Whacked out attribute point buy

[seasong]

This looks convuluted. I'm not sure what inspired me to do it. But it works pretty good.

Proposed variant (you can skip all the explanation following):
9 - 1 pts
10 - 2 pts
11 - 3 pts
12 - 4 pts
13 - 6 pts (WotC 5)
14 - 8 pts (WotC 6)
15 - 10 pts (WotC 8)
16 - 12 pts (WotC 10)
17 - 15 pts (WotC 13)
18 - 18 pts (WotC 16)

Use 27 points as your base or, if you are replacing 4d6 (drop the lowest) entirely, you might decide to use 28 points. The results are about the same for either.

Kobolds n Chickens: less than 12
"Average people" dirty-n-gritty campaign: 12-20 points.
Low heroic: 21-26 points.
Heroic D&D Standard: 27-30 points.
High Power Campaign (2d6+6): 31-40 points.
1d6+12 campaign: 60 points

Now for the reasons why I like this point distribution better.

I had a few minutes, an Exel program up, and an irritating work day, so I worked out the probabilities for 4d6, drop the lowest. They are (chance to roll a particular total):

3 - 0.08%
4 - 0.31%
5 - 0.77%
6 - 1.62%
7 - 2.93%
8 - 4.78%
9 - 7.02%
10 - 9.41%
11 - 11.42%
12 - 12.89%
13 - 13.27%
14 - 12.35%
15 - 10.11%
16 - 7.25%
17 - 4.17%
18 - 1.62%

Stacked, the percentage of people you are better than or equal to at any ability score is:

3 - 0.08%
4 - 0.39%
5 - 1.16%
6 - 2.78%
7 - 5.71%
8 - 10.49%
9 - 17.52%
10 - 26.93%
11 - 38.35%
12 - 51.23%
13 - 64.51%
14 - 76.85%
15 - 86.96%
16 - 94.21%
17 - 98.38%
18 - 100.00%

If you divide the % of the people you are better than at 4 by the % at 3, you get 5. At 5:4, you get 3. Continuing this trend (the proportion of the population you gain that you are now better than or equal to) looks like this:

4 - 5
5 - 3
6 - 2.4
7 - 2.055555556
8 - 1.837837838
9 - 1.669117647
10 - 1.537444934
11 - 1.424068768
12 - 1.336016097
13 - 1.259036145
14 - 1.19138756
15 - 1.131526104
16 - 1.083407276
17 - 1.044226044
18 - 1.016470588

If you assume that shifting from an ability score of 3 to an ability score of 4 is "worth" 1 point of advantage, you get the following costs:

4 - 1 (total cost 1)
5 - 3 (total cost 4)
6 - 7.2 (total cost 11.2)
7 - 14.8 (total cost 26)
8 - 27.2 (total cost 53.2)
9 - 45.4 (total cost 98.6)
10 - 69.8 (total cost 168.4)
11 - 99.4 (total cost 267.8)
12 - 132.8 (total cost 400.6)
13 - 167.2 (total cost 567.8)
14 - 199.2 (total cost 767)
15 - 225.4 (total cost 992.4)
16 - 244.2 (total cost 1236.6)
17 - 255 (total cost 1491.6)
18 - 259.2 (total cost 1750.8)

If you divide those point costs by 100, and round to the nearest, you get the following (ignoring costs of 0):

9 - 1 pts
10 - 2 pts
11 - 3 pts
12 - 4 pts
13 - 6 pts (WotC 5)
14 - 8 pts (WotC 6)
15 - 10 pts (WotC 8)
16 - 12 pts (WotC 10)
17 - 15 pts (WotC 13)
18 - 18 pts (WotC 16)

Eh? Ehhhh?

If you decide to use these costs instead of WotC's, you will need to set the default points to 28 instead of 25, in order to keep the proportion to the maximum the same. This will also result in a higher average if someone bought 12s across the board (avg 12.33 instead of 12.16; the average 4d6/drop lowest roll is 12.24). So... you might drop it to 27 points.

 

[ichabod]

The problem I see with this sort of thing is that using 4d6 drop lowest, you have almost a 10% chance of getting an 18 as your highest stat. But with your point buy, characters with an 18 stat are going to be rather focused. They can either get all 10's, or for each 12 they can take an 8. A guy with a high score of 17 isn't that much better off, and that is over a 30% chance with 4d6 drop lowest. I'd like to see a point buy system that takes this into account. Getting one 18 would be rather cheap, but getting two would be expensive.

 

[seasong]

The problem I see with this sort of thing is that using 4d6 drop lowest, you have almost a 10% chance of getting an 18 as your highest stat.

And? That means only one in ten characters will ever roll an 18. You have better odds with the point buy.

But with your point buy, characters with an 18 stat are going to be rather focused.

Er... with MY point buy, or with point buys in general?

Getting one 18 would be rather cheap, but getting two would be expensive.

Even with a 10% chance of getting one 18, that's one in ten characters that has an 18. Why should a point buy make that rather cheap?

Also, I should point out with 4d6/drop, you have 34% chance of having a 7 or less, something that doesn't happen at all with point buy. With a point buy system, you give up the chances of a truly amazing ability line-up in return for more control over the final product.

 

[Drawmack]

The problem with this is the problem with all point buy systems.

It is almost impossible to max even a single stat. I like what was said before, 10 = 1 (always); 11 = 2 (always); 12 = 3 (+1 for each additional 12); 13 = 4 (+1 for each additional 13); 14 = 5 (+2 for each additional 14); 15 = 6 (+2 for each additional 15); 16 = 7 (+3 for each additional 16); 17 = 8 (+3 for each additional 16); 18 = 9 (+4 for each additional 18)

This means that a single 18 would cost only 9 points but 2 18s would run you 22 points.

