GreatInca
2014-06-23, 10:47 PM
I think this is a good solution for guaranteeing a very reasonable but not overwhelmingly overpowered character but still having some randomness in the D&D ability scores. Start with a fixed matrix and add 1D4 to each stat (auto 18 for high-stat for 5D6k3 & 6D6k3 power levels).
It is intended to have a slightly bad / mediocre roll result in the bottom of the range, a fairly good roll in the middle, and a very good, but not extremely lucky roll in the top of the range. Max possible bonus total difference between two characters is 6 and will be more likely 2-4. It is to serve as a compromise for DMs that want dice while the players want point-buy. Dice are usually (highest power to lowest power) 5D6k3-assign, 2D6+6-assign, 4D6k3-assign, 4D6k3-Organic, 3D6-assign, or 3D6 Ironman. Dark Sun derived 5D4-2 and 4D4+2 are also viable alternatives.
Plain English:
~3D6:
Start with {13,11,9,9,7,5}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~4D6 keep best 3:
Start with {14,13,11,9,9,7}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~5D6 keep best 3:
Automatic 18 for 1st stat. For remaining 5 stats, start with {13,13,11,9,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~6D6 keep best 3:
Automatic 18 for 1st stat. For remaining 5 stats, start with {14,14,11,11,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
The numbers (standard deviations, percentiles, statistical z-scores, etc..):
All ranges other than the single fixed-18 in 5D6K3 and 6D6K3 are 1D4+xx. Z-Scores are for StatSum, BonusSum, and PointBuyPFSum. Z-Score is (Value-Avg)/StdDev. Percentiles are biased to the bonus total, then point buy values, then the stat sum. Point buy values and stat sums can be high compared to bonus totals due to the non-optimal odd valued stats.
3D6 targeted power level:
Min: {14,12,10,10, 8, 6}: 60 tot, 10.00 avg, 0 bonus, 12 PB-35, -1 PB-PF, 45.1 Ntile, -0.4/-0.0/-0.4 Z-score
Max: {17,15,13,13,11, 9}: 78 tot, 13.00 avg, 6 bonus, 35 PB-35, 26 PB-PF, 96.0 Ntile, +2.1/+1.6/+2.1 Z-score
Avg: {16,13,12,11,10, 7}: 69 tot, 11.83 av`g, 3 bonus, 23 PB-35, 12 PB-PF, 80.0 Ntile, +0.8/+0.8/+0.8 Z-score
1D4+11, 1D4+11, 1D4+9, 1D4+9, 1D4+7, 1D4+7
Start with {13,11,9,9,7,5}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
4D6K3 targeted power level:
Min: {15,14,12,10,10, 8}: 69 tot, 11.50 avg, 4 bonus, 22 PB-35, 12 PB-PF, 31.9 Ntile, -0.6/-0.3/-0.6 Z-score
Max: {18,17,15,13,13,11}: 87 tot, 14.50 avg, 11 bonus, 50 PB-35, 44 PB-PF, 96.4 Ntile, +1.9/+1.6/+2.2 Z-score
Avg: {17,15,14,12,11, 9}: 78 tot, 13.00 avg, 7 bonus, 35 PB-35, 27 PB-PF, 71.6 Ntile, +0.6/+0.5/+0.7 Z-score
1D4+14, 1D4+13, 1D4+11, 1D4+9, 1D4+9, 1D4+7
Start with {14,13,11,9,9,7}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
5D6K3 targeted power level:
Min: {18,14,14,12,10,10}: 78 tot, 13.00 avg, 9 bonus, 36 PB-35, 29 PB-PF, 49.0 Ntile, -0.4/+0.1/-0.1 Z-score
Max: {18,17,17,15,13,13}: 93 tot, 15.50 avg, 14 bonus, 60 PB-35, 56 PB-PF, 96.5 Ntile, +1.9/+1.6/+2.2 Z-score
