Thursday, July 28, 2011

Stat Rolling and Power Level

I greatly prefer rolling up characters rather than using point buy systems or standardized arrays, but I still want characters to be reasonably balanced amongst themselves and against the opposition they will face. Many games like D&D and Pathfinder provide power level guidelines for use with point buying but don't offer much in the way of help when rolling dice for stats. So I whipped up a program to help me see how different stat rolling methods ranked in terms of power level.

I used every dice rolling method I could think of that just used straight dice rolling or just dice plus or minus a set number. For power level comparisons, I used the point buy system and power levels given in Pathfinder. I did add two new levels to what they have- Gritty Fantasy (~5 points) and Super Hero Fantasy (~30 points).

Hopefully, the Methods are self explanatory. The Ranges are the limits of scores possible. The Avg. Stat is the mean score you would expect to roll. The Deviation is the standard deviation of the point values rolled for characters - the lower the better if you want your party to be fairly balanced. And the Avg. Cost is the average point buy value of characters.

Gritty Fantasy - 5 points or less

Method Range Avg. Stat Deviation Avg. Cost
1d10 + 2d4 3 - 18 10.5 13.0 2.5
3d6 3 - 18 10.5 11.5 2.6
5d6 drop high & low 3 - 18 10.5 11.0 2.7
5d4 - 2 3 - 18 10.5 8.7 2.8
2d8 + 2 4 - 18 11.0 13.1 7.7
3d6, ones = twos 6 - 18 11.0 9.0 7.7
3d6 reroll < 7 7 - 18 11.0 8.8 8.4

Low Fantasy - 10 points

Method Range Avg. Stat Deviation Avg. Cost
3d6 roll 7 times, take 6 best 3 - 18 11.2 10.0 9.1
3d6 reroll < 8 8 - 18 11.4 8.3 11.1
3d6, ones = threes 6 - 18 11.5 8.2 11.5
2d6 + 1d4 + 2 5 - 18 11.5 9.8 11.8
1d8 + 2d4 + 2 5 - 18 11.5 10.3 12.1
4d6 mirror 23 5 - 18 11.5 2.3 12.4
3d6 roll 8 times, take 6 best 3 - 18 11.6 9.6 12.7

Standard Fantasy - 15 points

Method Range Avg. Stat Deviation Avg. Cost
4d4 + 2 6 - 18 12.0 8.1 15.2
3d6, ones = fours 6 - 18 12.0 8.1 15.2
3d6 roll 9 times, take 6 best 3 - 18 12.0 9.4 15.4
3d6 reroll ones 6 - 18 12.0 9.2 15.9
1d8 + 1d6 + 4 6 - 18 12.0 11.3 17.3
3d6 roll twice each, keep best 3 - 18 12.2 9.4 17.3
1d10 + 1d4 + 4 6 - 18 12.0 12.2 18.1
4d6 drop lowest 3 - 18 12.2 11.5 18.7

High Fantasy - 20 points

Method Range Avg. Stat Deviation Avg. Cost
3d6, ones = fives 6 - 18 12.5 9.0 19.9
1d6 + 2d4 + 4 7 - 18 12.5 9.2 20.2
3d6 roll 12 times, take 6 best 3 - 18 12.7 9.5 21.2
4d6 mirror 25 7 - 18 12.5 3.9 21.5
4d6 mirror 27, 25, 23 - see comments 5 - 18 12.5 3.6 21.7

Epic Fantasy - 25 points

Method Range Avg. Stat Deviation Avg. Cost
1d12 + 6 7 - 18 12.5 15.0 25.5
2d6 + 6 8 - 18 13.0 10.6 25.7
3D6, ones = sixes 6 - 18 13.0 11.3 26.1
3d4 + 6 9 - 18 13.5 9.0 28.8

Super Hero Fantasy - 30 points or more

Method Range Avg. Stat Deviation Avg. Cost
5d6 drop 2 lowest 3 - 18 13.4 11.7 30.6
4d6 mirror 27 9 - 18 13.5 4.3 31.2
1d10 + 8 9 - 18 13.5 13.9 34.1
3d6, roll 6 times for each 3 - 18 14.2 9.5 36.7

And the Winners are...

My favorites for each power level are:

  • Gritty Fantasy: 3d6 Reroll < 7
    This method curbs a lot of the harshness of rolling up stats for an iron-man old school game. It's low deviation and high minimum of 7 should make for decent, if average, player characters.
  • Low Fantasy: 4d6 mirror 23
    It has a very low deviation and a decent minimum score.
  • Standard Fantasy: 4d4 + 2
    Comes in right at 15 points with a low deviation and a high minimum score.
  • High Fantasy: 4d6 mirror 25
    High minimum scores and a very low deviation make this a winner.
  • Epic Fantasy: 2d6 + 6
    This one comes closest to 25 points while also giving a smaller deviation.
  • Super Hero Fantasy: 4d6 mirror 27
    The best for creating a balanced group.

Thanks to Keith for reminding me of the mirror method (described in detail here- http://www.kjd-imc.org/2007/06/21/ability-score-generation/ and here- http://home.earthlink.net/~duanevp/dnd/stat_generation.htm). It really does work very well.