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The Quadratic Problem—Speculations on 4e
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<blockquote data-quote="mmadsen" data-source="post: 3757488" data-attributes="member: 1645"><p>Ah, but it will, UK, or it will come close, because the math is sneaky that way.</p><p></p><p>If a Fighter gained nothing at all per level except his one extra hit die, then his combat power would increase linearly. If he improves (linearly with level) just one of the other combat-power variables -- to-hit, damage, or armor class -- then his overall combat power increases <em>quadratically</em> (x[sup]2[/sup]). If he improves three of the four variables, his combat-power increases <em>cubically</em> (x[sup]3[/sup]). If he improves all four variables, his combat-power increases even faster (x[sup]4[/sup]). </p><p></p><p>Then we need to combine that with the sneaky math around armor class, where a linear increase in armor class yields a much faster increase in combat-power, if we assume low-level opponents.</p><p>I just added another sheet with 3E NPC Fighter stats -- and with iterative attacks calculated, all assuming a 1st-level NPC Fighter as the baseline (and the default opponent).</p><p></p><p>Addendum: A 20th-level NPC Fighter has more than 4,000 times the combat-power of a 1st-level NPC Fighter.</p></blockquote><p></p>
[QUOTE="mmadsen, post: 3757488, member: 1645"] Ah, but it will, UK, or it will come close, because the math is sneaky that way. If a Fighter gained nothing at all per level except his one extra hit die, then his combat power would increase linearly. If he improves (linearly with level) just one of the other combat-power variables -- to-hit, damage, or armor class -- then his overall combat power increases [i]quadratically[/i] (x[sup]2[/sup]). If he improves three of the four variables, his combat-power increases [i]cubically[/i] (x[sup]3[/sup]). If he improves all four variables, his combat-power increases even faster (x[sup]4[/sup]). Then we need to combine that with the sneaky math around armor class, where a linear increase in armor class yields a much faster increase in combat-power, if we assume low-level opponents. I just added another sheet with 3E NPC Fighter stats -- and with iterative attacks calculated, all assuming a 1st-level NPC Fighter as the baseline (and the default opponent). Addendum: A 20th-level NPC Fighter has more than 4,000 times the combat-power of a 1st-level NPC Fighter. [/QUOTE]
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