RPG Mechanics Workshop: Target Numbers, Take 2

After Mecha kindly pointed out that the numbers that I was assuming were play-tested had changed substantially after release. As a result, the numbers I used earlier today were quite off.

Here's my second take:

In fourth edition DnD (DnD 4e) the basic mechanic is to take a d20 and roll while hoping to roll equal or higher than the target number (TN). The standard target numbers are 5 for an easy difficulty roll, 10 for a medium difficulty roll and 15 for a hard roll. If the roll deals with something your character is good at, you'll have a bonus. For the purposes of this exercise, those bonuses range from -1 (no skill and you're below human average at the stat) to +8 (you've done everything possible to boost that number).

The above paragraph is an over simplification. It doesn't deal with the level "treadmill." As characters get more powerful, their challenges get more difficult. This is meant to keep things from getting boring. I factored out the treadmill to deriving the 5, 10, and 15 values mentioned above.    The base numbers are available in the DMG errata in the section under the header page 42.

After deriving what good target numbers for a uniform distribution d20 system, I had to figure out the equivalents in a normal distribution 2d6 system.  The match-ups aren’t perfect.  In a uniform distribution, if the target number increases by one, the probability of success goes down by a constant amount.  This is because every number is equally likely to be rolled.  That isn’t true for a normal distribution because with 2d6 there’s six ways to roll a 7 but only one way to roll a 2.  

Even with two different distributions, the curves match up reasonably well. 

• The DnD 4e D20 range from –1 to +8 translate to +0 to +4 in 2d6
• Easy 5/medium 10/hard 15 translates to a TN of 6, 8, and 10, respectively.
• There’s one key difference between easy rolls and medium/hard rolls in the DnD 4e table.  The medium/hard rolls  rise at at a rate of +2 / 3 levels.  The easy rolls rise at a rate of +1.5 / 3 levels.
• This means that the game assumes the characters are not specializing in the skills they’ll be using to make easy rolls.  This seems like a sensible trick, and I’ll steal it for Besm 3e’s benchmarks.
• I’m still pondering what to do with static targets a la DnD 4e defense values.  I’m thinking I’ll go with 7, so between medium and hard.  I haven’t made my mind up on that yet.

This all gets more complicated once I factor in tier-based expected minimums.  However, that can wait for another week.