D&D 5E Ability Score Point Cost − what does a 16 cost?

[Yaarel]

Using the weighted statistics of 4d6 Drop for the costs diverges from the official 5e costs.



4d6 Drop (Frequency, Increment): Resulting statistically determined cost

18 (.0162, 7.72): 20 points
17 (.0417, 3.00): 13 points
16 (.0725, 1.72): 10 points
15 (.1011, 1.24): 8 points
14 (.1235, 1.01): 7 points
13 (.1327, 0.94): 6 points
12 (.1289, 0.97): 5 points
11 (.1142, 1.09): 4 points
10 (.0941, 1.33): 3 points
9 (.0702, 1.78): 1 point
8 (...): 0 points



The official 5e calculations in the Players Handbook derive statistically from the 3d6 bell curve, rather than the weighted 4d6 Drop bell curve.



Moreover, the conscious control that the player has to choose how big the needed score needs to be, has value in itself, more value than the risks of too low and too many low scores if rolling 4d6 drop randomly. So, the unweighted 3d6 values feel more fair. And in the context of 5e bounded accuracy results in a better offering of balanced arrays.

 

[Ganymede81]

The 3e point buy costs never felt accurate. The upper scores seem too cheap. Meaning. The 3e costs fail to generate arrays that are equal and fair.

This thread calculates costs of scores that correlate exactly to their rarity. An 18 is so expensive because the chance of rolling a natural 18 is so unlikely.

I think that was more a function of the 3E modifier arms race than it was of their point-buy methods.

 

[Yaarel]

I think that was more a function of the 3E modifier arms race than it was of their point-buy methods.

Even looking at the pure 3e point arrays as raw numbers. Some 3e arrays look *obviously* more powerful than other 3e rays.



By contrast, the 5e arrays in this thread, look more equal in value. Indeed, some players are complaining the arrays with lower ability scores look more valuable than the arrays with an extremely high number for the primary ability score. Well, that is the 5e philosophy and is working as intended. An array with decent and modest scores should be valuable and desirable. It seems, these players are accustomed to the 3e inflated arrays, and are still acclimatizing to the 5e mathematical environment.

 

[Blue]

@Blue

Your reasoning seems inconsistent. The impression is, first it argues that high scores are crazy powerful, afterwards it recommends making high scores crazy easy to acquire. The recommendation seems obviously unbalanced?

I explicitly explained why they are inconsistent.

First, for multiple reasons I think that in general shouldn't start with a 16 point by and detailed why.

Then, so as to be helpful for what you want to do at your table, even if I wouldn't do it at mine, I put forth some thoughts on how I would do it if I thought it was a good idea.

I figured this from my post would explain:

I'm going to start with a comment contrary to where you are going, and then help address your point.

[...why not to do it...]

Okay, those are my reasons why I discourage it. Now onto helping figure out the right price for people who want it.

[..one way to do it if you want to move forward anyway...]

Seems completely clear.

 

[Yaarel]

I explicitly explained why they are inconsistent.

First, for multiple reasons I think that in general shouldn't start with a 16 point by and detailed why.

Then, so as to be helpful for what you want to do at your table, even if I wouldn't do it at mine, I put forth some thoughts on how I would do it if I thought it was a good idea.

I figured this from my post would explain:



Seems completely clear.

Ok, but still. The ‘right price’ for something extremely powerful should be extremely cheap? In which sense is this ‘right’?

 

[TheCosmicKid]

I emphatically recommend you don't gain points for dumping stats.

The point was: it breaks the nice pretty formula. [MENTION=6799753]lowkey13[/MENTION] got it.

Aesthetically, since the costs in this thread correlate exactly to a 3d6 roll...

"Exactly"? You're rounding 9.95 down to 9 there, bud.

 

[Krachek]

What mathematical statistics are you using here to show these numbers are balanced and fair?

Pure wild guess.
It could be fun if you want to allow a character with a 20 and a 5.
24 points for a 18 gives 18, 8, 8, 8, 8, 12. Perfectly possible to roll that.
You could play a dwarf with 20 str , 14 co and the rest of 8.
Seem playable. But it gives a one only way character.

 

[Blue]

Ok, but still. The ‘right price’ for something extremely powerful should be extremely cheap? In which sense is this ‘right’?

The fact that you call it extremely cheap does not make it so. Half of your entire point buy budget (well, 13 of 27) for a single stat is a large investment. Moving from a 15 to a 16 would fund an 8 to a 12 - a whole 2 point modifier shift just for that last "half a point" of modifier shift on your already expensive 15.

 

[Blue]

Using the weighted statistics of 4d6 Drop for the costs diverges from the official 5e costs.



4d6 Drop (Frequency, Increment): Resulting statistically determined cost

18 (.0162, 7.72): 20 points
17 (.0417, 3.00): 13 points
16 (.0725, 1.72): 10 points
15 (.1011, 1.24): 8 points
14 (.1235, 1.01): 7 points
13 (.1327, 0.94): 6 points
12 (.1289, 0.97): 5 points
11 (.1142, 1.09): 4 points
10 (.0941, 1.33): 3 points
9 (.0702, 1.78): 1 point
8 (...): 0 points

The official 5e calculations in the Players Handbook derive statistically from the 3d6 bell curve, rather than the weighted 4d6 Drop bell curve.

I don't think we should be making an assumption that the design team picked numbers only based on the mathematical distribution without injecting some of what they want to see from the game.

We can all dream up reasons behind the pricing. I could say (and have) that I doubt that they wanted more than a 1 point difference to climb out of scores that gave penalties because they didn't want to encourage multiple dump stats. In other words, giving a minimal of saved point by leaving 8s. I don't know if it's true, but it at least matches what they did give us, as opposed to the distribution you came up with that 50% more points saved with a dump stat.

They also bottomed out at 8 and topped out at 15. Heck, mathematically a 16 is more likely on 4d6 drop the lower than an 8, but you can get then 8 but not the 16. That's not them trying to be mathematically rigorous, it's them trying to craft something that fits the game they've designed well. Especially given the knowledge that you need a limited number of good scores for most builds and that some gamer will push their bonuses as high as the rules will allow.

 

[ccs]

What does a 16 (or higher) cost me....

About 5 seconds & a good dice roll.