Details of the Ability Score Modifier and Ability Damage
When discussing a creature’s ability as a numerical values, it can be represented in three separate ways: abilityScore, abilityModifier, and abilityPoints
abilityScore is a (traditionally integer) value for one of the six character abilities generated at the characters creation by one of the various methods presented in D&D / d20 variants, starting with the original 3d6 method. In the urXron campaign we use the Variable Min-Max Point Buy method. No matter the technique, it should generate a number greater than zero, and 10.5 is considered the value for a normal creature of a particular species.
After generation, the score is converted to the abilityModifier
- initialAbilityModifer = (abilityScore – 10.5) / 2
Almost all use of a character’s ability will be in terms of the ability modifier, so almost all adjustments, particularly race or size based, to the ability will be stated in terms of the modifier. (Note it should probably be called the abilityBasedModifier, as it’s not the ability itself that is being modified, just the amount that the ability modifies other calculations). For example, where traditionally dwarves are spoken of having a +2 bonus to their charisma score, we will treat this as a +1 bonus to their charisma (based) modifier value. The modifier is an unbounded floating point value able to take negative and positive values, with zero representing the average value of the abilityModifier for a typical human.
The ability modifier is almost always used, except when a creature takes temporary damage to their ability. In that situation we discuss the damage in terms of abilityPoints:
- abilityPoints = 10.5 * (exp(1/5.25))**abilityModifier
- abilityModifier = 5.25 * ln (abilityPoints / 10.5)
(The parenthetical term, the abilityPointScale, has a value of approximately 1.21.) With this definition, the typical human average modifier corresponds to 10.5 ability points. And as the abilityModifier approaches negative infinity, the abilityPoints approach zero. Ability points are used only for tracking damage and damageRestoration to the ability that a creature may receive, e.g. from poison. If a creature’s ability points reach a value of zero or less in any ability, that create is totally incapacitated, unable to take any action. In the case of constitution the creature is dead. In the case of any other ability, the creature will die within twenty four hours unless the ability receives some amount of damageRestoration.
Ability damage restoration/recovery follows the same exponential curve and requires the same circumstances as hit point healing, with the same modifications to the restoration rate for less than optimal situations. Also like hit point healing, the nominal fractional recovery rate is 0.1 per day.
Let’s give an example: Bib the Dwarf Barbarian, originally assigns a score of 17 to his constitution. This converts to a modifier of +3.25 = 19.5 constitution ability points. During a battle he begins to rage, and adds +2 to his modifier, for a net modifier of 5.25 or 28.5 constitution ability points. During the battle due to some terrible poison, bib is assessed 20 points of constitution damage. What would be mortal to most, Bib just shrugs off, though now with only 8.5 ability points, his constitution modifier (and adjustments to his hit points) is -1.10! If Bib were to end his rage at this point, though, it doesn’t just subtract 2 from this modifier to get -3.1, as bad as that might seem. Instead though it’s his undamaged modifier returns to 3.25, and now the damage takes him to -0.5 constitution ability points. He’s toast! Fortunately, a friendly druid, Dot, casts lesser restoration, and even though it’s a catastrophically bad roll, she still restores 1.2 points (total damage now of 20 – 1.2 =18.8 points), which gives his net ability points of 0.7 after the end of the rage, equal to a modifier of -14.2. (To understand if this causes him to need immediate healing, see Calculating Constitution effects on Hit Points.) Bib hopes that Dot will hang around to cast multiple lesser restorations to speed his recovery. Otherwise, after his first day of total rest, he has only increased his net ability by 0.08. Eventually after almost 27 days of high quality care he will have had his temporary hit point damage restored.
If ability points are permanently drained, this corresponds to a reduction in the maximum, unadjusted, point number, e.g. a 4 point permanent drain out of the 20 points of damage would decrease his unadjusted number of 15.5, and drop his “normal”, unraging modifier to +2.0.
In order to understand the origin of the factor of 5.25., its value is fixed by the condition that at a modifier of zero (or 10.5 ability points) the instantaneous rate of change of ability points per modifier is 2. (By the old 3.5 edition rules this rate of change applies for all modifier values, not just at zero.) From a little calculus, we ask how many abilityPoints we get if we change the modifier by on
- derivative of (abilityPoints vs abilityModifier) = 2 = 10.5 * ln(abilityPointScale)
which means that
- abilityPointScale = exp(2/10.5) = 1.21