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I've recently begun trying to understand and implement nonweapon proficiencies as written in the AD&D 2e Player's Handbook. Most aspects of the system seem to come across clearly enough; my understanding is that when undertaking a task for which one of their nonweapon proficiencies applies, a character makes an ability check. Ability checks in 2e succeed if the result is equal to or lower than the relevant ability. (For instance, a character with STR 16 making a STR check succeeds on a 16 or lower.)

The confusion comes in when you start adding modifiers. For example, Fire-Building requires a Wisdom check with a -1 modifier. Given that fire-building should be a reasonably easy task, I would assume that the "-1" here is a bonus — in other words, it applies to the roll to make the task easier. However, Engineering requires an Intelligence check at a -3 modifier! Engineering is certainly much more difficult than Firemaking, so I would expect the modifier to be worse for the character attempting the task. Thus, I must assume that modifiers to ability checks affect the target number, rather than the die roll.

This seems to be the logical conclusion (particularly as the blacksmithing example in the paragraphs following the table makes note of a "-3 penalty") but I felt it necessary nonetheless to seek confirmation:

How exactly are modifiers applied to ability checks in AD&D 2e, particularly in the context of proficiency checks?

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Negatives are applied to the target number, which is the relevant stat. So it's a base −3 penalty to Engineering checks, which means that a character with an Intelligence score of 16 would apply the −3 to that Int 16 to determine that they need to roll 13 or below on the d20.

This is described at the top of the third column on page 55 of the original PHB printings (black-and-blue text):

If a proficiency check is required, Table 37 lists which ability is used with each proficiency. Add the modifier (either positive or negative) listed in Table 37 to the appropriate ability score. Then the player rolls 1d20. If the roll is equal to or less than the character's adjusted ability score, the character accomplished what he [sic] was trying to do.

The reason Fire-building gets a −1 is because it is the ability to make fire without flint and steel — that is, just from wood and tinder and manual friction techniques. Given flint and steel, no Fire-building NWP is needed and no roll is required (and the time is presumably shorter than 2d20 minutes, but the DM needs to make a ruling on exactly how long, should time be important).

On that last note, keep in mind that NWPs are not a general skill system to use when any character attempts to do something covered by a NWP — these aren't used at all unless the character has the NWP involved. NWPs let you do things that you can't normally attempt or accomplish without training and specific knowledge — like lighting a fire without tools, fighting effectively while blind, or designing a cathedral. For skill-like checks, you're into DM judgement territory to call for and set modifiers on Ability Checks.

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