Some time ago I explored damage progression, how various things that increase damage might be represented with different roles. Much analysis happens there of various options and what they mean, I won’t repeat it here.

I recently had cause to look at the Pathfinder equivalent of the RSRD progression shown in that post, and it exhibits the same things that bothered me there. The Pathfinder table went a little farther than I initially did, so I decided to extend my table and see if I could make something that suited my taste better.

## New Damage Progression

The table below presents a new damage progression that provides a smoother mean increase in damage rolls. Not only do the values always increase, but the amount increased never gets smaller from grade to grade, though it does sometimes remain the same for two or three grades in a row.

Grade |
Damage |
Mean |
Delta Mean |
Min |
Max |

1 | 1 | 1 | – | 1 | 1 |

2 | 1d2 | 1.5 | 0.5 | 1 | 2 |

3 | 1d3 | 2 | 0.5 | 1 | 3 |

4 | 1d4 | 2.5 | 0.5 | 1 | 4 |

5 | 1d6 | 3.5 | 1 | 1 | 6 |

6 | 1d8 | 4.5 | 1 | 1 | 8 |

7 | 1d10 | 5.5 | 1 | 1 | 10 |

8 | 2d6 | 7 | 1.5 | 2 | 12 |

9 | 2d8 | 9 | 2 | 2 | 16 |

10 | 2d10 | 11 | 2 | 2 | 20 |

11 | 3d8 | 13.5 | 2.5 | 3 | 24 |

12 | 3d10 | 16.5 | 3 | 3 | 30 |

13 | 3d12 | 19.5 | 3 | 3 | 36 |

14 | 5d8 | 22.5 | 3 | 5 | 40 |

15 | 5d10 | 27.5 | 5 | 5 | 50 |

16 | 5d12 | 32.5 | 5 | 5 | 60 |

17 | 7d10 | 38.5 | 6 | 7 | 70 |

18 | 10d8 | 45 | 6.5 | 10 | 80 |

19 | 8d12 | 52 | 7 | 8 | 96 |

20 | 17d6 | 59.5 | 7.5 | 17 | 102 |

21 | 15d8 | 67.5 | 8 | 15 | 120 |

22 | 17d8 | 76.5 | 9 | 17 | 136 |

23 | 19d8 | 85.5 | 9 | 19 | 152 |

24 | 9d20 | 94.5 | 9 | 9 | 180 |

25 | 19d10 | 104.5 | 10 | 19 | 190 |

26 | 11d20 | 115.5 | 11 | 11 | 220 |

27 | 20d12 | 130 | 14.5 | 20 | 240 |

28 | 14d20 | 147 | 17 | 14 | 280 |

29 | 16d20 | 168 | 21 | 16 | 320 |

30 | 30d12 | 195 | 27 | 30 | 360 |

The minimum and maximum rolls do not progress as smoothly as the mean. This is mitigated by the number of dice involved: by the time it becomes significant the number of dice is large enough that the rolls will usually be nearer the mean than the extremes.

The number of dice gets pretty silly at the top end, but they are only likely to come up when you’re dealing with a truly big source of damage. I’m pretty sure the spectacle of 19d10 damage (I’m not even sure how you’d get there!) will be memorable.

## Pathfinder Damage Progression

This damage progression is taken from the Pathfinder FAQ. The mean values do not increase in as smooth a manner, but unlike the damage progression above neither the minimum nor maximum values ever decrease from one grade to the next. This does have value, but I think less than having the mean — which will come up more often as the number of dice increases — rising smoothly is more important.

Grade |
Damage |
Mean |
Delta Mean |
Min |
Max |

1 | 1 | 1 | – | 1 | 1 |

2 | 1d2 | 1.5 | 0.5 | 1 | 2 |

3 | 1d3 | 2 | 0.5 | 1 | 3 |

4 | 1d4 | 2.5 | 0.5 | 1 | 4 |

5 | 1d6 | 3.5 | 1 | 1 | 6 |

6 | 1d8 | 4.5 | 1 | 1 | 8 |

7 | 1d10 | 5.5 | 1 | 1 | 10 |

8 | 2d6 | 7 | 1.5 | 2 | 12 |

9 | 2d8 | 9 | 2 | 2 | 16 |

10 | 3d6 | 10.5 | 1.5 | 3 | 18 |

11 | 3d8 | 13.5 | 3 | 3 | 24 |

12 | 4d6 | 14 | 0.5 | 4 | 24 |

13 | 4d8 | 18 | 4 | 4 | 32 |

14 | 6d6 | 21 | 3 | 6 | 36 |

15 | 6d8 | 27 | 6 | 6 | 48 |

16 | 8d6 | 28 | 1 | 8 | 48 |

17 | 8d8 | 36 | 8 | 8 | 64 |

18 | 12d6 | 42 | 6 | 12 | 72 |

19 | 12d8 | 54 | 12 | 12 | 96 |

20 | 16d6 | 56 | 2 | 16 | 96 |

21 |
16d8 |
72 |
16 |
16 |
128 |

22 |
24d6 |
84 |
12 |
24 |
144 |

23 |
24d8 |
108 |
24 |
24 |
192 |

24 |
32d6 |
112 |
4 |
32 |
192 |

25 |
32d8 |
144 |
32 |
32 |
256 |

26 |
48d6 |
168 |
24 |
48 |
288 |

27 |
48d8 |
216 |
48 |
48 |
384 |

28 |
64d6 |
224 |
8 |
64 |
384 |

29 |
64d8 |
288 |
64 |
64 |
512 |

30 |
96d6 |
336 |
48 |
96 |
576 |

The rows *in italics* are my extension to the published table. The pattern is consistent: at every grade starting with the 12th, the dice rolled are twice as many as four grades earlier.

## Comparison

The tables above show the numbers, but I think the charts below make it even more evident how the new progression suits my taste better.

It’s pretty easy to see that the new progression is much smoother in how the mean (blue line) and maximum (yellow line) damage increase. The delta in the mean (orange line) increases more smoothly as well. The minimum (grey) damage is less smooth, but I’m not particularly interested in that.

It is also evident that the new progression is shallower than the Pathfinder progression. I actually like that, and expect it will work better for me when I finally reach into that range.

## Closing Comments

Both damage progressions are workable.

The Pathfinder progression is designed so that minimum and maximum values never decrease as the grades increase. It also sticks to more regular dice, using primarily d6 and d8. However, the change in the mean swings back and forth through the grades, so the expected improvement from grade to grade might not be all that much.

The progression I present is designed so the mean values and the delta between them, the expected improvement from grade to grade, never decrease. This requires use of a broader range of dice (d10 and d12 show up almost as often as d6 and d8, and even d20 shows up) and the number of dice will vary from grade to grade. As a result, the minimum value that can be rolled swings back and forth, but while the maximum value that can be rolled always increases, the amount of this increase is not always growing (from grades 15 through 18 the maximum grows by 10, then at grade 19 it increases by 16, then at grade 20 it increases by 6). On the other hand, it swings less than the Pathfinder progression (grade 16 increases by 0, but grade 17 increases by 16… then level 18 increases by 8, and grade 19 by 24).

Another significant difference lies in the values themselves. The Pathfinder progression runs consistently higher in mean, minimum, and maximum values at higher grades. They stay fairly close until grade 20, and then the doubling really starts to have effect and the results diverge. I’ll see if it makes a difference if I’m ever in a position to roll 96d6 damage for something, rather than 30d12.

I like your progression. The mean is much more important to me than the min, and it’s nice that the max is monotonic, too.

‘Monotonic’, not ‘monotonous’. Good :)

Math geekitude for “dependent variable is non-decreasing function of independent one”