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Message: <blockquote data-quote="MadLordOfMilk" data-source="post: 4645415" data-attributes="member: 77691">I originally posted this on the WotC boards, but I thought it might get a bigger response here.Goal of this post: To point out that AC (or other defenses, I'll just use AC to refer to them all for the sake of simplicity) is worth more the more of it you have, and that +to hit is worth less the more of it you have (they're non-linear!), and how to directly relate AC and +to hit bonuses to Damage Bonuses, Damage Reduction, &cFirst, let me define a term: Effective Hit Points (EHP). Essentially, this means how much HP you "really" have. The base line is 100% - if you get hit by every attack 100% of the time, you have 100% of your actual HP, so your EHP is 100%. Now, if you only get hit 50% of the time, it's as if your HP doubled, giving you 200% EHP. If you get hit 25% of the time, it's like your HP doubled from getting hit 50%, giving you 2 * 200% = 400% EHP.Essentially, this means that Hit % and EHP are inversely proportional:Effective Hit Points = 1 / Hit Chance %<a href="http://img145.imageshack.us/my.php?image=hitvsehppe9.png" target="_blank"><img src="http://img145.imageshack.us/img145/7854/hitvsehppe9.th.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /></a>Yes, that's a curve. Essentially, it means a 5% gain in to hit doesn't quite mean a 5% increase in damage (it does in one sense and doesn't in another; see <a href="http://www.enworld.org/forum/general-rpg-discussion/249500-d20-math-ac-hit-diminishing-returns.html#post4645474" target="_blank">Nightson's reply</a>). Cut chance to hit in half, EHP doubles. Double chance to hit, EHP is cut in half. Now, how does this correlate to D&D?<a href="http://img89.imageshack.us/my.php?image=d20mathfixedvl4.png" target="_blank"><img src="http://img89.imageshack.us/img89/3307/d20mathfixedvl4.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /></a>Min d20 Roll to Hit: The minimum d20 roll required to hit a target. 1 means 1-20 will hit, 2 means 2-20 will hit, 3 means 3-20 will hit, &cHit %: The % chance to hit given that d20 roll required (IE if they need a 20 to hit, that's only a 1/20 or 5% chance to hit)Miss %: The chance to miss. 100% - Hit%Target's EHP: The Effective HP of the target being attacked. EHP = 1 / Hit%HP Gain from Last +1AC: How much the target's last +1 ac increased their EHP. For example, if a 1 still hits the target, their last +1ac did nothing, so it's a 0% hp gain. If it made the target need a 2 to hit instead of a 1, it's EHP(2) - EHP(1), or 105.2632% - 100.0% = 5.2632% HP gained. The math is just the change in EHP.HP Reduced from Last +1 to Hit: How much the last +1 to hit the attacker gained "reduced" the target's EHP. Essentially, HP gain from AC, but diminishing in value. The reason that it looks the same in the chart is because essentially when you add +1 ac you go down the chart, but +1atk you go up the chart. So, going from needing a 20 to needing a 19 lowers EHP by 1000%.ALTHOUGH +hit and +defense appear to both be increasing in value per point just at a glance of the table, they're not. The difference is +1AC moves you down one spot on the table, +1atk moves you up one spot. They're going in different directions. Thus, each point of defense bonus you get is worth more than the last, and each point of +atk is worth less.Here's a graph in case you wanted a visual:<a href="http://img301.imageshack.us/my.php?image=d20vsehpuh8.png" target="_blank"><img src="http://img301.imageshack.us/img301/3331/d20vsehpuh8.th.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /></a>What you can do with this chart:Say you go from needing a 12+ to hit a target to needing a 10+. That means you essentially "reduced" their HP by 222-182 = about 40%; this essentially means you gained ~40% damage against that target (relative to Base HP of 100%) from that +2 to hit. However, say you went from only needing a 6 to needing a 4 to hit, that's only about 133-117 = ~16% increase in damage (I say about because I'm ignoring the decimal places for those calculations). You can do the same thing with seeing the net benefit of AC bonuses. You can then compare these numbers to things like damage reduction and +dmg bonuses compared to AC and +hit.Now, how do you relate the reduction in EHP to a relative increase in damage per hit? In a way, it's mildly confusing: going from needing a 20 to hit to needing a 19-20 is in one sense dealing "10x" as much damage, but in the typical sense most people would use (IE to apply it directly to damage rolls and whatnot) it's like doubling your damage (because you doubled your hit chance). Basically, it boils down to this:-For a straight relative damage increase, just do Final Hit % / Old Hit % (for example, going from 5% to 10% hit chance means you do .10/.05=2x damage).-For the change in EHP, use the final column of the table (the +atk bonus column)</blockquote>

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