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    Halfling in the Playground
     
    ElfPirate

    Join Date
    Aug 2012

    Default Class-Choice Resource: Best use of 720 Combinations (30*24) of 6 Attributes.

    Governing Rules: [Formatting, mine....]
    Quote Originally Posted by [b]PCs and NPCs[/b] [DMG 131]
    The NPC classes presented in Chapter 4 of this book showcase the difference between PCs and the rest of the world: The PCs are among the most capable members of the populace, or at least among those with the greatest potential. The variance of Ability Scores (from 3 to 18 or higher) shows that not all people in the world are created equal, and not all have the same opportunities.

    Having the same opportunities, in this case, means having training. Training is the difference between an Adept and a Wizard, a Warrior and a Fighter, a Commoner and an Expert. An NPC with good Ability Scores might still be a Warrior rather than a Fighter because she never had the opportunity to obtain the training to be a Fighter. She can swing a sword, but she does not have the finesse of a trained Fighter. In theory, however, she could be trained as a Fighter at some point after beginning her career as a Warrior, gaining Fighter levels through multiclassing.

    Obviously, however, training isn't always helpful. Someone with an Intelligence score of 6 is never going to be a Wizard, since he is unable to cast spells. In theory, though, anyone with the Intelligence, the inclination, and the training can learn Wizardry.
    Quote Originally Posted by [b]Chapter 3: Classes[/b] [PH 021]
    Class is probably the first choice you make about your Character -- just ahead of Race, or perhaps in conjunction with that decision. The Class you choose determines where you should best place your Character's Ability Scores and suggests which Races are best to support that Class choice.
    Quote Originally Posted by [b]Assign and Adjust Ability Scores:[/b] [PH 006]
    Now that you know your Character's Class and Race, take the Ability Scores you rolled earlier and assign each to one of the six Abilities:
    • Strength,
    • Dexterity,
    • Constitution,
    • Intelligence,
    • Wisdom, and
    • Charisma.

    Adjust these Scores up or down, according to your Race, as indicated on Table 2-1: Racial Ability Adjustments [PH 012]
    Quote Originally Posted by [b]Ability Scores:[/b] [PH 007]
    At this step, you need to know what kind of person your Character is going to be, including his or her Race and Class, in order to know how best to distribute the Ability Scores.
    Quote Originally Posted by [b]Rerolling:[/b] [PH 008]
    If your Scores are too low, you may scrap them and roll all six Scores again. Your Scores are considered too low:
    • If the sum of your Modifiers (before adjustments because of Race) is 0 or lower, or;
    • If your highest Score is 13 or lower.
    Quote Originally Posted by [b]Elite and Average Characters:[/b] [DMG 110]
    All PCs and all the NPCs described in this section [DMG 110-127] are "elite," a cut above the average.
    • Elite Characters (whether they are PCs or not) have above-average Ability Scores and automatically get maximum hit points from their first Hit Die.
    • Average Characters, on the other hand, have average Abilities (rolled on 3d6) and don't get maximum hit points from their first Hit Die.

    The monsters described in the Monster Manual are average Characters, rather than elite ones (though elite monsters also exist). Likewise, some Fighters, Wizards, and so on are average people rather than elites; they have fewer hit points and lower Ability Scores than the NPCs described here [DMG 110-127].
    Life in the Big City:
    Now, imagine a typical Large City with an adult population of 20k (population ranges for Settlements, as presented in the DMG, are not open-content, but per the DMG v3.5 web-enhancement -- Building a City -- a Large City can be expected to have 40 Districts, with a typical District having an adult population of about 500). Following the guidelines for determining the highest-level NPCs generated in such a city, and for enumerating the lower-level NPCs generated in their wake [DMG 139], we find that there will be at least 45 members of each of the most common core-classes -- Fighters and Rogues, in any area, as well as Monks and Barbarians in areas where such are common -- and exactly 45 members of the more exotic classes... including Wizards. (Whether the area within the bounds of a Large City may be an area where Barbarians are common is an issue the rules do not address.) Statistically, in a Large City of 20k NPC adults (generated using 3d6, per the rules for non-elite NPCs, as cited earlier), for any single one of the six Attributes, we can expect approximately 92 [(2*10^4)*((1/6)^3)] to be generated with an 18 in that Attribute (before including any stat-boosts for race, level, or equipment): that is, we can expect 92 NPC adults to have a baseline Intelligence of 18; we can expect 92 NPC adults to have a baseline Wisdom of 18; we can expect 92 NPC adults to have a baseline Charisma of 18; and so on for the physical Attributes. Yet, exactly 45 NPCs in this Large City, fewer than half of those NPC adults we can expect to have an 18 Intelligence, will become Wizards... and, per the rules discussing Elite and Average Characters, as cited above, not all of those Wizards will have an 18 Intelligence, since some members of each class will have Attributes lower than those provided for the sample NPC representing their class, and those NPCs use the elite-array. Given the Large City in this example, which of the 45 adults, residing therein, will become Wizards?

