# Smoother Damage Progression

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.

 Pathfinder Damage Progression New Damage Progression

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.

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.

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.

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1. David Lamb

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 :)

• David Lamb

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

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