Avg: {18,16,15,14,12,11}: 86 tot, 14.33 avg, 12 bonus, 47 PB-35, 42 PB-PF, 83.6 Ntile, +0.8/+1.0/+1.0 Z-score
18, 1D4+13, 1D4+13, 1D4+11, 1D4+9, 1D4+9
Automatic 18 for 1st stat. For remaining 5 stats, start with {13,13,11,9,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
6D6K3 targeted power level:
Min: {18,15,15,12,12,10}: 82 tot, 13.67 avg, 10 bonus, 42 PB-35, 35 PB-PF, 33.7 Ntile, -0.6/-0.5/-0.3 Z-score
Max: {18,18,18,15,15,13}: 97 tot, 16.17 avg, 17 bonus, 69 PB-35, 68 PB-PF, 98.1 Ntile, +2.0/+1.9/+2.1 Z-score
Avg: {18,17,16,14,13,12}: 90 tot, 15.00 avg, 14 bonus, 54 PB-35, 50 PB-PF, 80.6 Ntile, +0.8/+0.9/+0.8 Z-score
18, 1D4+14, 1D4+14, 1D4+11, 1D4+11, 1D4+9
Automatic 18 for 1st stat. For remaining 5 stats, start with {14,14,11,11,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
D&D Next (5E) point buy cost totals are always exactly 12 higher than the Pathfinder point-buy cost totals, as long as the lowest stat is 8 or higher.
As to my existing groups' ability score methods - all are very high powered for stats:
David @ East Mesa:
5D6k3-assign - Liberal on magic items, best storyline; 3-5 players
John @ Desert Sky Games:
52-pt point buy (3.5 point-buy rules) - Stingy on magic items; 5-8 players
Daryn @ Game Depot:
52-pt point buy (3.5 point-buy rules) - Large battles, high character mortality; 4-6 players
Mark @ Fountain Hills:
fixed array {18con, 18, 16, 14, 12, 10} - Lot of house rules, high-powered; 2-4 players
An online VTT game:
fixed array {18, 16, 16, 14, 14, 12} - Skill heavy, lot of up-levelled monsters; 5-6 players
It is intended to have a slightly bad / mediocre roll result in the bottom of the range, a fairly good roll in the middle, and a very good, but not extremely lucky roll in the top of the range. Max possible bonus total difference between two characters is 6 and will be more likely 2-4. It is to serve as a compromise for DMs that want dice while the players want point-buy. Dice are usually (highest power to lowest power) 5D6k3-assign, 2D6+6-assign, 4D6k3-assign, 4D6k3-Organic, 3D6-assign, or 3D6 Ironman. Dark Sun derived 5D4-2 and 4D4+2 are also viable alternatives.
Plain English:
~3D6:
Start with {13,11,9,9,7,5}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~4D6 keep best 3:
Start with {14,13,11,9,9,7}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~5D6 keep best 3:
Automatic 18 for 1st stat. For remaining 5 stats, start with {13,13,11,9,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
~6D6 keep best 3:
Automatic 18 for 1st stat. For remaining 5 stats, start with {14,14,11,11,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
The numbers (standard deviations, percentiles, statistical z-scores, etc..):
All ranges other than the single fixed-18 in 5D6K3 and 6D6K3 are 1D4+xx. Z-Scores are for StatSum, BonusSum, and PointBuyPFSum. Z-Score is (Value-Avg)/StdDev. Percentiles are biased to the bonus total, then point buy values, then the stat sum. Point buy values and stat sums can be high compared to bonus totals due to the non-optimal odd valued stats.
