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*Surf remixes monster Armor Class....*

Monster AC was probably the least difficult part of rebooting monster math...

__Armor Class__

#### Scaling Up

A modest amount of analysis reveals an obvious issue with the way monster AC in the final packet scales up. At level 1 same-level monsters can be hit on a 9, but this value *declines* as level increases. A level 20 PC can hit Asmodeus on an roll of 6 and a first level PC only needs to roll 13 to hit him. And this is in keeping with the AC progression evident in the current monsters. Ideally level 1&2 PCs would hit same-levels monsters on a 9, then from levels 5 through 20 they hit on 10 or 11, finally they'd hit level 25 *Normal* creatures with a roll of about 11 or 12.

Is it appropriate for level 1 PCs to only hit level 20 monsters on a 19 or 20? I think so.

These actual required dice roll numbers are a very good fit for a simple power equation (roll=9 x Level ^ 0.08). For a derived formula we simply add the PC attack bonus (attack_bonus=Level x 0.368 + 3.798) to this required roll. The result of this isn't something we can easily match with a simple Power or Logarithmic formula, much less a Linear formula. It is, however, trivially matched using a simple Polynomial formula.

A little curve matching gives us a poly2 formula which produces results functionally equivalent to our derived formula, after rounding. Note the graphs on this page plot data before rounding. Once rounding is applied the derived and poly2 curves have only three minor points of difference. There is significantly more variation within monster samples of the same type an level than this variation represents. We can make a choice between a simpler variation and a perfect match at this point. I personally was happy to this poly2 formula for some time and it's perfectly appropriate for most DMs' use.

That said I know there will be those who strongly desire a closer match. For these readers I have provided a poly3 equation which exactly reproduces the derived curve, once rounded.

Level | Derived | Poly2 | Poly3 |
---|---|---|---|

1 | 13 | 13 | 13 |

2 | 14 | 14 | 14 |

3 | 15 | 14 | 15 |

4 | 15 | 15 | 15 |

5 | 16 | 16 | 16 |

6 | 16 | 16 | 16 |

7 | 17 | 17 | 17 |

8 | 17 | 17 | 17 |

9 | 18 | 18 | 18 |

10 | 18 | 18 | 18 |

11 | 19 | 19 | 19 |

12 | 19 | 19 | 19 |

13 | 20 | 20 | 20 |

14 | 20 | 20 | 20 |

15 | 20 | 21 | 20 |

16 | 21 | 21 | 21 |

17 | 21 | 21 | 21 |

18 | 22 | 22 | 22 |

19 | 22 | 22 | 22 |

20 | 22 | 23 | 22 |

21 | 23 | 23 | 23 |

22 | 23 | 23 | 23 |

23 | 24 | 24 | 24 |

24 | 24 | 24 | 24 |

25 | 25 | 25 | 25 |

#### Scaling Out

My review didn't suggest that any corrections to the previously discussed method for scaling out AC were required. The Easy (-2), Hard (+1) and Tough (+2) multipliers appear to still be quite appropriate.

#### Formulae

To summarise the formulae discussed for the AC reboot...- AC (derived) = (9 x Level ^ 0.08) + (Level x 0.368 + 3.798)
- AC (poly2) = -0.0049 x Level ^ 2 + 0.5959 x Level + 12.681
- AC (poly3) = 0.0004 x Level ^ 3 - 0.0205 x Level ^ 2 + 0.7453 x Level + 12.445
- Easy AC = AC - 2
- Tough AC = AC + 1
- Solo AC = AC + 2

And to the left you will find a table containing the "scaling up" values for the two key formulae, after appropriate rounding.

Check back in a couple of days for the Hit Points review...