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The Quadratic Problem—Speculations on 4e
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<blockquote data-quote="Wulf Ratbane" data-source="post: 3794522" data-attributes="member: 94"><p>More than ever I am convinced that the solution is to rebuild both characters and monsters from the ground up. See "the challenge" several posts back. We're coming back to it-- and I am dramatically expanding the challenge.</p><p></p><p><strong>I believe it is to our advantage to keep the process abstracted as much as possible.</strong> Applying "precision" does not give us any added security in "accuracy." The more moving parts our model has, the more places it will break down. We can all agree that D&D is <em>infinitely</em> more complex than we can imagine or that any model can predict. But that does not invalidate the exercise-- it should simply keep us focused on the big picture.</p><p></p><p>Assumptions/Processes:</p><p></p><p>1) We want encounters to remain "moderately difficult." </p><p></p><p>1a) I believe this means that encounters must be somewhere between "equal power" (the proverbial coin-flip) and 1/4 the power of the party.</p><p></p><p>1b) Because we are shifting to a per encounter format, with the assumption that the party tackles each successive encounter relatively "fresh," I believe that the proper ratio of party quality to encounter quality should be about 2x (although it looks like Saga is more along the lines of 3x, if starting HD are the primary indicator). Indeed, in <em>Unearthed Arcana</em>, p159, Andy suggests with respect to "Recharge Magic" that PCs can probably handle EL+2 encounters. Ultimately, we want the PCs to be challenged, but we want them to win. I don't think 4x is sufficiently challenging, certainly not once "per encounter" is taken into account.</p><p></p><p>2) Therefore, a Level 1 brute-- which term I am using quite incorrectly to refer to "a creature designed to meet the PCs in equal numbers," but bear with me-- should be designed with about half the quality of a single PC.</p><p></p><p>2a) We'll further assume that overall quality in fact <em>may be</em> derived from the product of offense and defense.</p><p></p><p>2b) We'll assume that the basic unit of offensive quality is measured in either <em>dice of damage</em> or <em>actual points of damage</em>; and the basic unit of defensive quality is measured in either <em>Hit Dice</em> or <em>hit points</em>.</p><p></p><p>2c) However, for simplicity sake, to keep things easy at 1st level, we'll measure both in dice, not points.</p><p></p><p>2d) Therefore our Level 1 brute should have 1 HD and do 1 die of damage; by extension the 1st level PC will have 2 HD and do 1 die of damage. </p><p></p><p>2e) If you prefer using points to dice, which granted is much more granular, assume that 1 die = 4 points. Therefore the PC has 8 hps and averages 4 damage, for a total quality of "32" (abstracted); the brute has 4 hps and averages 4 damage for a total quality of "16" (abstracted).</p><p></p><p>3) Now we can also design the Level 1 mook, who is designed to be used in a 2:1 ratio against the party. This creature, therefore, will have 1/4 the overall quality of a 1st level PC-- he will do 1 die of damage and have 1/2 HD. </p><p></p><p>3a) If you are using the more granular points, we know that the PCs have a total quality of "32" (abstracted) so we want the mooks to have a total quality of "8" (abstracted). We can convert this to 8 hit points, averaging 1 hp/round damage; 4 hit points averaging 2 hp/round in damage; we can even fudge it a little and call it 3 hit points, averaging 2-3 hp/round damage.</p><p></p><p>4) Now we go back and increment the PC to 2nd level in a way that makes sense, and hopefully bears some resemblance to the game we know. He gains 1 HD in defense (because everyone likes rolling a new hit die when they level up!), and he gains some (likely smaller) improvement in offense-- anywhere from +1 die (in the case of a spell based on full caster level, for example) or some portion less than one full die, all the way down to as little as a 5% increase from BAB and nothing else.</p><p></p><p>4a) Derive the new total quality of the 2nd level PC as a product of offense and defense.</p><p></p><p>4b) Derive the new total quality of a Level 2 brute-- half the quality of the 2nd level PCs-- and determine stats accordingly.</p><p></p><p>4c) Derive the new total quality of a Level 2 mook-- 1/4 the quality of the 2nd level PCs-- and determine stats accordingly.