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Thank you Haldrik for all this data, it is going to influence the way I allow characters to be rolled in the future.

If they dont want to use the sensible option of point buy or array, I will allow 2d6+4 as a compromise

I am still holding out hope that WotC undoes their prior simplification that really complicated things - by which I refer to their decision to make ability modifiers +/- 1 for every 2 points away from 10.

It made remember what modifier each score had a touch easier, but made rolling your ability scores much more difficult to accurately balance the game around.

Below, I have included a summary of the way ability score bonuses were staggered in D&D (AD&D has similar ranges, but much more granular results) prior to 3rd Edition, and the statistical probability of each modifier if using the then-standard 3d6 method.

3 -3
4-5 -2
6-8 -1
9-12 no modifier
13-15 +1
16-17 +2
18 +3

Easy (enough) to remember because the middle 4 numbers have no modifier, then 3 numbers have +1 or -1, then 2 numbers have +2 or -2, then only one number has +3 or -3.

+/-3 Modifier 0.46% chance
+/-2 Modifier 4.17% chance
+/-1 Modifier 21.29% chance
0 modifier 48.14% chance

Chance of negative modifier 25.92%, with same chance of positive modifier.

Then compare to the same die method with the 3rd editon (and forward) ability modifiers

+/-4 Modifier 0.46% chance, a widening of bonus range being an inherent difficulty in balance calculation.
+/-3 Modifier 4.17% chance, a roughly 900% increase in likelyhood.
+/-2 Modifier 11.57% chance, a roughly 277% increase in likelyhood.
+/-1 Modifier 21.29% chance, the only range that doesn't change.
0 Modifier 25% chance, a roughly 50% decrease in likelyhood.

Chance of negative modifier 37.5%, a roughly 144% increase in likelyhood, and the same for chance of positive modifier.

Used to be the modifiers were based specifically around the idea that most scores would be in the "no modifier' range, so the game math could assume that you didn't have any modifiers - and then each plus was a genuine bonus and each minus a geniune obstacle, but not all that likely to be majorly significant.

...then they decided simple calculation of modifier was more important than being able to set their "benchmark" at a +0 modifier, and decided (if you look at the game math) that they would instead set the benchmark so high as to make people genuinely feel they had to max out their prime ability score or face "uselessness".

With D&D Next aiming for a bounded accuracy system that stands up to the stress of accomodating multipl play (and character generation) styles, I'd have figured putting ability modifiers back the way they were would have been the first step.

@Aaron. I can support the increase of bonuses, by every three score points:

Heroic Human
• −1 (7-9)
• +0 (10-12)
• +1 (13-15)
• +2 (16-18)

Superhuman
• +3 (19-21)



But so far, D&D Next seems to solve the problem of disruptively high bonuses by narrowing scores, generally from 10-15. That seems a good solution to me too.

There are two mechanisms that need to be reconciled here. The first is that some people desire randomness and the second is that some people desire stability amongst players. In order to manage both  you need to create a system that has a autocorrelating factor than diminishes that likelihood of good rolls after already rolling a good roll or bad rolls after already rolling a bad roll. There are ways to do this while still maintaining random distribtuions of stats, but it would be very complicated to explain to a player why they have to go through so much trouble just to simulate a pointsbought array.

Um...I'm not sure how much this affects the math in this thread, but the current ability score array is 15/14/13/12/10/8, not 15/14/13/12/11/10, which corresponds exactly to what is possible in the 27 point point-buying option.