thoroughlyS
2016-10-10, 06:54 PM
One of the first things you do when you make a character is determine your ability scores. Methods of generating these scores vary, with some being widely more popular than others. Some of these methods are given on pages 169-170 of the Dungeon Master's Guide, but I want to focus on a few loose "styles" of ability score generation:
Rolling
Arrays
Point Buy
As far as I know, rolling was the first method, introduced with OD&D. Initially, players rolled 3d6, and recorded their results in order, which gave players an organic character, with its own attributes to play. Since its introduction, this method has been "refined" in a few ways (allowing players to arrange their results, rolling 4 dice and dropping the lowest result, etc.).
Arrays are the statistician's answer to rolling. Supposedly, the elite array (15, 14, 13, 12, 10, 8) was meant to be the average roll of "4d6, drop lowest". This could save people time, if they wanted to make a character, NPC, or monster, with ability scores on par with the players. The nonelite array (13, 12, 11, 10, 9, 8) was meant to customize NPCs and monsters, without making them necessarily more powerful than the standard array (11, 11, 11, 10, 10, 10).
Point Buy (by far the most popular on these boards) was introduced to allow players a much higher degree of control over the creation of their characters than any other generation system, at the cost of being more time consuming. It was also intended to allow DMs to steer the power of the players, by allotting more or fewer points.
Ability Score
Point Cost
Ability Score
Point Cost
9
1
14
6
10
2
15
8
11
3
16
10
12
4
17
13
13
5
18
16
I recently found this simulation (https://docs.google.com/spreadsheets/d/1G2n2zj_iyi1sF0jCTjuB9rG41IpGKau6fYNKVNRvUNQ/edit#gid=0) for rolling ability scores, and found the average rolls for some common methods (I tweaked a copy in order to get 5d6, drop 2 lowest).
Method
Highest
2nd
3rd
4th
5th
Lowest
3d6
14.2
12.4/12.5
11.1
9.9
8.5
6.8
4d6b3
15.7
14.2
13.0
11.8
10.4
8.5
5d6b3
16.4
15.2
14.1
13.1
11.8
9.9
Comparing the average of 3d6 to the nonelite array shows that WotC was fairly accurate. In fact, the average results (rounded to 14, 12, 11, 10 9, 7) and the nonelite array would each cost 15 points with point buy. The difference is that the average rolls are slightly more diverse, having a +2 and a -2 modifier amongst them. Both of them also have the benefit of starting with 3 odd scores, which means a 20th level character with these scores would end with all even scores.
The averages of 4d6b3 and the elite array are similarly comparable. I've heard that WotC originally meant to have the elite array be an accurate average, but made a few miscalculations. I have no idea whether that is true or not, but it is definitely possible. The most accurate rounding of the averages would be "16, 14, 13, 12, 10, 9", but I have a small problem with it. This set has only two odd scores, which would mean a 20th level character will waste one ability score adjustment. The easiest fix would be to change 1 of the scores by 1 point (with my vote to change the lowest score from 9 to 8*). The elite array has a similar problem, with two even scores, but this is made worse by lowering the highest score (which also lowers that modifier). With point buy, the elite array would cost the standard 25 (to be expected, as point buy was based on these scores), while the rounded averages would run 28 points.
Finally, the averages of 5d6b3 have an interesting result. There is no array to compare them to, but the point buy cost of the rounded averages (16, 15, 14, 13, 12, 10) tally a whopping 35 points. Again you have the issue of only two odd scores.
An interesting point is the linear values found between these "tiers" of power (low power, standard, and high power). The nonelite array/3d6 averages cost 15, the elite array costs 25, and the 5d6b3 averages cost 35. The outlier here being the averages of 4d6b3, which would cost 28/27 points. Also of interest is the sum of the modifiers: the nonelite array and 3d6 averages both total 0, the 4d6b3 averages total +6, and the 5d6b3 averages total +9. The outlier in this pattern is the elite array, with a total modifier of +5.
I would like to codify these three styles as follows:
Campaign Power Level
Roll
Array
Point Buy
Lowest Power
-
Basic
11, 11, 11, 10, 10, 10
-
Low Power
3d6
Nonelite
14, 12, 11, 10, 9, 7
0
Standard Power
4d6b3
Standard
16, 14, 13, 12, 10, 8
15
High Power
5d6b3
Elite
16, 15, 14, 13, 12, 11
25
This would involve a change to the Point Buy calculations.
*I believe this is the best option for three reasons: Firstly, the rounding error for that value would be the smallest of the available options. Lowering the 15.7 to a 15 results in an error of 0.7, raising the 14.2 to 15 would be 0.8, changing the 13 either way would be 1.0, lowering the 11.8 to 11 would be 0.8, raising the 10.4 to 11 would be 0.6, and finally, lowering the 8.5 would only result in an error of 0.5. The second is that this change would be closer to the elite array. Lastly, this would mean only one abiliy score is odd, which means players can get all even scores in low-level play.