</p><p></p><p>5) Repeat this process as a complete redesign of all PC levels, and all monsters, across all levels from 1-30.</p><p></p><p>ENworld's rycanada has already performed an analysis of all 3e monsters across all CRs, giving us a "fudge table" of expected, typical, or "appropriate" values for all monsters. </p><p></p><p>Our final work should look very much the same-- the barest mechanical skeleton on which we can hang all the creative, fluffy design we want. The brute-1s we call "orcs," our mook-1s are "goblins," our brute-2 are "troglodytes" and so forth. We may even have "mook's mooks" at 1st level and beyond-- Level-1 "kobolds" designed to outnumber 1st level PCs four to one (at 1/16 the quality). </p><p></p><p>We can push the numbers around in all sorts of ways and eventually we flesh out the entire MM.</p><p></p><p>6) Now we build our new XP charts and new Encounter Design system. First, graph the power curve of the PC from 1st-30th level.</p><p></p><p>6a) Assign a fixed XP value for "A 1st level encounter" such that ~13.333 encounters, with all XP totalled and divided by 5 PCs, accumulates enough XP to make 2nd level. (There's nothing special about 13.333 encounters that I know of, other than it is probably the "average" number of encounters that "average" game groups like to tackle before levelling up-- in other words, it probably has its basis in real-world game time.)</p><p></p><p>6b) Using 300 xp as particularly utile base value, we can derive from this that 5 brutes are worth 300 xp; 1 brute is worth 60 xp. An equal encounter, 10 mooks, is also worth 300 xp; thus 1 mook is worth 30 xp. (And our kobolds, worth 15 xp.)</p><p></p><p>6c) Multiply out the baseline XP awards across the same power curve of PC power, and derive encounter XP values for 2nd-30th level. (Yes, there will be some considerable "smoothing out" of the actual values.)</p><p></p><p>6d) Derive a new XP advancement chart using these new fixed XP awards.</p><p></p><p>7) As pointed out above, using mixed groups cannot account for Lanchester's square law. However, by giving the DM some guidelines ("Use anywhere between 1/2x and 2x the size of the party, and/or monsters within 2 levels of the average PC level.") we should be able to get any encounter into a reasonable framework, and handwave any differential predicted by Lanchester. Give or take 25% seems reasonable to handwave, especially as the system has already been pre-designed with a bias in the PCs favor.</p><p></p><p>Comments?</p></blockquote><p></p>
[QUOTE="Wulf Ratbane, post: 3794522, member: 94"] More than ever I am convinced that the solution is to rebuild both characters and monsters from the ground up. See "the challenge" several posts back. We're coming back to it-- and I am dramatically expanding the challenge. [b]I believe it is to our advantage to keep the process abstracted as much as possible.[/b] Applying "precision" does not give us any added security in "accuracy." The more moving parts our model has, the more places it will break down. We can all agree that D&D is [i]infinitely[/i] more complex than we can imagine or that any model can predict. But that does not invalidate the exercise-- it should simply keep us focused on the big picture. Assumptions/Processes: 1) We want encounters to remain "moderately difficult." 1a) I believe this means that encounters must be somewhere between "equal power" (the proverbial coin-flip) and 1/4 the power of the party. 1b) Because we are shifting to a per encounter format, with the assumption that the party tackles each successive encounter relatively "fresh," I believe that the proper ratio of party quality to encounter quality should be about 2x (although it looks like Saga is more along the lines of 3x, if starting HD are the primary indicator). Indeed, in [i]Unearthed Arcana[/i], p159, Andy suggests with respect to "Recharge Magic" that PCs can probably handle EL+2 encounters. Ultimately, we want the PCs to be challenged, but we want them to win. I don't think 4x is sufficiently challenging, certainly not once "per encounter" is taken into account. 2) Therefore, a Level 1 brute-- which term I am using quite incorrectly to refer to "a creature designed to meet the PCs in equal numbers," but bear with me-- should be designed with about half the quality of a single PC. 2a) We'll further assume that overall quality in fact [i]may be[/i] derived from the product of offense and defense. 