Even where people aren't cheating, most groups that roll use fairly generous reroll methods. I think people aren't always aware of the effect that things like "reroll if your modifiers don't sum to a certain amount" have on the expected values of rolls. There's nothing wrong with wanting to use generous rolling methods, of course, but you don't have to do much before you push them to a point where they tend to generally produce better results than point buy pretty reliably.
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Anybody know the average to 4D6, drop the lowest for scores? What if the average for rolling is significantly higher than the array or point buy systems?
I did not mean the "6x4d6, drop the lowest of scores" variant I meant the "24/28x6, drop the lowest of scores and then combine the dices as you see fit" variant.
The average of the top 18 dice of 24d6 is 75.63, so the average attribute is 12.605.
For the top 18 of 28d6 the average is 81.23 so the average attribute is 13.538.
However the average of the top *6* dice is is 33.63 or 34.28, which means it's almost guaranteed that you can get at least one 18 and you have a nearly-even chance of getting two (assuming you want them).
On the other end, the average dump stat is 7.26 or 8.95. Where with 18d6 you have a barely better than even chance of getting 4 or higher on your 3 lowest dice.
Simply rolling 3d6 six times your dump stat will average 6.77, and your high stat will average 14.23 (I think - if I figured out how to do that right on anydice.com ).
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Huh... If no rule forbids it that has got to be the most house ruled thing in D&D...
I think the idea is that rolling gives a nice bell curve. Point buy sits just below the top of the bell curve as a safe but not optimal choice where as rolling gives the ability to get lucky and get above average stats but also the ability to end up messing yourself up and having very poor stats.
Point-buy can do a bell curve if you assume the dump stat from the start and then allow no lowering of stats. The closest approximation to the average rolled array is 9, 10, 12, 13, 14, 16. But lets say the first thing we want to do is dump. Anything less than 6 is absurd for an adventurer, so lets shift the array to that bottom end. That gives us a before-points starting array of 6, 7, 9, 10, 11, 13 (and an 18-point difference that we need to make up).
Now, offer your players that array and this point-buying rule: "Spend two points raising a stat towards 12, and then a third point raising whatever you want. Do this six times, but never raise any stat over 18."
This allows for plenty of flexibility, but even the extremes of this buying system are pushed into a bell curve. Here are some examples of resulting arrays:
(You could alternatively start with 5, 6, 8, 9, 10, 12; use 24 points; and thereby make a result of 6, 12, 12, 13, 13, 18 possible. But that presents a lot more opportunity for human calculation error. To mitigate error even further and force a tighter range of possibilities, you might use 7, 8, 10, 11, 12, 13 and spread 12 points; but that leaves only a single choice of array to get an 18. So I think the solution I presented above is the happy medium for this type of point-buy system.)
(The simplest alternative of all would be a starting array of 8, 9, 11, 12, 13, 14 and 6 points, with no limits on how to spend them other than a max stat of 18. But that doesn't so much incentivize a bell curve as put us in a tight range and incentivize leaving it but restricting how much one can. It's an opposite approach altogether, then, but still produces fairly reasonable results.)
As I understand it, the argument for rolling is that with point buy, you can fully optimize, and therefore "all the fighters feel the same". The complaint about rolling is that since you only roll once, rolling can lead to one person feeling permanently gimped. It feels like the first one could be fixed with interesting trade offs so there's no optimal solution.
Given the choice, I'd design the system do that point buy is always better. You generally don't want to permanently punish a newby for feeling lucky, so have the better default be dice. Also, you want your system to discourage retool through suicide, and if your system is balanced to average roll, rolling a char and killing him if he isn't average becomes tempting.
However, it doesn't much matter since those who like balance will demand everyone point buy, so they don't Care what the average roll is. At least, if I dm, that'll be my plan.
The average roll matters even for a point-buy system because that's what the rest of the game will have been optimally balanced off of. There should be plenty of leeway, but the game should be most balanced and most easily balanced for GMs when everyone is right at the average roll. A point-buy system that is not constructed towards the average roll will therefore be inherently unbalanced.
I don't care if the point buy is on average sub-par compared to rolling. My group will still use point buy because we'd rather everybody suck equally and the DM have an easy time adjusting minorly to that than half the party be awesome and the other half suck horrifically and the DM have a more difficult time adjusting to that.
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With just a choice, I'd say point buy is fairer than rolling. However, one could allow a player to roll all stats using the 4d6 drop lowest method "X" number of times With the sets the player rolled, they would choose their best set and compare it to what would be offered by the appropriate point buy method for the campaign(for high powered, difficult campaigns, the DM may assign a higher value than is regarded as standard for point buy, for instance). They can either stick with their best set or opt for the point buy.
The drawback is that someone may still roll really good and outclass the point buy. Still, it eliminates the greatest potential disparity of someone rolling low and someone rolling high on stats. It also allows players who want to roll stats to do so and have a safety net that they can fall into. I am a fan of higher powered campaigns though(especially since I like to keep magic items very rare).
That said, I don't really feel that there is anything wrong with using only point buy