Rolling
Arrays
Point Buy
As far as I know, rolling was the first method, introduced with OD&D. Initially, players rolled 3d6, and recorded their results in order, which gave players an organic character, with its own attributes to play. Since its introduction, this method has been "refined" in a few ways (allowing players to arrange their results, rolling 4 dice and dropping the lowest result, etc.).
Arrays are the statistician's answer to rolling. Supposedly, the elite array (15, 14, 13, 12, 10, 8) was meant to be the average roll of "4d6, drop lowest". This could save people time, if they wanted to make a character, NPC, or monster, with ability scores on par with the players. The nonelite array (13, 12, 11, 10, 9, 8) was meant to customize NPCs and monsters, without making them necessarily more powerful than the standard array (11, 11, 11, 10, 10, 10).
Point Buy (by far the most popular on these boards) was introduced to allow players a much higher degree of control over the creation of their characters than any other generation system, at the cost of being more time consuming. It was also intended to allow DMs to steer the power of the players, by allotting more or fewer points.
Ability Score
Point Cost
Ability Score
Point Cost
9
1
14
6
10
2
15
8
11
3
16
10
12
4
17
13
13
5
18
16
I recently found this simulation (https://docs.google.com/spreadsheets/d/1G2n2zj_iyi1sF0jCTjuB9rG41IpGKau6fYNKVNRvUNQ/edit#gid=0) for rolling ability scores, and found the average rolls for some common methods (I tweaked a copy in order to get 5d6, drop 2 lowest).
Method
Highest
2nd
3rd
4th
5th
Lowest
3d6
14.2
12.4/12.5
11.1
9.9
8.5
6.8
4d6b3
15.7
14.2
13.0
11.8
10.4
8.5
5d6b3
16.4
15.2
14.1
13.1
11.8
9.9
Comparing the average of 3d6 to the nonelite array shows that WotC was fairly accurate. In fact, the average results (rounded to 14, 12, 11, 10 9, 7) and the nonelite array would each cost 15 points with point buy. The difference is that the average rolls are slightly more diverse, having a +2 and a -2 modifier amongst them. Both of them also have the benefit of starting with 3 odd scores, which means a 20th level character with these scores would end with all even scores.
The averages of 4d6b3 and the elite array are similarly comparable. I've heard that WotC originally meant to have the elite array be an accurate average, but made a few miscalculations. I have no idea whether that is true or not, but it is definitely possible. The most accurate rounding of the averages would be "16, 14, 13, 12, 10, 9", but I have a small problem with it. This set has only two odd scores, which would mean a 20th level character will waste one ability score adjustment. The easiest fix would be to change 1 of the scores by 1 point (with my vote to change the lowest score from 9 to 8*). The elite array has a similar problem, with two even scores, but this is made worse by lowering the highest score (which also lowers that modifier). With point buy, the elite array would cost the standard 25 (to be expected, as point buy was based on these scores), while the rounded averages would run 28 points.
Finally, the averages of 5d6b3 have an interesting result. There is no array to compare them to, but the point buy cost of the rounded averages (16, 15, 14, 13, 12, 10) tally a whopping 35 points. Again you have the issue of only two odd scores.
An interesting point is the linear values found between these "tiers" of power (low power, standard, and high power). The nonelite array/3d6 averages cost 15, the elite array costs 25, and the 5d6b3 averages cost 35. The outlier here being the averages of 4d6b3, which would cost 28/27 points. Also of interest is the sum of the modifiers: the nonelite array and 3d6 averages both total 0, the 4d6b3 averages total +6, and the 5d6b3 averages total +9. The outlier in this pattern is the elite array, with a total modifier of +5.
I would like to codify these three styles as follows:
Campaign Power Level
Roll
Array
Point Buy
Lowest Power
-
Basic
11, 11, 11, 10, 10, 10
-
Low Power
3d6
Nonelite
14, 12, 11, 10, 9, 7
0
Standard Power
4d6b3
Standard
16, 14, 13, 12, 10, 8
15
High Power
5d6b3
Elite
16, 15, 14, 13, 12, 11
25
This would involve a change to the Point Buy calculations.
*I believe this is the best option for three reasons: Firstly, the rounding error for that value would be the smallest of the available options. Lowering the 15.7 to a 15 results in an error of 0.7, raising the 14.2 to 15 would be 0.8, changing the 13 either way would be 1.0, lowering the 11.8 to 11 would be 0.8, raising the 10.4 to 11 would be 0.6, and finally, lowering the 8.5 would only result in an error of 0.5. The second is that this change would be closer to the elite array. Lastly, this would mean only one abiliy score is odd, which means players can get all even scores in low-level play.