Whacked out attribute point buy

[seasong]

There is another way to represent 4d6/drop. Rather than represent eh advantage of possessing an ability score better than xx% of the population, you give points that allow you to average the same.

In this system, you would start with 3s in every ability score, and then have 56 points to buy the ability scores up with, at a 1:1 rate. This will allow you to end up with (for example), 18, 18, 18, 7, 7, 6, which is the extreme top end of probability for 4d6/drop.

The 56 points will always average out to 12.33 (a hair above the 12.245 avg of 4d6/drop), so you may wish to drop it to 55 points to give random rollers a slight edge.

 

[ichabod]

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).

Easy to get a couple 16's and a decent range of other numbers? Under your system, a 16 costs 12 points. You buy 2 16's and you have four points left. That means you can get one 12 and three 8's, or four 9's. Three or four -1 mods is not a 'decent range of other numbers.'

If you like your system, fine with me. It's not like anyone is making me use it. I'm just saying I would never want to use it, and it does not do what you claim it does (replace 4d6 low).

 

[Drawmack]

The problem is seasong that your way does not modle 4d6 drop the lowest method, and as a matter of fact no point buy system can modle a rolling system. and here's why.

When you roll dice you have x probability to get n score.

When you roll those dice again you still have x probability to get n score.

(There is a variance in the probability factors but it is minute and requires complex chaos theory to calculate.)

With a point buy method you sacrafice one score to get better at another score.


If you would like to represent the entire range of ability scores with my system here is the general formula

n score costs x points + repetition modifier (rm).

rm = bonus/penalty of score * (number of times the score is used-1)

x = 0 or (ability score - 9) whichever is greater.

BTW: Even if you modled a single roll in the 4d6-lowest method your points are still messed up attached is the spread sheet that proves it.

Conclusion attempting to model dice with the point buy is impossible. Point buy should be used when the GM wants every player at an equal power level so that they don't turn into a bunch of winy snivelly little brats.

 

[seasong]

If you like your system, fine with me. It's not like anyone is making me use it. I'm just saying I would never want to use it, and it does not do what you claim it does (replace 4d6 low)

Dude, I'm PLAYING WITH NUMBERS. And the system does exactly what I claim it does: represent the advantage of one set of rolls over another. See the post immediately prior to yours for one that represents any perfectly average 4d6/low roll, which is a very different thing (and may be more to your liking).

And I also never claimed it replaced 4d6/low. I claimed that it could replace (reasonably well) the current point buy system.

I'm not proposing a point buy system that will bring celestial angels down, or that is even necessarily GOOD and JUST. I'm reverse engineering WotC's system for it, and making it better fit the pattern I thought I saw in it. And I think I did a bang on job of it.

Again: This is me at play in the numeric sandbox. That's all this is.

I've presented a few other dice probabilities using the same construction method, you might like those better. I also presented a system that averages the 4d6 roll and lets you assign totals (the 56 point system prior to yours). I've gone well and above the call of duty here, because I thought you might like an alternative to what was (obviously) unsatisfactory to you.

 

[seasong]

Okay, quick disclaimer: Drawmack and ichabod are smart people, and I can respect that. In point of fact, reading very carefully, everything they've said is completely true - it just doesn't apply to what I'm doing.

The problem is seasong that your way does not modle 4d6 drop the lowest method, and as a matter of fact no point buy system can modle a rolling system. and here's why.

This is all correct and true. I cheerfully acknowledge that my system does not model every possible roll with 4d6/low. Fortunately for me, then, that my system does not attempt such a herculean feat, eh?

The two systems I've posted do, I think, achieve something valuable. The first models the advantage (in terms of population statistics) of having a particular set of ability scores, much like I think WotC's system originally attempted. The second models all possible average distributions of 4d6/low. Both do a bang up job of their respective tasks, but they do not, as you said, model all possible outcomes of 4d6/low.

I am a little disconcerted that you think I would try, when such is obviously impossible.

When you roll dice you have x probability to get n score.

When you roll those dice again you still have x probability to get n score.

(There is a variance in the probability factors but it is minute and requires complex chaos theory to calculate.)

With a point buy method you sacrafice one score to get better at another score.

Yes, a very nice explanation of why randomness can not be represented with a non-random system. Again, it is fortunate indeed that I was not attempting to.

BTW: Even if you modled a single roll in the 4d6-lowest method your points are still messed up attached is the spread sheet that proves it.

Your spreadsheet does not seem to include any options for dropping the lowest. Please add and repost.

 

[ichabod]

And I also never claimed it replaced 4d6/low. I claimed that it could replace (reasonably well) the current point buy system.

I'm sorry, but you've claimed it replaced 4d6/low three or four times in this thread. If it's not intended to do that, fine. Just do us all a favor and be more clear about that.

 

[Mike Sullivan]

One minor thing, seasong:

People's who generate their stats with the default system (4d6, drop lowest, etc) are going to have slightly higher stats, on average, than your calculations suggest, because of the "these stats suck, reroll the whole lot of 'em" rule. That chops off the low end of that particular probability curve, which will rachet up the mean a bit.

I can't model that without doing a Monte Carlo, but, at a intuitive guess, I'd imagine that if you took your point-buy system and put it at more like 30 points, you'd have a better "rough equivalency" to the default die system.

 

[seasong]

Originally posted by seasong
"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."

"The system I wrote was an attempt to better represent the 4d6 curve than WotC's original attempt."

"If you roll six times, one in ten characters will have ONE 18. I think this system simulates that rather nicely."

Those are the closest to what you say I said that I can find. I think they are pretty clear about what is and is not being simulated or represented. And that's without the plethora of words I've used everywhere else where the line is clearly demarcated, such as

"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"

and

"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."

and

"The system I wrote was an attempt to better represent the 4d6 curve than WotC's original attempt."

and

"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."

How much clearer did I need to be?

 

[seasong]

People's who generate their stats with the default system (4d6, drop lowest, etc) are going to have slightly higher stats, on average, than your calculations suggest, because of the "these stats suck, reroll the whole lot of 'em" rule. That chops off the low end of that particular probability curve, which will rachet up the mean a bit.

Hm... good point! 30 points sounds about right as a fix for that, but I think that individual GMs and players will have different tolerances for "how many rerolls are enough" to get perfect ability scores.

Somewhat off-topic, but here's a way to switch between randomized and point-based .

1. Have everyone roll their stats.
2. If you allow rerolls of entire stat blocks, wait until that is finished.
3. Each individual may then, at their option, redistribute their points at a 3:2 ratio. That is, they can take -3 from any ability score or combination of ability scores, and give one ability score a +2 inherent bonus. They may do this as often as they like, to a maximum of 18. If I am feeling kind, I shall let them split the +2 bonus between two odd-numbered ability scores.

For example, if I rolled an 18, 18, 18, 12, 4, 4 (a very average roll, by the way), I could change that to an 18, 15, 14, 10, 8, 6 to shore up my weaknesses, or to an 18, 18, 15, 14, 4, 4 to give myself a bit of a middle range while retaining my weaknesses.

 

[Drawmack]

Your spreadsheet does not seem to include any options for dropping the lowest. Please add and repost. [/B]

sorry posted the wrong sheet, here is the correct one.