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.

5 comments:

  1. Hmmm... What if instead of a separate roll for each item, each +1 from your total number of items or whatever gave you another "magic number." So if you had a cloak of protection +1, a ring of protection +1, and a shield, that would allow you to pick three numbers. You might put a cap on how many they can use at any time, like four such or something.

    ReplyDelete
  2. @Trollsmyth

    Yeah, I think it depends on if your players 1) have multiple d10's/d20's are fast at rolling them vs 2) can quickly come up with and remember 1-4 "magic numbers" after rolling die.

    btw, part of the coolness I think is allowing players to pick their own magic number.

    ReplyDelete
  3. We haven't found the extra dice rolls to be onerous - but then we already have a dice-rolling step when a player is hit, because of the way we do hit dice.

    I think part of the coolness is allowing players to roll during the monster phase; that's a fun thing to do when it has the chance of saving your bacon! On this theory it might be a good and time-saving idea to have the players roll their own rolls to be hit (either by having them roll the dice for the monster attacking them, or doing a mathematical transform so that they're doing a roll-high "dodge roll" against a monster's fixed to-hit number), and rolling their armor save as part of that handful.

    trollsmyth, giving extra magic numbers would work (at least up to the point where they have so many pluses that any number is a save), and would reduce the need to roll multiple dice - although many of my players do have just one d20 and IMO the extra time spent rolling it is worth the tension and concrete visualization of saying "does my magic armor save? okay, what about my cloak?"
    - Tavis

    ReplyDelete
  4. This comment has been removed by the author.

    ReplyDelete
  5. If it seems like players are taking a long time to call out their lucky numbers before rolling, the DM could just institute a rule that each player picks his or her lucky numbers at the beginning of each session, writes them down, and uses them for that day. They can change their lucky numbers if they want, but not during combat.

    ReplyDelete

All Time Most Popular Posts