Skill and Ability Modifiers

A few months ago I began to theorize on task resolution and dice mechanics for a hypothetical game system. In those two posts, I concluded that using 3d6 seems to be a good dice mechanic, and for task resolution I decided on the following difficulties/target numbers:

 Difficulty Probability Roll 3d6 Trivial 100% 3+ Easy 95% 6+ Routine 74.07% 9+ Difficult 37.5% 12+ Very Difficult 9.26% 15+ Impossible 0.46% 18+

However, these decisions require that the bonuses given by skills, attributes, and so on stay within certain boundaries. Or, in other words, the capabilities we grant the characters need to be balanced against those difficulties.

So what happens when we modify dice rolls? We just shift the probability of achieving a certain result around. The following table shows the percentage of success for our difficulties for a range of dice modifiers of -6 .. +6:

 Difficulty Trivial Easy Routine Difficult Very Difficult Impossible Roll.. 3 6 9 12 15 18 Dice Mod. -6 74,07% 37,50% 9,26% 0,46% 0 0 -5 83,80% 50,00% 16,20% 1,85% 0 0 -4 90,74% 62,50% 25,93% 4,63% 0 0 -3 95,37% 74,07% 37,50% 9,26% 0,46% 0 -2 98,15% 83,80% 50,00% 16,20% 1,85% 0 -1 99,54% 90,74% 62,50% 25,93% 4,63% 0 0 100,00% 95,00% 74,07% 37,50% 9,26% 0,46% 1 100,00% 98,15% 83,80% 50,00% 9,26% 1,85% 2 100,00% 99,54% 90,74% 62,50% 16,20% 4,63% 3 100,00% 100,00% 95,00% 74,07% 25,93% 9,26% 4 100,00% 100,00% 98,15% 83,80% 37,50% 16,20% 5 100,00% 100,00% 99,54% 90,74% 50,00% 25,93% 6 100,00% 100,00% 100,00% 95,00% 62,50% 37,50%

Judging by these numbers, +4 to +5 is the range that a trained, experienced professional will have. +5 turns Routine tasks into (almost) automatic successes, and lowers the chance of failure for difficult tasks to just under 10%. If our hypothetical trained professional can take things slowly, prepare, or otherwise gain a situational bonus, Difficult checks quickly become automatic successes for him.

At the same time, our +5 professional will still fail Impossible tasks 75% of the time. They are truly challenging, and will require good preparation or a lot of experience to complete successfully.

Freshly-created characters should probably have most of their skills no higher than +1 to +2, and their core skills – their specialization – should be +3 for a few skills, maybe +4 for one skill if they are really pushing it.

 Bonus Definition 0 You took the basic course or picked up some basics informally, perhaps as a hobby. 1 You used the skill professionally for some time, or as a hobby for many, many years. 2 You used the skill professionally for a year or two. 3 4 Your professional specialization for several years, or a side skill used regularly for many years 5 6 Expert in the field 7 8 Top of the field

That’s not a very big budget for handing out numbers. It has to cover skills and, presumably, attributes. And we have to keep in mind that it has to allow for improvement during actual game play; if a character starts out “at the top of his field”, the players will quickly get bored with that.

It also means that attribute modifiers either need to be kept very low – if, say, an exceptional intelligence were to give +3 to all knowledge, science and similar skills it is easy to see that attributes would quickly dominate the game’s balance. That kind of bonus should be limited to exceptionally “gifted” individuals.

Perhaps there is another solution, though. For certain things, I will not argue that natural ability will give a person a head start. To continue our intelligence example: A really smart person has an easy time picking up mathematics. But math is not something you just invent for yourself (unless your are a Newton or a Leibniz, and even then you basically spend years teaching yourself). A less intelligent person who spends time studying math will outperform the smart person who has no training very quickly.

So instead of applying ability bonuses to skills, perhaps we should see the two independently from each other. A high ability score could make acquisition of associated skills easier, or it could perhaps allow for higher overall skill levels for this particular character. In the later case, though, we will have to allow a player fairly fine control over his ability scores, and the possibility to raise them in-game – doesn’t have to be easy, but it has to be possible.

However, this is getting to the point at which we have to formulate an actual character generation system and to actually play-test it to see if all this theory works out after all. And that’s for the next post in this series.

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