Thursday, March 11, 2010

AC Bonus vs Save, Death Match!

For various reasons I'm really wanting AC to be only armor and not a bunch of other stuff e.g. dex bonus, magic bonus, spell buff. I'm also trying to eliminate as many modifiers during game play as possible.

Using Target 20 with only positive AC (10-0). No Dex modifiers. I was also gonna ditch +x items until I read this magical +x bonus dice mechanic. Which is a great method for handling +x protective items. (well not so sure about picking two numbers and rolling multiple d20's rather than one number and d10's or picking one number per bonus and rolling single d10). Might even use it for shield bonus. Although, keeping "magic" as a separate/special mechanic has appeal.


It So Awesome

It makes +x magic less mundane. It also has the same effect of "Saving throws must be requested by players"(lost link). It puts more of players fate in to their hands. Like The Mule said it provides dramatic tension and excitement at the table over rolling dice.
"... take aspects of the game that normally get resolved off-screen beforehand and instead make them happen at the table as the spotlighted consequence of a dramatic event."

"... even if a PC’s magical protection will stop a blow most of the time, I want to make the players sweat in the interval between when I announce the hit and when their magic save comes through for them!"
And it speeds combat resolution.
"... dozens of men-at-arms in the combat it’s much easier if I can just roll a handful of dice and count all the 17s or above, knowing that such rolls always have a chance of hitting any target."

Lies, and Damn Lies

I was real curious about the statistical analysis. So, I broke out my Python dice code and ran (a lot) of tests. First, some results I'm not gonna bother showing you:
  • picking one number and rolling d10 was close enough to picking two numbers and rolling d20 that I'm only using former.
  • picking one number and rolling d20 caused even greater variation than d10s so ditched that idea.
So, pick one number, roll d10's equal to bonus, if number comes up then no hit (a save). Bonus from 1 to 3, to hit from 1 to 9, even ACs 10 to 2. Random results (rather than calculated) so 100,000 swings were made per row.

d20 + (AC-bonus) + tohit >= 20 is a hit
d20 + AC + tohit >= 20 and failed save(s) is a hit

100000 iterations of +1 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 54.92% | AC 10 53.94% | 0.98% |
AC 7 45.07% | AC 8 44.94% | 0.13% |
AC 5 34.93% | AC 6 35.96% | -1.03% |
AC 3 24.85% | AC 4 26.88% | -2.03% |
AC 1 15.02% | AC 2 18.06% | -3.04% |

100000 iterations of +1 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 50.27% | AC 10 48.79% | 1.48% |
AC 6 40.05% | AC 8 40.63% | -0.58% |
AC 4 30.09% | AC 6 32.64% | -2.55% |
AC 2 20.12% | AC 4 24.42% | -4.30% |
AC 0 9.97% | AC 2 16.18% | -6.22% |

100000 iterations of +1 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 44.84% | AC 10 43.78% | 1.06% |
AC 5 35.04% | AC 8 36.30% | -1.26% |
AC 3 25.00% | AC 6 29.23% | -4.23% |
AC 1 15.03% | AC 4 21.96% | -6.93% |
AC -1 5.00% | AC 2 14.53% | -9.52% |


100000 iterations of +2 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 60.14% | AC 10 58.63% | 1.51% |
AC 7 49.67% | AC 8 49.26% | 0.42% |
AC 5 40.20% | AC 6 40.66% | -0.46% |
AC 3 29.76% | AC 4 31.36% | -1.60% |
AC 1 19.88% | AC 2 22.25% | -2.37% |

100000 iterations of +2 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 54.93% | AC 10 52.52% | 2.41% |
AC 6 45.04% | AC 8 44.53% | 0.51% |
AC 4 35.14% | AC 6 36.41% | -1.26% |
AC 2 24.88% | AC 4 28.32% | -3.44% |
AC 0 15.02% | AC 2 20.10% | -5.08% |

100000 iterations of +2 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 49.80% | AC 10 47.04% | 2.76% |
AC 5 40.08% | AC 8 40.14% | -0.05% |
AC 3 29.80% | AC 6 32.88% | -3.07% |
AC 1 20.01% | AC 4 25.37% | -5.36% |
AC -1 9.88% | AC 2 17.97% | -8.09% |


100000 iterations of +3 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 64.88% | AC 10 62.93% | 1.95% |
AC 7 54.92% | AC 8 53.98% | 0.94% |
AC 5 45.21% | AC 6 45.25% | -0.04% |
AC 3 34.89% | AC 4 35.91% | -1.02% |
AC 1 24.94% | AC 2 27.00% | -2.06% |

100000 iterations of +3 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 60.03% | AC 10 56.57% | 3.46% |
AC 6 50.16% | AC 8 48.76% | 1.40% |
AC 4 40.01% | AC 6 40.51% | -0.50% |
AC 2 29.96% | AC 4 32.17% | -2.21% |
AC 0 19.80% | AC 2 24.21% | -4.41% |

