# Who else wants unified mechanics in RPGs?

I’m thinking about running a *Beyond the Wall and Other Adventures* game,
so I sat down and read through the rules. Everything felt very familiar.
Characters can be one of three types: warriors, rogues, or mages. Levels range
from 1^{st} (a bit above ordinay) to 10^{th} (heroes of the
land). Ability scores range from 1 to 19, and each character has six abilities:
strength, dexterity, constitution, intelligence, wisdom, and charisma.

I use abilities by rolling a twenty sided dice (1d20) and trying to get less than or equal to my ability score. So if want to jump over a stream, and my dexterity is 16, rolling a 19 means I fall in the water.

I also get to use abilities in combat. Ability scores map to bonuses. I attack
by rolling a twenty sided dice, adding my bonuses, and trying to get greater
than or equal to my opponent’s armor. So if I want to shoot a bow at a
cockatrice (14 armor), and I’m a 1^{st} level rogue (+0 bonus)
whose dexterity is 16 (+2 bonus), rolling a 19 means my I hit the cockatrice.

Wait, what? Rolling a 19 when shooting a bow is a success, but rolling a 19 when jumping is a failure. I find that confusing. I kind of expect that when I’m rolling a twenty sided dice, 1 is going to be a failure and 20 is going to be a success, and the stuff in the middle is going to be a probability curve with bigger numbers meaning “more likely to be a success”.

New player experiences matter. I was teaching a friend Gloomhaven, and we talked about how lowest initiative goes first, and they said, “That doesn’t make any sense. If I have more initiative, I should go first.” They were right. I’ve played Gloomhaven so much that I’ve internalized the “lower initiative goes first” rule, so I didn’t bother to question it.

But I haven’t played *Beyond the Wall*, yet. So I’m going to question these
“roll low for ability checks; roll high for combat” rules, and see how I might
change them.

What does it mean, mathematically, for my character to have a dexterity of 16? It means that I’m going to succeed at 80% of my dexterity checks, because 16 divided by 20 is 0.8. So the probability of any ability check succeeding is the value of that check divided by 20.

P(A) = A 20

Here’s a table of ability scores, from 1 to 19, as a percentage success rate.

Ability Score | Success Rate |
---|---|

1 | 5% |

2 | 10% |

3 | 15% |

4 | 20% |

5 | 25% |

6 | 30% |

7 | 35% |

8 | 40% |

9 | 45% |

10 | 50% |

11 | 55% |

12 | 60% |

13 | 65% |

14 | 70% |

15 | 75% |

16 | 80% |

17 | 85% |

18 | 90% |

19 | 95% |

If I want to change the math for ability scores, I can’t break this table. Having a dexterity of 16 should always mean I have an 80% chance of success on a dexterity ability check.

I want ability checks to feel simlar to combat rolls. I roll a twenty sided dice, add my ability score, and check if the total is greater than or equal to a target number. If it is, I succeed; otherwise, I fail.

1d20 + A ≥ ?

What should that target number be? The design notes in Ben Milton’s game
*Knave*, have some clues.

Requiring saves to exceed 15 means that new PCs have around a 25% chance of success, while level 10 characters have around a 75% chance of success, since ability bonuses can get up to +10 by level 10. This reflects the general pattern found in the save mechanics of early D&D.

Ability bonuses in *Knave* range from 0 to 6. Characters make saving throws by
rolling a twenty sided dice, adding their ability bonus, and checking to see if
the total is greater than 15. If it is, they succeed; otherwise, they fail.
That’s pretty much what I want, so I need some way to map the ability scores in
*Beyond the Wall* to the ability bonuses in *Knave*.

The character playbooks in *Beyond the Wall* start most ability scores at 8, a
40% success rate. So I can subtract 8 from an ability score to get something
that fits in the smaller range of the *Knave* system.

1d20 + A - 8 > ?

Witht this formula, a target value of 15 gives a new character a 25% success rate. The success rate is the number of ways to roll a twenty sided dice and get greater than the target value. Mathematically, that’s 20 minus the target value, divided by 20.

S = 20 - T 20

Because I don’t want to break *Beyond the Wall*, I need to find a target value
that keeps the success rate for new characters stays at 40%.

0.4 = 20 - T 20

20 × 0.4 = 20 - T

8 = 20 - T

8 + T = 20

T = 20 - 8

T = 12

I can use a target value of 12 for ability chceks. Since I subtracted 8 to move
ability scores into a *Knave* range, I can add 8 to move them back to a
*Beyond the Wall* range. Finally, I can change “greater than” to “greater than
or equal”, so ability checks follow the same “my character wins ties” rule as
combat rolls.

1d20 + A - 8 > 12

1d20 + A > 12 + 8

1d20 + A > 20

1d20 + A ≥ 21

So I can use abilities in *Beyond the Wall* by rolling a twenty sided dice,
adding my ability score, and trying to get greater than or equal to 21.

Does the success rate math still work? If I’ve got a dexterity of 16, that should be an 80% success rate. If I roll a 5 or more, I’ll pass the skill check. There are sixteen ways to do that with a twenty sided dice, and 16 divided by 20 is 0.8. It works!

I’m not the first person to figure this out. As Saelorn points out in an En World thread about dice mechanics

If you already have the concept of DCs [difficulty checks] in place for things like attack rolls and saving throws, then you could use a mechanic of d20 + stat score against a constant DC 21, and it would give the exact same distribution.

Now all my checks can use a unified mechanic: roll a twenty sided dice, add bonuses, and compare with a target value. An unmodified roll of 20 is always a success, while a 1 is always a failure.