Upgrade your account to a Community Supporter account and remove most of the site ads.

Reply to thread

Message: <blockquote data-quote="Esker" data-source="post: 7859136" data-attributes="member: 6966824">In DPR analyses it's common to combine to-hit and damage into a single number representing the expected damage done if we assume a certain level-appropriate monster AC; that is, we convert to-hit bonuses into damage bonuses. But I haven't seen many quantitative analyses on the defense side that consolidate the defensive counterparts of to-hit and damage, namely AC and HP, into a single defensive number. I realize that it's more complicated than this: some things (concentration saves, for instance) work very differently if you take lots of small hits vs one big one, etc., but then, most DPR analyses also ignore whether you're doing your damage in one big attack vs spreading it out over multiple attacks to the same target, even though this can matter, so on a first pass it seems reasonable to set those wrinkles aside.Non-combat damage and things like concentration checks aside, the main reason HP and AC matter is that they govern how many combat rounds you last before going down. So the operative quantity seems to be your expected "RTU" (rounds-til-unconsciousness). A nice thing about this measure is that you can add together the RTUs of a party to figure out how many actual combat rounds it would take, on average (if they share the incoming damage equally), for them all to go down. You can also factor in sources of healing as additions to the HP pool when calculating a party's RTU.For fixed AC, RTU will scale proportionally with HP, with the proportionality constant being a function of your enemies' DPR vs your AC. So we have RTU = HP / enemyDPR. But how does AC affect your RTU?Well, enemyDPR is equal to baseDPH * toHit, where toHit is (21 - AC + atkBonus) / 20. So all together, assuming neither advantage or disadvantage, we haveRTU = HP / [baseDPH * (21 - AC + atkBonus) / 20]For example, suppose you have 40 HP and the enemy's attack damage on hits is 20 per round, with a 60% chance to hit you vs your current armor class (let's say it's 15 and their attack bonus is +6).  Their DPR against you will be 12, giving you, on average 40/12 = 3.33 rounds of getting attacked before you go down. So your RTU is 3.33.If we set aside advantage and disadvantage, and assume a fixed enemy attack bonus, then each additional point of AC reduces enemyDPR by 5 percent of their base DPH; that is, it's linear. However, this doesn't translate to a linear effect on your RTU, since RTU is inversely related to enemy DPR.The table below shows, for each additional point of AC, what the DPR of the enemy in the example above becomes (eDPR), what your RTU becomes vs this enemy, and, using AC 15 as a baseline, how many HP you would need to have to achieve that same RTU (eqHP). The columns labeled dRTU and dHP are the marginal increases in RTU and HP associated with the last point of AC.[CODE]AC  hit% eDPR   RTU  dRTU  eqHP   dHP15   60    12  3.33  --    --      --16   55    11  3.64  0.31  43.7   3.717   50    10  4.00  0.36  48.0   4.318   45     9  4.44  0.44  53.3   5.319   40     8  5.00  0.56  60.0   6.720   35     7  5.71  0.71  68.5   8.521   30     6  6.67  0.95  80.0  11.522   25     5  8.00  1.33  96.0  16.023   20     4 10.00  2.00 120.0  24.0[/CODE]So we have a crude way of quantifying how much each additional point of AC is worth, in terms of RTU, and in terms of HP.What we can see is that each additional point of AC is worth more than the one before, and moreover that the rate of change increases as well, with the second point of AC being worth 0.6 more than the first, and the third being worth 1.0 more than the second, etc. Going from AC 22 to AC 23 is worth over 6x as many HP as going from 15 to 16!Now, a caveat, this doesn't factor in crits, which is important since as you go up in AC a higher percentage of the hits against you are crits; but it's easy to include them by just treating crit damage as a bonus to the to-hit roll: if the enemy has a 60% chance to hit and a 5% chance to crit, and half their damage is from dice, then their average damage is the same as if they had a 62.5% chance to hit. 55% to hit becomes 57.5%, etc. So crits don't change the shape of the curve; they just offset it a bit. Altering the enemy's base damage will just rescale these values; whereas changing their attack bonus will of course shift them (increase their to-hit by 1 and an AC of 16 becomes like an AC of 15 before, etc.)I don't have any grand point to make here; just had been thinking about this and wanted to share it, since I don't know that I've seen a metric like this come up here.</blockquote>

Verification