D&D 5E Point buy vs roll

[DND_Reborn]

I played around with some dice models in Excel, using the RANDBETWEEN variable and 25,000 iterations. (Hey, it was a slow day and I was bored.) I thought I'd share my findings.

[1]: The average result of a single d6 is 3.5. No surprise there, (1+2+3+4+5+6)/6 gives the same result.
[2]: The average result of 2d6 is 7.0. This makes sense, because it's mathematically identical to [1] + [1].
[3]: The average result of 3d6 is 10.5. Also makes sense, because it's just [1] + [1] + [1]
And so on. nd6 = 3.5n.

Things get interesting when you drop the lowest die in a set of rolls.

[4]: The average result of 2d6 drop the lowest is 4.45. This is almost 1 point higher than the expected average of 1d6.
In other words, rolling 1d6 with Advantage is like getting a +0.95 to the roll.

[5]: The average result of 3d6 drop the lowest is 8.46. This is 1.46 points higher than the expected result of 2d6.
In other words, 3d6 drop lowest = 2d6+1.46.

[6]: The average result of 4d6 drop the lowest is 12.25. This is 2.25 points higher than the expected result of rolling 3d6.
Another way to express it: 4d6 drop lowest = 3d6+2.25.

And so on. The average result of nd6 drop lowest is 3.9n - 3.31

[7]: The average result of rolling 5d6 and dropping both the highest and the lowest results is 10.50. I wouldn't have thought the highest roll and the lowest roll would 'cancel out' each other, but apparently they do when you reiterate the equation a hundred thousand times or so.

Therefore, 5d6 drop lowest and highest = 3d6.

Ah well, I thought it was interesting.

AnyDice does things pretty easily and isn't too hard to learn.

Here is the idea of 5d6, take the middle 3

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

 

[Maxperson]

[3]: The average result of 3d6 is 10.5. Also makes sense, because it's just [1] + [1] + [1]
And so on. nd6 = 3.5n.

Things get interesting when you drop the lowest die in a set of rolls.

[4]: The average result of 2d6 drop the lowest is 4.45. This is almost 1 point higher than the expected average of 1d6.
In other words, rolling 1d6 with Advantage is like getting a +0.95 to the roll.

[5]: The average result of 3d6 drop the lowest is 8.46. This is 1.46 points higher than the expected result of 2d6.
In other words, 3d6 drop lowest = 2d6+1.46.

[6]: The average result of 4d6 drop the lowest is 12.25. This is 2.25 points higher than the expected result of rolling 3d6.
Another way to express it: 4d6 drop lowest = 3d6+2.25.

Your math is off there. 10.5+1.75=12.25. It's not 2.25 higher.

 

[Cadence]

I played around with some dice models in Excel, using the RANDBETWEEN variable and 25,000 iterations. (Hey, it was a slow day and I was bored.) I thought I'd share my findings.

[1]: The average result of a single d6 is 3.5. No surprise there, (1+2+3+4+5+6)/6 gives the same result.
[2]: The average result of 2d6 is 7.0. This makes sense, because it's mathematically identical to [1] + [1].
[3]: The average result of 3d6 is 10.5. Also makes sense, because it's just [1] + [1] + [1]
And so on. nd6 = 3.5n.

Things get interesting when you drop the lowest die in a set of rolls.

[4]: The average result of 2d6 drop the lowest is 4.45. This is almost 1 point higher than the expected average of 1d6.
In other words, rolling 1d6 with Advantage is like getting a +0.95 to the roll.

[5]: The average result of 3d6 drop the lowest is 8.46. This is 1.46 points higher than the expected result of 2d6.
In other words, 3d6 drop lowest = 2d6+1.46.

[6]: The average result of 4d6 drop the lowest is 12.25. This is 2.25 points higher than the expected result of rolling 3d6.
Another way to express it: 4d6 drop lowest = 3d6+2.25.

And so on. The average result of nd6 drop lowest is 3.9n - 3.31

[7]: The average result of rolling 5d6 and dropping both the highest and the lowest results is 10.50. I wouldn't have thought the highest roll and the lowest roll would 'cancel out' each other, but apparently they do when you reiterate the equation a hundred thousand times or so.

Therefore, 5d6 drop lowest and highest = 3d6.

Ah well, I thought it was interesting.

All pretty good, but AnyDice does things pretty easily and isn't too hard to learn.

Here is the idea of 5d6, take the middle 3

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

While the mean is the same, you are very slightly less likely to get extreme rolls. (I was surprised it didn't change it more).

 

[TwoSix]

Such an array is much too high to my tastes, but to each their own.

Regardless, I understand your point about focusing on feats and not ASI. As such, we do the following:

At 5th level, you get +1 to one ability score.
At 10th level, you get two +1's, which must be used in different scores.
At 15th level, you get three +1's, which must be used in different scores.

So, you could increase one ability by +3 by 15th level, allowing a point-buy or standard array 15 with +2 ASI for race to reach 20.

You can still take feats with ASIs to increase an ability quicker.

Pretty much the same idea, but too much delayed gratification for my taste.

 

[DND_Reborn]

While the mean is the same, you are very slightly less likely to get extreme rolls. (I was surprised it didn't change it more).

View attachment 150076

There isn't a whole lot to change though.

This is why I toyed with the idea of 3d20 take middle to replace normal d20 rolls, much less swingy.

 

[Cadence]

There isn't a whole lot to change though.

This is why I toyed with the idea of 3d20 take middle to replace normal d20 rolls, much less swingy.

I am apparently so in to avoiding doing anything more productive today that I will now note that middle 1 of 9d20 is really close to 3d6.

(It was unhappy with middle of 11d20 or 13d20, and I'm not quite bored enough to simulate it).

 

[Oofta]

Our first 5E campaign (my wife ran it) we used the point buy from 3.5 using 32 points.

Truth be told, I kinda wished we hadn't done that and had used standard point buy instead since our PCs were kind of overpowered.

 

[DND_Reborn]

I am apparently so in to avoiding doing anything more productive today that I will now note that middle 1 of 9d20 is really close to 3d6.

(It was unhappy with middle of 11d20 or 13d20, and I'm not quite bored enough to simulate it).

LOL, I get it.

How about this:

A while ago I liked the idea that each +1 for the ability modifier represented 1 standard deviation in a normal distribution.

So, how to roll ability scores to reflect that and get as close to a normal distribution as possible?

What I finally resolved on was 15d2 - 12.

 

[Maxperson]

Our first 5E campaign (my wife ran it) we used the point buy from 3.5 using 32 points.

Truth be told, I kinda wished we hadn't done that and had used standard point buy instead since our PCs were kind of overpowered.

Stats mattered much more in 3.5 than they do in 5e. The bonuses and improvements were baked into the math.

 

[MNblockhead]

Did you mean point-buy? Because it is getting the most votes.

I must have sloppily misread the poll. It makes sense to me that point-buy is the most popular.