D&D 5E (2014) Is Point Buy Balanced?

[Lanefan]

And I would insist on the rolls being done together, very publically, at Sesssion 0, with each player taking their turn while the others watch.

This should be SOP for rolling any player-side dice for any reason in the game (though not everyone else has to watch, just the DM). "Roll on the board where we can see it" has been a hard-line player rule here since forever.

 

[CleverNickName]

I do point buy while friends roll. My stats are usually lower. Hmmmm

I decided to model this in Excel, to see if it's a math thing or a perception thing (or a cheating thing).

Using the Standard Array (15, 14, 13, 12, 10, 8), you end up with a total of 72.

For the Point-Buy Method, I pulled up a complete list of all 65 valid ability scores that you can get using the Point Buy method (Source). I put them into a spreadsheet, and summed each result (15+15+15+8+8+8=69, 13+13+13+12+12+12=75, and everything in between.) Then I added them together and averaged the result.

The average for Point Buy is 72.3, but that's moot: the player chooses a result between 69 and 75.

And for the 4d6 Method, I had Excel generate six stats using the 4d6 method, and add up the total of all six stats.
And then I had it repeat that calculation a total of 2,560 times, and then average the result.
The average result from the 4d6 method was 73.5.

So it does look like the 4d6 method will---on average, across thousands of iterations--generate stats that are about 1.5 points better than the Standard Array, and about 1 point higher than the average value of Point Buy...but you can get results as high as 75 using Point-Buy, through careful selection of stats. (13, 13, 13, 13, 12, 11 gives you 75 points, which is much higher than any other method and it's 100% reliable.)

TL;DR: I think Point Buy is fairly well-balanced with the other methods. The advantage for point-buy is that the player can choose how over- or under-powered they want their stats to be, by as much as +/- 3 whole points from the standard array, while with the 4d6 method you are probably going to end up at +1.5.

 

[FarBeyondC]

I decided to model this in Excel, to see if it's a math thing or a perception thing (or a cheating thing).

Using the Standard Array (15, 14, 13, 12, 10, 8), you end up with a total of 72.

For the Point-Buy Method, I pulled up a complete list of all 65 valid ability scores that you can get using the Point Buy method (Source). I put them into a spreadsheet, and summed each result (15+15+15+8+8+8=69, 13+13+13+12+12+12=75, and everything in between.) Then I added them together and averaged the result.

The average for Point Buy is 72.3, but that's moot: the player chooses a result between 69 and 75.

And for the 4d6 Method, I had Excel generate six stats using the 4d6 method, and add up the total of all six stats.
And then I had it repeat that calculation a total of 2,560 times, and then average the result.
The average result from the 4d6 method was 73.5.

So it does look like the 4d6 method will---on average, across thousands of iterations--generate stats that are about 1.5 points better than the Standard Array, and about 1 point higher than the average value of Point Buy...but you can get results as high as 75 using Point-Buy, through careful selection of stats. (13, 13, 13, 13, 12, 11 gives you 75 points, which is much higher than any other method and it's 100% reliable.)

TL;DR: I think Point Buy is fairly well-balanced with the other methods. The advantage for point-buy is that the player can choose how over- or under-powered they want their stats to be, by as much as +/- 3 whole points from the standard array, while with the 4d6 method you are probably going to end up at +1.5.

The funny thing about point buy is that, for players who only need/want certain stats to be good, the lower total arrays are better than the higher total arrays. For instance, I'd almost never pick the 75-point (13, 13, 13, 12, 12, 12) over the 71-point (15, 15, 13, 10, 10, 8).

 

[CleverNickName]

That first histogram looked strange to me--I expected to see a smooth bell curve, and there were these really weird gaps in it. So I ran it again, and this time I pushed Excel even harder to generate over twenty thousand iterations. And this is what I got:

So there are now FOUR big gaps in the curve, where the statistical average drops to almost zero (about 1 result out of 20,480, or about a 0.0048% chance). Pretty weird, huh?

I was scratching my head until I realized what was happening: this 0.0048% is the chance of rolling four identical results on 4d6, for all six ability scores...not impossible, but highly improbable. There are the four gaps you can see, which occurred when Excel rolled all 2s, 3s, 4s, and 5s...and there are two gaps on either end of the graph where Excel rolled all 1s and all 6s. You just can't see them as well because they are at the far ends of the graph.

Stats are cool.

 

[M_Natas]

Your point about feats is well taken; in 5e feats allow a lot more customization and even a 1 point advantage to the initial set of scores allows you to take an extra feat while still letting you maximize your essential attributes.

Yeah, that is also my problem with the standard array. Basically you start with two 16s or one 17 and one 15 in your two important stats (after racial/origin boni) and then, yeah, you can take a half feat on level 4, but then level 8 is an ASI, so you can only really start taking feats at level 12, which is where most games end.
Because getting the main attribute to 20 first is the most efficient way to play.
Yes, you can take feats at levdl 4 and 8, but you will.soon be running behind the other players in ability, which is not fun.

 

[FarBeyondC]

Because getting the main attribute to 20 first is the most efficient way to play.
Yes, you can take feats at levdl 4 and 8, but you will.soon be running behind the other players in ability, which is not fun.

See, I know other people feel this way, but I've never really understood why.

Like, if there's any feat at all that's actually relevant for my character concept, getting that as soon as possible is always going to outweigh going from 16 to 18 or 18 to 20, because missing that aspect of my character hurts more than missing by 1 or 2.