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

[Yaarel]

I would simply suggest you erase the 8 (-1) and write in 6(-1) or 3(-1) or whatever.

Note the ability modifier (the only thing that matters in actual play) doesn't change.

If the player insists on having a lower ability modifier as well, I would say "Go ahead, feel free. You gain no extra points, though. If you want to play someone less gifted overall that's your call."

Volunteer to drop a score lower. The only reward is roleplay.

Sounds good to me.

 

[Yaarel]

Aesthetically, since the costs in this thread correlate exactly to a 3d6 roll, the resulting arrays *feel* more like this roll generated them − and feel more equal in worth. So, when different players choose different arrays, no one needs to feel cheated.

These ‘higher-than-3e’ costs also work better for 5e because of bounded accuracy. An 18 score is beyond the budget of the 27 point array, but that is just as well. Purchasing an 18 score, can improve by race to a 20 score, right out of the gate at level 1, which tends to be somewhat disruptive. The more accurate high cost can still result in an 18 score by race, and even this is concerning. Players that roll their abilities sometimes get very high scores, and we hear problematics because of this at the lowest tier levels. But with this point cost for the array, a high score in the primary ability will at least cause lower scores elsewhere, and in 5e these low scores hurt. So, the overall array feels fair despite the exceptionally powerful primary score.

 

[Hriston]

Here is the math behind the point method to customize an ability score array. For example, to buy a 16 costs 14 points.

The official ability score array (15 14 13 12 10 8) costs 27 points total. With this budget, it is possible to buy a 16 (costing 14 points), even a 17 (costing 23 points). But to buy an 18 (costing 50 points) is way out of reach.

Calculations for Ability Score Point Cost

[B]3d6   Freq    1/Freq   x 1/8   Sum     Round Down   Official[/B]
[B]
[COLOR=#0000cd]18[/COLOR]    [/B].0046   217.39   27.17   50.61   [B][COLOR=#0000cd]50[/COLOR]           [/B]
[B][COLOR=#0000cd]17[/COLOR]    [/B].0139    71.94    8.99   23.44   [B][COLOR=#0000cd]23[/COLOR]           [/B]
[B][COLOR=#0000cd]16[/COLOR]    [/B].0278    35.97    4.50   14.45   [B][COLOR=#0000cd]14[/COLOR]           [/B]

[B][COLOR=#0000cd]15[/COLOR]    [/B].0463    21.60    2.70    9.95   [B] [COLOR=#0000cd]9[/COLOR]           [/B]9
[B][COLOR=#0000cd]14[/COLOR]    [/B].0694    14.41    1.80    7.25   [B] [COLOR=#0000cd]7[/COLOR]           [/B]7
[B][COLOR=#0000cd]13[/COLOR]    [/B].0972    10.29    1.29    5.45   [B] [COLOR=#0000cd]5[/COLOR]           [/B]5
[B][COLOR=#0000cd]12[/COLOR]    [/B].1157     8.64    1.08    4.16   [B] [COLOR=#0000cd]4[/COLOR]           [/B]4
[B][COLOR=#0000cd]11[/COLOR]    [/B].1250     8       1       3.08   [B] [COLOR=#0000cd]3[/COLOR]           [/B]3
[B][COLOR=#0000cd]10[/COLOR]    [/B].1250     8       1       2.08   [B] [COLOR=#0000cd]2[/COLOR]           [/B]2[B]
[COLOR=#0000cd] 9[/COLOR]    [/B].1157     8.64    1.08    1.08   [B] [COLOR=#0000cd]1[/COLOR][/B]           1[B]
[COLOR=#0000cd] 8[/COLOR]    [/B].0972      ...     ...    0      [B] [COLOR=#0000cd]0[/COLOR]           [/B]0

[B] 7[/B]    .0694
 [B]6[/B]    .0463
 [B]5[/B]    .0278
 [B]4[/B]    .0139
 [B]3[/B]    .0046

I see your calculations are based on a 3d6 roll. Shouldn't you be using 4d6 drop lowest given that we're talking about a point buy system for PCs in fifth edition? I believe 3d6 was the stat generation method used for PCs in the original edition of the game, published in 1974.

 

[Yaarel]

Incidentally, I suspect, the calculations in the second post are how the 5e Players Handbook determined its costs for the point method. Notice the 5e costs differ from the 3e costs.

Supplying the costs for the rest of the numbers remains in step with the 5e method.

 

[Krachek]

Put 16 at 13 points.
Put 17 at 18 points
Put 18 at 24 points

And add :
Having a 7 gives you an extra point.
Having a 5 gives you 2 extra points.

 

[Yaarel]

Put 16 at 13 points.
Put 17 at 18 points
Put 18 at 24 points

And add :
Having a 7 gives you an extra point.
Having a 5 gives you 2 extra points.

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

 

[Yaarel]

Remember, it is possible to buy an 18 score. It just means this array has a 50 point budget.

Thus, other players at the same table, who might instead need multiple high scores, wont be able to afford an 18, but they will be able to purchase two 17s, three 16s, or so on, thus generate an array that is about equal to the player with the 18 for the primary ability score.

 

[Tormyr]

Here is the math behind the point method to customize an ability score array. For example, to buy a 16 costs 14 points.

