Monday, March 1, 2021

Generation of Ability Scores

There are six ability scores for each character which limit physical, mental and social limitations of the character: strength, intelligence, wisdom, constitution, dexterity & charisma.

These abilities are determined through rolling six-sided dice.  The simplest way of doing this is to throw 3 six-sided dice, abbreviated "3d6."  Since each die has a minimum number of 1, and a maximum number of 6, the result allows us to produce a number between 3 and 18.  Overall, there are 216 possible combinations of dice; only 1 combination out of 216, three rolled ones, is able to produce a total of 3.  Therefore, 3s are quite rare.  Only one combination exists that will produce an 18, also (three sixes), so 18s are also rare.

Here are the number of combinations that will produce each possible result:

As we can see, chances are we're going to roll a result between 8 and 13, with 48% of rolling a result between 9 and 12.  Rolling 3d6 six times, we have no better than a 56% chance of getting any roll above 14.  These results are unfortunate, as most of the real benefits to ability scores only apply when those scores are 15 or better.

To get better results, one favoured method is to roll 3d6 twelve times, keeping the six highest rolls.  This gives us a better average of getting 15 or better ability, but unfortunately this only increases the chance of one ability above 14 to 69%.  This still isn't very good.

A third method is to roll 3d6 six times for strength, then for intelligence, then for wisdom and so on, and then keeping the highest roll of each grouping.  This would mean that each ability would have a 44% chance of being above 14; the odds are slightly less than even that the character would end up with a 69% chance of at least one ability stats of 15 or better.  That's fair.  The chances of rolling a "natural" 18 on 3d6, rolled 36 times, is 15%.

Of course, this method takes a lot of time, and some have argued that this is something of an overkill where it comes to dishing out ability stats.  That is why a quite different method is popular, one in which 4d6 are rolled only six times (reducing the amount of rolling), and the lowest die of the four rolled is discarded (not actually thrown away, just not counted).

This skews the random odds somewhat.  First of all, there are now 1296 possible combinations of die rolls, with the odds of rolling four ones only 1 in 1296.  Here below is a list of possible combinations for each result, with one table showing how they compare to rolling 3d6, and one showing the combinations out of 1296 (shown in comparison with the 3d6 table):



It isn't surprising that this is by far the most popular method of rolling ability stats ... or rather, it was, until the world changed.

See, here in 1979, hardly anyone feels concern that the random generation of ability stats will create envy and discord between players.  We all know that every game with dice tends to favour some players over others, and that some characters will be generated with a bunch of high results, while other characters will be less lucky.  In general, since the game is a joint effort between the players, logic dictates that if any character has a lot of high scores, this will benefit the whole group.  After all, not every member of a sports team has the same level of proficiency ... yet everyone on the winning team is grateful for one or two players who have really spectacular skills.  It means, we all win.

Having looked into our crystal ball, we've seen that in the future, this randomness in ability generation scores has produced a great deal of pettiness and one-upmanship, not to mention swaggering and lording one's ability scores over the other players.  We've seen that our future company has been forced to get rid of the randomness altogether, in favour of "balancing" the fragile emotional states of the participants, who aren't able to recognize that not everyone is equal.  We're somewhat distressed here in 1979, and don't know what to think.  Clearly, it's very important that people enjoy the game, and that no one feels left out, or made to feel small and unimportant because they don't have high ability scores.  On the other hand, we also feel that having high ability scores is in no way proof of a character's survivability.  Any character who does not pay attention to what's going on, or runs into bad luck in a hundred other ways throughout game play, or ultimately does something stupid, will absolutely die no matter what their ability scores are.  We can't figure out here, why the people in 2021 don't seem to know this.

Similarly, a good player, one who can figure things out or who knows best how to work with what they have, ought to be able to circumvent a set of low ability scores, so that far from being a short-lived character, they should survive through caution.  The game ought to be run so as to let players live based on how well they play, rather than the numbers they play with.

Oh well.  It is a simpler time where we are.

6 comments:

  1. Add to this the irrelevance (in 1979) of some “high” scores with regard to many character classes (there is minimal advantage to a non-fighter possessing a CON greater than 16, or a non-magic-used possessing a high Intelligence, for example).

    Was having a discussion with my son just today about ability scores and how a half-orc’s strength bonus was UNlikely to make more of a difference to combat ability than an elf’s attack bonus with favored weapons...and make even less difference when pitted against a fighter just a level or two higher.

    I hate the ability score inflation of latter day editions. I hate that it models...nothing. Just points for points’ sake; a new form of bragging rights. It’s almost enough to make me go back to the original game where the only benefit of a high stat was a bonus to x.p..

    Almost.

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  2. For others reading this, there isn't a "minimal" advantage to a non-fighter having a 17 or 18 constitution. Both a 17 and an 18 give a +2 hit point bonus to constitution, just as a 16, if the class is not a fighter. This is in part to encourage non-fighter classes to place higher scores into other abilities, and in part to provide an elitist recognition of the fighting abilities. Good sense indicates that if a non-fighter character has a 17 or 18 constitution, and wishes to take full advantage of it, because they have so many high scores they can provide for both their primary and secondary traits, then said non-fighter should become a MULTI-CLASS character, improving themselves on many levels, and not just another +1 or +2 constitution bonus above what they would normally get.

    This note has been added purely to explain that there is a logic to the rules behind AD&D, and that they are not merely arbitrary.

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  3. The standardization of bonuses in 3.x could only ever have led to stat inflation and then standardization. The game creators couldn't abide randomness for long. When removing stat requirements from class suddenly there isn't a reason to roll for stats at all, and thus we get the Elite Array.

    People still do roll for stats in home games sometimes, but really there's little point, because now the game has other levers to increase your stats: I managed a 20 pretty early on, and could probably have gotten a second soon enough.

    I personally prefer that stats are mostly meaningless outside of the very high and very low. Does having six 13s feel better than six 12s? Sure, but mechanically they are almost exactly the same. Having a 9 doesn't sting so bad because frankly it probably doesn't do anything. I can focus on what I qualify for and then just play that thing.

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  4. Most adult humans are pretty close in physical ability (and mental capacity). It is training and education that generally distinguishes our capabilities.

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  5. You say that, Pandred, but I don't know a single player who would forsake that 5% difference when it comes time to make an ability check. Should I start counting your fighter character's charisma as a "12" going forward?

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  6. My guy, I might not even notice that dip for months.

    Every stat of mine that isn't the 15 Con and the 18 Str is functionally interchange-able on a given week of our sessions. If we were to go back over the logs, I've had to check them like, what, once per month of playtime? So maybe once every three or four real life sessions?

    I'd have to check an equivalent stat like once per hour of gameplay in a later edition. A 1 point dip would hurt a lot more, and a lot more often. There's a lot more rolling for everything.

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