3D6 targeted power level:
Min: {14,12,10,10, 8, 6}: 60 tot, 10.00 avg, 0 bonus, 12 PB-35, -1 PB-PF, 45.1 Ntile, -0.4/-0.0/-0.4 Z-score
Max: {17,15,13,13,11, 9}: 78 tot, 13.00 avg, 6 bonus, 35 PB-35, 26 PB-PF, 96.0 Ntile, +2.1/+1.6/+2.1 Z-score
Avg: {16,13,12,11,10, 7}: 69 tot, 11.83 av`g, 3 bonus, 23 PB-35, 12 PB-PF, 80.0 Ntile, +0.8/+0.8/+0.8 Z-score
1D4+11, 1D4+11, 1D4+9, 1D4+9, 1D4+7, 1D4+7
Start with {13,11,9,9,7,5}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
4D6K3 targeted power level:
Min: {15,14,12,10,10, 8}: 69 tot, 11.50 avg, 4 bonus, 22 PB-35, 12 PB-PF, 31.9 Ntile, -0.6/-0.3/-0.6 Z-score
Max: {18,17,15,13,13,11}: 87 tot, 14.50 avg, 11 bonus, 50 PB-35, 44 PB-PF, 96.4 Ntile, +1.9/+1.6/+2.2 Z-score
Avg: {17,15,14,12,11, 9}: 78 tot, 13.00 avg, 7 bonus, 35 PB-35, 27 PB-PF, 71.6 Ntile, +0.6/+0.5/+0.7 Z-score
1D4+14, 1D4+13, 1D4+11, 1D4+9, 1D4+9, 1D4+7
Start with {14,13,11,9,9,7}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
5D6K3 targeted power level:
Min: {18,14,14,12,10,10}: 78 tot, 13.00 avg, 9 bonus, 36 PB-35, 29 PB-PF, 49.0 Ntile, -0.4/+0.1/-0.1 Z-score
Max: {18,17,17,15,13,13}: 93 tot, 15.50 avg, 14 bonus, 60 PB-35, 56 PB-PF, 96.5 Ntile, +1.9/+1.6/+2.2 Z-score
Avg: {18,16,15,14,12,11}: 86 tot, 14.33 avg, 12 bonus, 47 PB-35, 42 PB-PF, 83.6 Ntile, +0.8/+1.0/+1.0 Z-score
18, 1D4+13, 1D4+13, 1D4+11, 1D4+9, 1D4+9
Automatic 18 for 1st stat. For remaining 5 stats, start with {13,13,11,9,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
6D6K3 targeted power level:
Min: {18,15,15,12,12,10}: 82 tot, 13.67 avg, 10 bonus, 42 PB-35, 35 PB-PF, 33.7 Ntile, -0.6/-0.5/-0.3 Z-score
Max: {18,18,18,15,15,13}: 97 tot, 16.17 avg, 17 bonus, 69 PB-35, 68 PB-PF, 98.1 Ntile, +2.0/+1.9/+2.1 Z-score
Avg: {18,17,16,14,13,12}: 90 tot, 15.00 avg, 14 bonus, 54 PB-35, 50 PB-PF, 80.6 Ntile, +0.8/+0.9/+0.8 Z-score
18, 1D4+14, 1D4+14, 1D4+11, 1D4+11, 1D4+9
Automatic 18 for 1st stat. For remaining 5 stats, start with {14,14,11,11,9}. Roll 1D4 for each stat and add the result to that stat. Assign as desired.
D&D Next (5E) point buy cost totals are always exactly 12 higher than the Pathfinder point-buy cost totals, as long as the lowest stat is 8 or higher.
As to my existing groups' ability score methods - all are very high powered for stats:
David @ East Mesa:
5D6k3-assign - Liberal on magic items, best storyline; 3-5 players
John @ Desert Sky Games:
52-pt point buy (3.5 point-buy rules) - Stingy on magic items; 5-8 players
Daryn @ Game Depot:
52-pt point buy (3.5 point-buy rules) - Large battles, high character mortality; 4-6 players
Mark @ Fountain Hills:
fixed array {18con, 18, 16, 14, 12, 10} - Lot of house rules, high-powered; 2-4 players
An online VTT game:
fixed array {18, 16, 16, 14, 14, 12} - Skill heavy, lot of up-levelled monsters; 5-6 players