    As Above, so Below:
    The above results are not an artifact of the rules limited to the NPC adults populating a Large City. It can easily be seen that, according to the rules, in a Large Town having an adult population of 4100 or so (a convenient number, because it is very nearly a multiple of 216) we can expect to find 19 adults with a baseline Intelligence of 18, yet in that Large Town, we will find exactly 7 Wizards. How best to determine which of those 4100 adults becomes one of those 7 Wizards?

    Great Expectations
    Above, I have italicized one term, expect, several times. Why? I am using it in the statistical sense: the number that we expect to see is the average for the distribution. To give you a sense of how far values may vary from this, I have prepared the following (correctly, I hope):

    Spoiler
    Show

    Still working on this....

    In a Large Town
    {table]P(L<=n<=H)|L|H|Ratio|3d20|Down-Iff
    0.999963587|--|38|--|0.999875|3d20<60
    0.999923280|00|37|0.999959692|0.999875|3d20<60
    0.999842218|01|36|0.999918932|0.999875|3d20<60
    0.999682924|02|35|0.999840681|0.9995|3d20<59
    0.999375565|03|34|0.999692543|0.9995|3d20<59
    0.998789159|04|33|0.999413228|0.99875|3d20<58
    0.997676425|05|32|0.998885917|0.99875|3d20<58
    0.995575528|06|31|0.997894209|0.9975|3d20<57
    0.991655766|07|30|0.996062819|0.995625|3d20<56
    0.984514132|08|29|0.992798273|0.993|3d20<55
    0.971967312|09|28|0.987255826|0.985|3d20<53
    0.950927135|10|27|0.978352999|0.9725|3d20<51
    0.917471373|11|26|0.964817744|0.96425|3d20<50
    0.867200358|12|25|0.945206994|0.943125|3d20<48
    0.795894787|13|24|0.917774975|0.915|3d20<46
    0.700382016|14|23|0.879993219|0.878875|3d20<44
    0.579420102|15|22|0.827291519|0.8075|3d20<41
    0.434364684|16|21|0.749654150|0.7485|3d20<39
    0.269415284|17|20|0.620251356|0.6115|3d20<35
    0.091334792|18|19|0.339011176|0.3175|3d20<27
    [/table]

    To provide some scope and context, have a look at Dungeon Magazine's map of the Flanaess, the Eastern portion of the continent of Oerik -- the default "World of Greyhawk" setting for 3.x D&D, often implicit (and sometimes explicit) in the Core Rulebooks -- made freely available by Paizo Publishing. (In contrast, the classic map by Darlene Pekul -- now, simply Darlene -- is not freely available, though well worth a look.) There are certainly over 16,000 hexes, arranged in about 99 rows and about 166 columns (assuming I counted correctly... I grew a little cross-eyed, counting columns, and each row includes partial hexes.) At the top of the table, above, you will note a 0.999963587 chance (with 1.0 being a perfect chance) that in a Large Town of 4100, there are no more than 38 adults having a baseline Score of 18 in a given Attribute. This represents a chance of less than 1-in-27,400 that there are more than 38 such adults in a given Settlement of this size. Even were there a Large Town of 4100 in every single one of the more than 16,000 hexes in the map for Dungeon, there would be well under half-a-chance that even one of them had more than 38 such adults. The throw of 3d20 provides an adequate approximation of the odds involved -- though it only goes so far as 1-in-8,000 -- it does provide a fair amount of granularity.

    Purpose:
    This will be a resource for discussion of which classes are best suited to characters, whether PCs or NPCs, with a given arrangement of attributes.

    Assumptions:
    • The primary score will be further boosted (prioritized through leveling and item choice);
    • At least one secondary score will begin reasonably high, and another may be sufficient to qualify for gateway feats (e.g., Str 13 for Power Attack);
    • In any given array, one stat will, of necessity, be a dump-stat.
      (Even when a randomly generated array produces a character from Lake Wobegon, whose every attribute is at or above the average, every PC/NPC has restrictions on their budget such that not all stats can benefit equally from items.)

    All Else Being Equal....
    While the elite-array {15, 14, 13, 12, 10, 8} [DMG 169] is one example of an array demonstrating the assumed characteristics, for purposes of this thread, it not the specific values represented in a sequence, but instead the order in which the array is sequenced, which is of importance. However, the elite-array remains convenient as a basis for discussion, in that it not only demonstrates the assumed characteristics, but also puts on theoretically equal footing any two Characters generated with it. One might say the same of point-buy, but one need only compare the standard array {11, 11, 11, 10, 10, 10}, used for Monsters the DM cannot be bothered to better flesh-out, with the marginally more individualized non-elite array {13, 12, 11, 10, 9, 8}, which shares the same point-buy value but allows a certain degree of optimization toward a role: an NPC Warrior with Strength 13 and Charisma 8 is likely to be more effective in its role than an NPC Warrior with Strength 11 and Charisma 10, for example.

