Stat Generation

[Tyger]

Hey all,

A DM is proposing the following methods of stat determination. They seem rather unbalanced, and I want to point it out to him, but my math skills are, at best, atrocious.

Can anyone point out, in plain English, why these aren't balanced? Or if they are, just tell me to shut up. :smallbiggrin:


Option 1: 8 rolls, 6 sets, normal rules.
Option 2: 10 rolls, 3 sets, normal rules.
Option 3: 7 rolls, 4 sets. In this option, you roll only 3d6 per roll, but '1's and '2's are re-rolled. This will provide the player with a minimum of 9 for each ability score.
Option 4: 7 rolls, 4 sets. In this option all ability scores start with a base of 6, then you roll 3d6 dropping the lowest. This will provide the player with a minimum of 8 for each ability score.
Option 5: 24pt, point-for-point build, base ability score 10, Max starting attribute 18

A roll is 4d6 dropping the lowest.
A set is the final values from which you would pull your stats.
I.e. Option 2 would mean you would roll ten stats from which you would chose 6 to represent your stats. You could repeat this process up to three times, each time, discarding all the previous rolls.

And point-for-point in option 5 would mean that an 18 (base 10 + 8) would cost 8 of your 24 points.

So, mathmatics folks. Why is this not balanced? Or is it?

[tainsouvra]

Balanced against what? Each other? 3d6? 4d6 drop lowest? Elite array?

[Crow]

Maybe a better course of action would be to ask your DM what is wrong with the stat generation methods the game already provides.

[Telonius]

These will certainly give a more powerful character than a normal 4d6 drop lowest. However, "balanced" is a relative term. If the DM is scaling up the difficulty of all of your encounters, and generating the bad guy NPCs' stats using the same method, it can still be balanced.

[Tyger]

Sorry, should have been more specific. These are the five options all players are given when generating their characters. So the question is, are they balanced against one another?

It seems to me that option four is liable to produce statistaically higher stats. You are starting with a 6, and adding the best of 3d6. The likelihood of rolling two decent die out of three seems pretty high to me. And you get to do it 4 times, so there's a good chance at least one set will be pretty high.

And option 5 is pretty high too. Hell, you could make a character with 6 14s. Or if you want to specialize, 2 18s, and 4 12s.

Yes, it appears that they are going to generate higher than average (hell, way higher than average) stats. I just need some actual math to explain why.

[Logic]

I use a variant that is random, and also pretty fair.

Roll 3d6 36 times, arraigning in a 6x6 grid in the order rolled.

The player may selest any of the columns, rows, or either of the two diagonals.

You may add 3 restrictions to this.
1: Players may not sum any of the totals, they look, and pick.
2: Players must place them in the order they appear.*
3: You as DM may exclude one set if it is WAY out of line with the rest**

* For example if the line the player chose is 13-12-15-17-9-10 then the 17 will be going in either constitution, or Intellegence, and the 10 will be either strength or Charisma.
** Such as 4 18s

[Dizlag]

Ok, I just wrote a little Ruby script to generate the following results. For over 50000 rolls, here are some averages for a single roll using three different methods:

4d6 dropping the lowest = 12.25026 average roll for Options 1 & 2
3d6 rerolling 1s and 2s = 13.50342 average roll for Option 3
3d6 dropping the lowest and adding 6 = 14.4752 average roll for Option 4

So, it would seem the methods aren't quite balanced. Granted, rolling multiple sets for Option 1 & 2 would probably get you better results. I would go with Option 4, it's got the highest result for an individual roll.

I know that it's not actual math, I just ran a program to roll a bunch of dice. These are the numbers I'm getting. Is that good enough for ya?

Good luck,

Dizlag

[Kiero]

Maybe a better course of action would be to ask your DM what is wrong with the stat generation methods the game already provides.

Why shouldn't it be the GM's prerogative to use whatever stat-generation method they please in their game (assuming their players are happy with it)?

[Fax Celestis]

I usually use 4d6, reroll 1s, drop the lowest die, eight times (keeping highest six).

My players have learned that this is necessary for their continued survival. I am a vicious DM.

[Cruiser1]

And option 5 is pretty high too. Hell, you could make a character with 6 14s. Or if you want to specialize, 2 18s, and 4 12s.Option 5 is indeed great, and looks to be the best. In D&D, extreme stats are better than average stats, even if they both have the same total modifier count. Given point buy, go for 3 18's and 3 10's. Imagine a Wizard with INT/DEX/CON 18, a Fighter with STR/DEX/CON 18, or a Druid with INT/WIS/CHA 18 (who spends all their time wildshaped into something with good physical stats).

You say option 5 is a 24 point buy above straight 10's. Note however normal point buy is above straight 8's, and your point buy avoids the usual penalty of 2 points to raise a 14 or 15, and 3 points to raise a 16 or 17. In other words, 3 18's and 3 10's is equivalent to a 54 point buy based on the standard way of counting! (Straight 14's is only a 36 point buy.)

3d6 dropping the lowest and adding 6 = 14.4752 average roll for Option 4
I would go with Option 4, it's got the highest result for an individual roll.
Option 5 gives an average stat of 14. However that 14 should be considered higher because the numbers go exactly where you want to (i.e. no odd numbered stats), and the numbers can give you extremes (such as the 3 18's mentioned) as opposed to the more average distributions the other methods give you.

[Chronos]

Dizlag, you need a little more detail in your scripts. The first two methods aren't just 4d6 drop lowest; you also get to drop two (in option 1) or four (in option 2) ability scores generated that way. And then, if you don't like any of the scores you generated, you can scrap everything and try again, multiple times (a total of 6 times in the first method, and a total of 3 times in the second). So even for a Monte Carlo simulation of those, you have to have some criterion to tell you whether to try again (since, if I'm understanding the OP correctly, once you make a new set, you can't go back to an old set).

That said, I think I'd just go with the last option, since you know exactly what you're getting. You can make an exceedingly powerful character with three 18s and three 10s. Few classes gain direct benefits from more than three ability scores, and a 10 isn't low enough to really handicap a character in a party. A barbarian with 10 int, wis, and cha, for instance, is at least smart enough to let the wizard handle the puzzles, sensible enough to ask the cleric for advice, and sociable enough to know to keep his mouth shut when the bard is negotiating for things. Heck, that's enough point buy to even make things like a duelist monk paladin work (a 14 in every score isn't too shabby).