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View Full Version : How's this hybrid matrix/dice method for 3.5/PF/4E/5E ability scores?



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

Altair_the_Vexed
2014-06-24, 07:19 AM
To me, the randomness is too large to give the benefit of points buy, and too small to give the benefit of true dice rolling.

If I'm rolling dice to assign my abilities scores, I want that to be a part of the game - the rolls determine how good my character will be, just like the rolls in combat.
If I'm using points buy, it's because I have my character in mind, and will assign the scores as required.

GreatInca
2014-06-24, 01:19 PM
To me, the randomness is too large to give the benefit of points buy, and too small to give the benefit of true dice rolling.

This is the objective, to be in-between point-buy and true dice rolling. For legitimate use it is a compromise when the DM wants dice but the players want point-buy (or vice-versa).

Players being told to roll dice for stats, but doing so unsupervised can also use these methods, or just simply assign stats within the min/max ranges for the rolling method and produce a character that appears to actually be legitimately rolled as you will have your mix of odds and evens and produce stats with -0.5 to 2.0 standard deviations of the mean for the rolling method so you will generally not be over-cheating (it is more for getting what you want than full-on cheat-munchkin powergaming). This won't work for in-order or organic methods or any method where order is not FFA, but those would rarely be allowed to be done unsupervised.

Altair_the_Vexed
2014-06-24, 02:19 PM
Yup: I understand that this is your objective, and I see that you've put extensive proof of the distribution of the results in the OP - I just don't find it an attractive or useful objective.
Your mileage may vary, of course.

Knaight
2014-06-24, 02:24 PM
Are you familiar with the 27-25-23 system? Basically, you make 3 rolls. Roll A generates stat A and stat 27 - A, Roll B generates stat B and 25 - B, and Roll C generates stat C and 23 - C. It's a rolled system that guarantees 3 even and 3 odd scores which come to a consistent total (75 between all 6 scores, for an average of 12.5). The rolls are increased to 9-7-5 if below that.

As an example: Say I'm using 3d6 rolls. I roll a 8, 13, and 11. The 8 gets bumped up to a 9, the other two are fine. So the stats are 9, 27-9, 13, 25-13, 11, 23-11. This gets: 9, 18, 13, 12, 11, 12.

GreatInca
2014-06-24, 04:01 PM
Are you familiar with the 27-25-23 system? Basically, you make 3 rolls. Roll A generates stat A and stat 27 - A, Roll B generates stat B and 25 - B, and Roll C generates stat C and 23 - C. It's a rolled system that guarantees 3 even and 3 odd scores which come to a consistent total (75 between all 6 scores, for an average of 12.5). The rolls are increased to 9-7-5 if below that.

Kinda like that. The bonus total is always 6 with those 3 specific numbers. It is +0.2 standard deviations above the mean for 4D6K3. Wonder how tweakable it is for other target bonus totals. I think a static bonus total should be around 0.5 to 1.0 standard deviations above the mean for the targeted dice method being emulated.

3D6: 3
4D6K3: 8
5D6K3: 11
6D6K3: 14
2D6+6: 10
3D6K2+6: 14
4D6K2+6: 16

GreatInca
2014-06-24, 08:09 PM
Looks like 27-25-23 can be easily modified for other target bonus totals. Moving all the numbers up or down by two shifts the bonus total up or down by 3 each.

My main criticism for 27-25-23 is that low rolls cause excessive high/low stat extremes. Higher offsets also mean more carrying, which is more math. But compared to mine, it certainly creates randomness without any variance in bonus totals.

A significant advantage of 27-25-23 over mine (matrix+D4) is that it could be used as a semi-cheat for DMs that are using order-sensitive dice methods (in-order or organic, or choose from ordered sets) where mine cannot.

25-23-21; 10,10,10: 10,15,10,13,10,11 3
27-25-23; 10,10,10: 10,17,10,15,10,13 6
29-27-25; 10,10,10: 11,18,10,17,10,15 9
31-29-27; 10,10,10: 13,18,11,18,10,17 12

25-23-21; 8, 8, 8: 8,17, 8,15, 8,13 3
27-25-23; 8, 8, 8: 9,18, 8,17, 8,15 6
29-27-25; 8, 8, 8: 11,18, 9,18, 8,17 9
31-29-27; 8, 8, 8: 13,18,11,18, 9,18 12


So the spectrum of randomness vs equality:

Dice legit
My Matrix+1D4 method
27-25-23
Point-buy