    PCs:
    While players are typically able to assign attributes to their characters according to the type of character they envision playing, as outlined in the character creation method provided in the Player’s Handbook [PHB 007], this is not always the case. While randomly generated elite attributes allocated in a custom array are thus the default, for some games, another character generation method will be used by all players. Several of these alternative methods, presented among other optional rules in Chapter 6 of the DMG [DMG 169], do not allow players to allocate their character’s attributes so as to best fit a pre-existing concept. That is, in addition to those methods which allow generated attributes to be sequenced in a custom array, the DMG also presents methods of character generation which explicitly produce random arrays. A character created using the organic generation method [DMG 169], for example, has only a limited ability to swap the assignment of attributes. If a character is created with a random array of some type, rather than a custom array, or if the generated array cannot be made to support the player’s concept for the character even with custom-allocation of attributes, then the player will no doubt want to know how to make best use of the available array.

    NPCs:
    Similarly, NPCs, when not purpose-built to fill a particular niche (as the campaign BBEG likely will be) typically have their stats assigned in the order they were generated. Alternatively, the Dungeon Master may know just what class an NPC should be, but not what array of attributes to assign to that NPC: while the DMG provides examples of NPCs with class-levels [DMG 110-127], each assigned the elite-array, is this the best -- or the only -- distribution for a given class? For example, the sample Wizard prioritizes Intelligence, as one would expect, but then favors Dexterity above the other attributes [DMG 125 ??? AFB]. I know that many on these boards would advise that a Wizard favor Constitution over Dexterity. Surely, if only for the sake of encounter variety, not every NPC of a given class should share the same attribute allocation: from which other arrays could an effective, or at least credible, NPC of a given class benefit? Additionally, data of this sort may be useful when populating a database to populate a settlement (or city-district) with randomly-generated characters (particularly NPCs).

    I Riddle Thee, with Questions Three:
    So, the question for both randomly generated NPCs, and those PCs organically (or randomly) generated, is how to make best use of the array the dice have dealt. There are three questions here:
    • Given a specified array, to which class should a character (PC or NPC) aspire?
    • Given an NPC Master of their class virtually swimming in a pool of pontential pupils (an array of arrays) -- each vying and vowing to catch the Master's eye -- which will the Master select as Apprentice?
    • What is your favourite colour?


    Question, the First:
    For the first, while a character with Intelligence paramount would make a fine Wizard, a player may also enjoy (and be effective) playing a Rogue with such an allocation, or even a Factotum, if classes beyond core are available. This is really a question of which classes make best use of a given array.

    Question, the Second:
    For the second, not every brilliant NPC that aspires to be a Wizard will be taken on as an apprentice: the DMG sets a hard limit on the number of NPCs of a given class, based on the highest-level NPC generated for that class [DMG 139]; not all those who are qualified for a given class can be assigned to that class, assuming others who are similarly qualified are present. This is really a question of which arrays are best for a given class.

    Question, the Third:
    We'll cross that bridge when we come to it....

    Work in Progress:
    These two questions are closely bound, but not identical, and this thread seeks to answer these two questions for each of the 720 Combinations one may generate when arranging 6 attributes. In this thread, these 720 Combinations are ordered into 30 sets of 24 because, at least in my browser, GiantITP defaults to 30 posts per page. Although, since these correspond to a standardized-month of 30 days (not a true, lunar-month of 28 days), and a 24-hour day, this division could also be used to sequence a randomly generated set of 6 attributes as if according to Astrology, which may be fun as the basis for a pseudo-mediaeval world.

    Please Note:
    I am limited in that I am posting from a computer at the public library: I have to take my turn; it is a long wait to post for a relatively brief while; no person gets more than 2 turns per day; and I have other demands on my time, such that I cannot visit the library (or post) every day.

    Expect further edits, as I clean-up, format, and add to the prior 30 posts, and use this 31st post to provide a better idea of what function this resource is intended to fill.

    A Note on Recent Inactivity:
    Last month, I learned that a brick-and-mortar retailer I used to frequent -- one stocking recorded media, such as music and movies -- would be closing. I spent most of the past month poring over their selection of stock, and purchasing what I could afford (much of it at 40% off). Now that the outlet in question has closed (27 October), I expect that I will be posting here more frequently, just as I used to do.

    I have been updating/editing this post, periodically, but 11/13 will be my first new post in a while (previously 10/01): I had intended to come in 11/12, but the library was closed for Veteran's Day. Since I have been updating and adding to this post, several times a week, I hope this will not be considered Thread Necromancy (the normal limit for the original poster is six-weeks, IIRC, which would technically set 11/12 as the deadline, but hopefully, Holidays don't count towards that limit).

    This posting session is at an end.
    I am presently editing a post in this thread.
    Last edited by PureMutation; 2012-12-14 at 04:37 PM.

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