So on a 25 point buy system:
18 = 9+
11 = 2+
12 = 3+
12 = 4+
12 = 5+
11 = 2
---------
____25

So you can still be pretty well rounded with a single 18 stat but taking 2 18s is really cripling. Actually you couldn't even do it with all 10's for the other scores an 18 an a 17 is the best you could do. Though you could do a couple of 17s and still have a couple of 12's it would still take you until 8th level to get two seveteen's upto 18's

I actualy kind of like this breakdown. I may implement it.

 

[seasong]

"It is almost impossible to max even a single stat."

...without spending the points? Wham, bam, I've spent 'em!

You don't seem to have a problem with the point buy so much as you do with the results of 4d6/drop the lowest. Set the point-buy at 36-37 points and you get near-identical results... they just won't be in line with the 4d6 method.

The system I wrote was an attempt to better represent the 4d6 curve than WotC's original attempt. It was not an attempt to rewrite "what a good ability score" is, or to provide even higher averages.

In fact, your system better represents 1d10+8. Which is fine, if that's what you prefer. But 36 points also does that pretty decently well.

 

[kenjib]

Well done. Great reasoning. I think that, practically, there is only a very subtle difference, but I do like how it is based off of the 4d6 probabilities better.

 

[ichabod]

[BThe system I wrote was an attempt to better represent the 4d6 curve than WotC's original attempt. It was not an attempt to rewrite "what a good ability score" is, or to provide even higher averages.
[/B]

The problem is your system simulates ONE 4d6 drop one roll, but it doesn't simulate six of them. That's what we're talking about.

 

[Saeviomagy]

The other problem is that I'd much prefer a system which really covers the entire range.

Otherwise everyone starts thinking that an '8' in a stat makes that character a complete loser in that regard, when really that should be saved for someone with a 3 in a stat.

 

[seasong]

Saeviomagy: Regarding managing the whole range, just don't divide the cost by 100 (somewhat rounded off):

4 - 1 (total 1)
5 - 3 (total 4)
6 - 7 (total 11)
7 - 15 (total 26)
8 - 30 (total 56)
9 - 45 (total 101)
10 - 70 (total 171)
11 - 100 (total 271)
12 - 130 (total 401)
13 - 160 (total 561)
14 - 200 (total 761)
15 - 225 (total 986)
16 - 250 (total 1236)
17 - 255 (total 1491)
18 - 260 (total 1751)

You could round those off a bit more, of course. Then, you would need to provide about 2,750 points to stick to the 4d6 range. I think you can see why I didn't .

Regarding ichabod's point - I would disagree. If you roll six times, one in ten characters will have ONE 18. I think this system simulates that rather nicely. A more generous system will simulate something closer to one in one or one in two characters having a single 18.

As it stands, it is very easy to get a couple of 16s, and a decent range of other numbers, on 28 points, which is fairly typical of rolling 4d6/drop six times in a row. Remember, in order to simulate 4d6, it needs to average out to somewhere around 12.24 (the closest you'll get on six attributes is 12.16 or 12.33, which is the range my system mostly hovers in).

If you mean it doesn't simulate the random fluctuations outside of that, well, no, it doesn't. That's why it's a point system, and not a randomized system.

And like I have said before: if you want higher averages, just assign more points to the players - WotC has no problems with that, and neither do I.

 

[seasong]

Well done. Great reasoning. I think that, practically, there is only a very subtle difference, but I do like how it is based off of the 4d6 probabilities better.

That's the only reason I did it . I could almost see the probabilities in the original numbers, so I had to check my suspicions. It really looks like the designer of the original point system did the same thing I did, then shaved a few points off to make it a cleaner progression (+1/2/3), and shaved a few points off (from 28 to 25) to account for the new total.

In case anyone's still interested at this point, here's the same treatment for 3d6 progression. I've skipped most of the steps (but it's exactly the same process as for the 4d6). I divided by 5 instead of 100 for this one:

6 - 1 (1 total)
7 - 2 (3 total)
8 - 3 (6 total)
9 - 4 (10 total)
10 - 5 (15 total)
11 - 7 (22 total)
12 - 8 (30 total)
13 - 9 (39 total)
14 - 10 (49 total)
15 - 10 (59 total)
16 - 11 (70 total)
17 - 11 (81 total)
18 - 11 (92 total)

To simulate 3d6 reasonable well, you need 111 (eleventy-eleven) points to divide among the attributes. To get an 18 out of that, you'll need 7s and 8s in everything else. Which (protests to come aside) is very reasonable, probability wise, for 3d6.

And here's 2d6+6, for those who prefer a better likelihood of most characters getting an 18. This one I did not divide at all:

9 - 1 (1 total)
10 - 2 (3 total)
11 - 3 (6 total)
12 - 5 (11 total)
13 - 7 (18 total)
14 - 9 (27 total)
15 - 10 (37 total)
16 - 11 (48 total)
17 - 12 (60 total)
18 - 12 (72 total)

To simulate 2d6+6, you'll need to give 161 points. That may seem high (and indeed, it is), but the bell curve is flatter for 2d6, and so you need to be able to have a result of 8, 10, 12, 14, 16, 18. The only problem with 2d6+6 is that you can't get the average - you'll average somewhere between 13 and 14 (a bit high for the roll).