D&D General Sampling Random Ability Scores


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3d5 was pretty impractical in the pre-Internet era unless you wanted to code it up yourself (and computers were pretty pricey before the 90s or so).

Interesting 3d6 reroll 1's matches the standard array best.
 

OptionalRule

Adventurer
3d6 reroll 1s - isn't that exactly the same as 3d5+3 only with more rolling?
Yes it's exactly the same. If you look at the anydice, I actually am using 3d5+3 as the model, but the system is more typically described as 3d6/reroll 1s and I didn't want people reacting to that and have to explain it's exactly the same all the time.
 




So the interesting thing here to me is: if you roll the way the PHB say to roll, you'll probably have a 16 to put in your best ability, before racial mods. Ergo, starting with a 16 regardless of race is well within the tested range of ability scores.

The conclusion I draw: elf barbarians starting with a 16 str is an intended result of default chargen, not an outlier. Standard array and point buy, not rolling, create the impression of 'needing' a race with the 'right' ASI to playa class.
 

jgsugden

Legend
2d6+4 six times is my system. If you take them in order, you get a weak feat, too. If you want to reorder them, you can swap up to three, but the other three need to stay fixed.
 

Ovinomancer

No flips for you!
Yes it's exactly the same. If you look at the anydice, I actually am using 3d5+3 as the model, but the system is more typically described as 3d6/reroll 1s and I didn't want people reacting to that and have to explain it's exactly the same all the time.
Pedantically, no, they're not the same. They have a different mean, to start: 11.75 vs 12, respectively. I'm not sure this difference is enough to not use a shortcut (although, with anydice, it's trivial to do reroll 1's), but it isn't quite true that these are exactly the same.
 

Hussar

Legend
The issue with randomly generated stats isn't with the averages though. There are two main issues here:

1. Luck. Whether good or bad. The thing is, the stats you randomly generate will be used for a character that will be played for a long, long time. Which means that a single set of die rolls is going to impact an entire campaign. And, if you get a somewhat out of average result - say two players get really good rolls, one gets average and one gets a bad set, then it can really negatively impact the game. Not that it necessarily must, I'm not saying that. But, it can get rather frustrating when your character is just bad at stuff when you didn't want to play that character.

2. Cheating. Let's be honest here. We've all seen it. I've done it. I'm pretty sure at some point in time, most of us have. "Oh, that die is... err... cocked, yeah, look, it's sitting slightly on an angle! It needs to be rerolled!" Oh the far more common, "Gee, I have this pretty good set except for this one number pleading look at the DM" which can result in, "Oops, look at that, I accidentally erased that bad number. Guess you need to reroll that one!"

I'm really against random stat generation anymore. I won't stop players who do it, but, I really discourage it. Even down to randomly rolled HP. I'd much rather just not bother. The risk/reward is never worth the randomness. If I have a chance of having a 4 stat, say, then I should have a chance of having a 20 shouldn't I? And my chances of getting that 20 should be much higher than my chances of getting that 4. Or it's a suckers bet. Which, of course, is why you get all these stat gen methods like 4d6 or whatnot. It's just playing into people's gambling fixation and the fact that people are really, really bad at it.
 

Galandris

Foggy Bottom Campaign Setting Fan
So the interesting thing here to me is: if you roll the way the PHB say to roll, you'll probably have a 16 to put in your best ability, before racial mods. Ergo, starting with a 16 regardless of race is well within the tested range of ability scores.

The conclusion I draw: elf barbarians starting with a 16 str is an intended result of default chargen, not an outlier. Standard array and point buy, not rolling, create the impression of 'needing' a race with the 'right' ASI to playa class.

Yes. Unless I am mistaken, since the probability of rolling a 16 or better on 4d6 drop lowest is 13%, the probability of not having a 16 over the six rolls is 0.87^6 or 43%. In more than half the cases, someone will have a 16... Given the importance of the top ability (both for SAD classes and for satisfying the feeling of playing someone good at his schtick), I don't understand why they capped the standard array and point-buy at 15 in 5e.
 

DeviousQuail

Adventurer
Pedantically, no, they're not the same. They have a different mean, to start: 11.75 vs 12, respectively. I'm not sure this difference is enough to not use a shortcut (although, with anydice, it's trivial to do reroll 1's), but it isn't quite true that these are exactly the same.
I'm getting a mean of 12 (and identical probabilities for all outcomes) for both using anydice.

Edit: link isn't working right. Here are my inputs.
output 3d5+3
output 3d{2,3,4,5,6}
 

Ovinomancer

No flips for you!
I'm getting a mean of 12 (and identical probabilities for all outcomes) for both using anydice.

Edit: link isn't working right. Here are my inputs.
output 3d5+3
output 3d{2,3,4,5,6}
Reroll ones is vague. I took it as reroll once. If it's continuous rerolls, then, yes, the math ends up as approaching the same mean as 3d5+3. It's functionally the same, although there's a result where you never roll anything but a one and trail off into infinity wondering why, God, why.
 

DeviousQuail

Adventurer
Reroll ones is vague. I took it as reroll once. If it's continuous rerolls, then, yes, the math ends up as approaching the same mean as 3d5+3. It's functionally the same, although there's a result where you never roll anything but a one and trail off into infinity wondering why, God, why.
I should've figured.
 

Lakesidefantasy

Adventurer
Yes. Unless I am mistaken, since the probability of rolling a 16 or better on 4d6 drop lowest is 13%, the probability of not having a 16 over the six rolls is 0.87^6 or 43%. In more than half the cases, someone will have a 16... Given the importance of the top ability (both for SAD classes and for satisfying the feeling of playing someone good at his schtick), I don't understand why they capped the standard array and point-buy at 15 in 5e.
And yet, we still play the game, and have fun doing it.

I think I know why they capped the standard array at 15*.

No offense, but in contrast to Hussar, I am really for randomly generated ability scores. I am in the minority on this point, and I have accepted that truth. I'm not against Point Buy or the Standard Array, and that's okay.

At my table, we can choose between the Standard random method of rolling 4d6, the Standard Array, Point Buy, or my patented Dice Point** method. Plus, if we decide to roll, but dislike what the dice gave us, we can take the Standard Array instead. However, we can only roll once. I like to reward risk***, and I think that is why they cap the Standard Array and Point Buy at 15.

If we're willing to risk it all on the toss of a die, then our reward is the possibility of a 16, 17, or even an 18. If we don't want to take the risk then we will never get more than a 15. And that's okay. When I noticed that both the Standard Array and Point Buy are capped at 15, that is when I became okay with the two methods.

Someday, I may write about why I prefer randomly generated scores, but not now. It's a much larger topic for me than just ability scores. It's not about math, or balance, or fairness (obviously).

Anyway, I hope I did not offend anybody. It certainly is not the intent. But, we "Randos" do exist, and by golly we have fun--believe it or not.

🙃

* In no way am I implying that I have special knowledge or understanding that others do not.
** A combination of Point Buy and Dice Rolling that brings out the best of both worlds. And completely eliminates dump scores. Satisfaction guaranteed or your money back!
*** Again, not trying to imply that I'm better than anybody.
 


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