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.

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.

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.

Grade	New Roll	New Mean	New Delta Mean	New Min	New Max		PF Roll	PF Mean	PF Delta Mean	PF Min	PF Max
1	1	1	–	1	1		1	1	–	1	1
2	1d2	1.5	0.5	1	2		1d2	1.5	0.5	1	2
3	1d3	2	0.5	1	3		1d3	2	0.5	1	3
4	1d4	2.5	0.5	1	4		1d4	2.5	0.5	1	4
5	1d6	3.5	1	1	6		1d6	3.5	1	1	6
6	1d8	4.5	1	1	8		1d8	4.5	1	1	8
7	1d10	5.5	1	1	10		1d10	5.5	1	1	10
8	2d6	7	1.5	2	12		2d6	7	1.5	2	12
9	2d8	9	2	2	16		2d8	9	2	2	16
10	2d10	11	2	2	20		3d6	10.5	1.5	3	18
11	3d8	13.5	2.5	3	24		3d8	13.5	3	3	24
12	3d10	16.5	3	3	30		4d6	14	0.5	4	24
13	3d12	19.5	3	3	36		4d8	18	4	4	32
14	5d8	22.5	3	5	40		6d6	21	3	6	36
15	5d10	27.5	5	5	50		6d8	27	6	6	48
16	5d12	32.5	5	5	60		8d6	28	1	8	48
17	7d10	38.5	6	7	70		8d8	36	8	8	64
18	10d8	45	6.5	10	80		12d6	42	6	12	72
19	8d12	52	7	8	96		12d8	54	12	12	96
20	17d6	59.5	7.5	17	102		16d6	56	2	16	96
21	15d8	67.5	8	15	120		16d8	72	16	16	128
22	17d8	76.5	9	17	136		24d6	84	12	24	144
23	19d8	85.5	9	19	152		24d8	108	24	24	192
24	9d20	94.5	9	9	180		32d6	112	4	32	192
25	19d10	104.5	10	19	190		32d8	144	32	32	256
26	11d20	115.5	11	11	220		48d6	168	24	48	288
27	20d12	130	14.5	20	240		48d8	216	48	48	384
28	14d20	147	17	14	280		64d6	224	8	64	384
29	16d20	168	21	16	320		64d8	288	64	64	512
30	30d12	195	27	30	360		96d6	336	48	96	576

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.