The official ability score array (15 14 13 12 10 8) costs 27 points total. With this budget, it is possible to buy a 16 (costing 14 points), even a 17 (costing 23 points). But to buy an 18 (costing 50 points) is way out of reach.

Calculations for Ability Score Point Cost

[B]3d6   Freq    1/Freq   x 1/8   Sum     Round Down   Official[/B]
[B]
[COLOR=#0000cd]18[/COLOR]    [/B].0046   217.39   27.17   50.61   [B][COLOR=#0000cd]50[/COLOR]           [/B]
[B][COLOR=#0000cd]17[/COLOR]    [/B].0139    71.94    8.99   23.44   [B][COLOR=#0000cd]23[/COLOR]           [/B]
[B][COLOR=#0000cd]16[/COLOR]    [/B].0278    35.97    4.50   14.45   [B][COLOR=#0000cd]14[/COLOR]           [/B]

[B][COLOR=#0000cd]15[/COLOR]    [/B].0463    21.60    2.70    9.95   [B] [COLOR=#0000cd]9[/COLOR]           [/B]9
[B][COLOR=#0000cd]14[/COLOR]    [/B].0694    14.41    1.80    7.25   [B] [COLOR=#0000cd]7[/COLOR]           [/B]7
[B][COLOR=#0000cd]13[/COLOR]    [/B].0972    10.29    1.29    5.45   [B] [COLOR=#0000cd]5[/COLOR]           [/B]5
[B][COLOR=#0000cd]12[/COLOR]    [/B].1157     8.64    1.08    4.16   [B] [COLOR=#0000cd]4[/COLOR]           [/B]4
[B][COLOR=#0000cd]11[/COLOR]    [/B].1250     8       1       3.08   [B] [COLOR=#0000cd]3[/COLOR]           [/B]3
[B][COLOR=#0000cd]10[/COLOR]    [/B].1250     8       1       2.08   [B] [COLOR=#0000cd]2[/COLOR]           [/B]2[B]
[COLOR=#0000cd] 9[/COLOR]    [/B].1157     8.64    1.08    1.08   [B] [COLOR=#0000cd]1[/COLOR][/B]           1[B]
[COLOR=#0000cd] 8[/COLOR]    [/B].0972      ...     ...    0      [B] [COLOR=#0000cd]0[/COLOR]           [/B]0

[B] 7[/B]    .0694
 [B]6[/B]    .0463
 [B]5[/B]    .0278
 [B]4[/B]    .0139
 [B]3[/B]    .0046

So I am not following all of what you are doing here, but the buying a 16 with 14 points seems off. The official point buy runs 1 additional point for each score above 8 up to 13. After that, each additional ability score costs the ability modifier more than the previous ability score. 14 means a +2 modifier, so it costs 2 more than a 13, and 15 costs 2 more than 14. Following that progression:

Score	Cost	Modifier/Increase over previous ability score's cost.
16	12	+3
17	15	+3
18	19	+4
19	23	+4
20	28	+5

EDIT: Okay, now I see you were using a modified dice probability to fit your curve to the official point buy costs. If it gives you what you want and allows roughly equivalent scores then go for it, but I would suggest looking at the ability score modifier to determine cost if you have not done so already.

EDIT2: Taking another look at it, the 50 point cap in the system you propose allows a character to start with 3 16s and 3 -1 modifiers versus the standard point buy of 3 15s and 3 -1 modifiers. So it definitely allows for stronger characters being created.

 

[Blue]

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

I think the cost of a 16 is /you can't start there/.

1. The balance point of ASI vs. feat needs to be a real tradeoff to have meaning.
2. Some builds can excel with a single very high stat (rogue, various archers) that covers the majority of what they do while others require multiple abilitiy scores and would be well behind if someone could just focus on one.
3. One of the more common "X is overpowered" threads are when people are using rolled scores and starting with high abilities score. I think there's one now complaining that Bladesinger AC is overpowered because at low levels their character has 20 INT and 20 DEX.
4. Starting with a +4 and going to a +5 breaks a bit out of bounded accuracy for those levels.
5. Spending a lot of point buy on a 16 then ends up with lots of mediocre or dump stats. "Well, I've got an 18 DEX after racials, but everything else gives +0 or worse.
6. This encourages only playing classes with a +2 racial ability to the score you want to maximize, so you'll further restrict class/race combinations.

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

Breaking down the point buy costs compared to the distribution of 4d6 drop the lowest. A 13 is the most likely result, I'd like to treat that those all cost 1 as a given and not worry about it. (By the distribution, 8 to 9 and 9 to 10 should probably cost 2 points, but that would encourage more dump stats by saving twice as many points leaving at 8, so I'm on board with it.)

I would strongly recommend having two abilities scores with the same price increase - 14 and 15 are the same, 16 and 17 would be the same. This is to prevent the issue with races that only give +1 racial becoming too far behind the curve. And anyway, to get to 17 you need to have already paid the higher cost for 16 as well.

I'm torn. Looking at the distribution, I'd got up by 3 for 16 and 17, but I think that that makes 16 too accessible because of the possibility of starting with an 18 so I'd rather go for increasing the cost by 4.

16 ... 13 points
17 ... 17 points

Progression: output [highest 3 of 4d6]
http://anydice.com/program/9b26

 

[Yaarel]

@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?