the square of their numbers. The mook has a quality of 1. Now please note, this number "1" is not drawn from their DPS-- I am not using 1 because they do 1 damage/round. Their quality is 1 because they are the baseline. In comparison, the brute has a quality of 4. So by Lanchester's, mooks perform at a rate = (1)(8^2), and brutes perform at a rate (4)(4^2). In both cases, 64. Two brutes and four mooks have 120 hit points-- 40+40+(10x4). This puts the rate (using your method) at 1/72, which is confirmed by Lanchester's square law that I performed above. I just eyeballed the figures and deduced that average quality was the only way for the equation to work out-- I wasn't certain when I did it that it was the proper way to calculate mixed groups. However, as it turns out, the paper I linked above confirms this (3.3 Mixed Forces, page 4). EDIT: Just a placeholder edit-- remind me to revisit "Drilling Down on Quality." EDIT2: Lancaster? Fixed. I blame my buddy Lasater who's been emailing me all day. [/QUOTE]
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