2b) We'll assume that the basic unit of offensive quality is measured in either [i]dice of damage[/i] or [i]actual points of damage[/i]; and the basic unit of defensive quality is measured in either [i]Hit Dice[/i] or [i]hit points[/i]. 2c) However, for simplicity sake, to keep things easy at 1st level, we'll measure both in dice, not points. 2d) Therefore our Level 1 brute should have 1 HD and do 1 die of damage; by extension the 1st level PC will have 2 HD and do 1 die of damage. 2e) If you prefer using points to dice, which granted is much more granular, assume that 1 die = 4 points. Therefore the PC has 8 hps and averages 4 damage, for a total quality of "32" (abstracted); the brute has 4 hps and averages 4 damage for a total quality of "16" (abstracted). 3) Now we can also design the Level 1 mook, who is designed to be used in a 2:1 ratio against the party. This creature, therefore, will have 1/4 the overall quality of a 1st level PC-- he will do 1 die of damage and have 1/2 HD. 3a) If you are using the more granular points, we know that the PCs have a total quality of "32" (abstracted) so we want the mooks to have a total quality of "8" (abstracted). We can convert this to 8 hit points, averaging 1 hp/round damage; 4 hit points averaging 2 hp/round in damage; we can even fudge it a little and call it 3 hit points, averaging 2-3 hp/round damage. 4) Now we go back and increment the PC to 2nd level in a way that makes sense, and hopefully bears some resemblance to the game we know. He gains 1 HD in defense (because everyone likes rolling a new hit die when they level up!), and he gains some (likely smaller) improvement in offense-- anywhere from +1 die (in the case of a spell based on full caster level, for example) or some portion less than one full die, all the way down to as little as a 5% increase from BAB and nothing else. 4a) Derive the new total quality of the 2nd level PC as a product of offense and defense. 4b) Derive the new total quality of a Level 2 brute-- half the quality of the 2nd level PCs-- and determine stats accordingly. 4c) Derive the new total quality of a Level 2 mook-- 1/4 the quality of the 2nd level PCs-- and determine stats accordingly. 5) Repeat this process as a complete redesign of all PC levels, and all monsters, across all levels from 1-30. ENworld's rycanada has already performed an analysis of all 3e monsters across all CRs, giving us a "fudge table" of expected, typical, or "appropriate" values for all monsters. Our final work should look very much the same-- the barest mechanical skeleton on which we can hang all the creative, fluffy design we want. The brute-1s we call "orcs," our mook-1s are "goblins," our brute-2 are "troglodytes" and so forth. We may even have "mook's mooks" at 1st level and beyond-- Level-1 "kobolds" designed to outnumber 1st level PCs four to one (at 1/16 the quality). We can push the numbers around in all sorts of ways and eventually we flesh out the entire MM. 6) Now we build our new XP charts and new Encounter Design system. First, graph the power curve of the PC from 1st-30th level. 6a) Assign a fixed XP value for "A 1st level encounter" such that ~13.333 encounters, with all XP totalled and divided by 5 PCs, accumulates enough XP to make 2nd level. (There's nothing special about 13.333 encounters that I know of, other than it is probably the "average" number of encounters that "average" game groups like to tackle before levelling up-- in other words, it probably has its basis in real-world game time.) 6b) Using 300 xp as particularly utile base value, we can derive from this that 5 brutes are worth 300 xp; 1 brute is worth 60 xp. An equal encounter, 10 mooks, is also worth 300 xp; thus 1 mook is worth 30 xp. (And our kobolds, worth 15 xp.) 6c) Multiply out the baseline XP awards across the same power curve of PC power, and derive encounter XP values for 2nd-30th level. (Yes, there will be some considerable "smoothing out" of the actual values.) 6d) Derive a new XP advancement chart using these new fixed XP awards. 7) As pointed out above, using mixed groups cannot account for Lanchester's square law. However, by giving the DM some guidelines ("Use anywhere between 1/2x and 2x the size of the party, and/or monsters within 2 levels of the average PC level.") we should be able to get any encounter into a reasonable framework, and handwave any differential predicted by Lanchester. Give or take 25% seems reasonable to handwave, especially as the system has already been pre-designed with a bias in the PCs favor. Comments? [/QUOTE]
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