100000 iterations of +3 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 55.19% | AC 10 51.02% | 4.17% |
AC 5 44.88% | AC 8 43.71% | 1.17% |
AC 3 35.09% | AC 6 36.39% | -1.30% |
AC 1 25.08% | AC 4 29.24% | -4.16% |
AC -1 14.93% | AC 2 21.82% | -6.89% |


100000 iterations of +4 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 69.88% | AC 10 67.56% | 2.32% |
AC 7 59.88% | AC 8 58.40% | 1.48% |
AC 5 49.88% | AC 6 49.41% | 0.46% |
AC 3 39.81% | AC 4 40.42% | -0.61% |
AC 1 29.93% | AC 2 31.30% | -1.36% |

100000 iterations of +4 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 65.08% | AC 10 60.70% | 4.39% |
AC 6 55.06% | AC 8 52.74% | 2.33% |
AC 4 44.89% | AC 6 44.57% | 0.32% |
AC 2 34.79% | AC 4 36.24% | -1.44% |
AC 0 24.91% | AC 2 28.47% | -3.55% |

100000 iterations of +4 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 59.88% | AC 10 54.75% | 5.12% |
AC 5 49.85% | AC 8 47.28% | 2.58% |
AC 3 39.95% | AC 6 39.99% | -0.04% |
AC 1 30.00% | AC 4 33.13% | -3.12% |
AC -1 20.10% | AC 2 25.47% | -5.37% |


100000 iterations of +5 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 75.06% | AC 10 72.03% | 3.03% |
AC 7 65.09% | AC 8 63.13% | 1.96% |
AC 5 55.04% | AC 6 54.02% | 1.02% |
AC 3 45.02% | AC 4 45.05% | -0.03% |
AC 1 35.12% | AC 2 36.18% | -1.06% |

100000 iterations of +5 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 70.03% | AC 10 64.62% | 5.41% |
AC 6 60.14% | AC 8 56.71% | 3.43% |
AC 4 50.14% | AC 6 48.62% | 1.52% |
AC 2 40.18% | AC 4 40.70% | -0.52% |
AC 0 29.88% | AC 2 32.31% | -2.43% |

100000 iterations of +5 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 65.13% | AC 10 58.43% | 6.70% |
AC 5 54.95% | AC 8 51.22% | 3.74% |
AC 3 45.00% | AC 6 43.71% | 1.29% |
AC 1 34.64% | AC 4 36.24% | -1.60% |
AC -1 24.99% | AC 2 29.20% | -4.21% |


I think you get the idea. Here's the last one, +9 tohit.


100000 iterations of +9 tohit vs +1 to AC or 1d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 9 94.98% | AC 10 90.01% | 4.97% |
AC 7 84.99% | AC 8 81.21% | 3.79% |
AC 5 75.22% | AC 6 72.21% | 3.00% |
AC 3 65.39% | AC 4 63.32% | 2.07% |
AC 1 55.01% | AC 2 53.99% | 1.02% |

100000 iterations of +9 tohit vs +2 to AC or 2d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 8 90.07% | AC 10 80.90% | 9.18% |
AC 6 79.95% | AC 8 72.97% | 6.99% |
AC 4 69.93% | AC 6 65.15% | 4.78% |
AC 2 59.94% | AC 4 56.60% | 3.34% |
AC 0 50.31% | AC 2 48.89% | 1.41% |

100000 iterations of +9 tohit vs +3 to AC or 3d10 save rolls.
hit w/ bonus | hit w/ saves | diff |
AC 7 85.17% | AC 10 72.73% | 12.44% |
AC 5 74.89% | AC 8 65.72% | 9.17% |
AC 3 64.87% | AC 6 58.25% | 6.62% |
AC 1 54.97% | AC 4 51.16% | 3.81% |
AC -1 45.11% | AC 2 43.69% | 1.42% |

Conclusion
  • The difference between normal AC modification and save mechanic vary greatly depending on mix of AC, tohit, bonus.
  • The difference between normal AC modification and save mechanic regularly very large 5-10%
  • Save mechanic starts out mostly worse than AC modification. This gradually changes as tohit bonus increases. At +9 save is always better than AC modification.
  • Save mechanic compresses to hit percentage range i.e. AC10 is less likely and AC2 more likely to be hit.
  • The worse your AC is, the more beneficial saves are. Means bonus items are more valuable to low AC types.
  • The better tohit bonus opponent has, the more beneficial saves are. Means bonus items are less helpful vs weak opponents and very helpful against high lvl threats.
I don't think it bothers me much that this mechanic produces quite different results than modifying AC.

This save mechanic fits very well my ideal for shields. Providing large bonus to light armor and less and less as armor improves. Not mucking up AC, would blend nicely with shields shall be shattered, no changing ac if shield is / is not used. But then I thought of all the freakin dice rolls. Even if used just for +x protective magics I gotta think 1/2 the party is gonna have those and need to make extra dice rolls during combat.

I've become less sold. I really need to try it out in play.

BTW this mechanic is "reversable" for use with +x weapons. If miss with one use similar save mechanic to see if magic makes it a hit anyways. Very powerful for those who can't hit worth a damn. Less useful to martial masters. That sits well with my sensibilities.

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