Whacked out attribute point buy

[Drawmack]

Actually I blend the point buy/roll mixture is such a way as to aleviate the reroll problem.

If you roll and then you're stats do not equal 32 points on the WotC point buy system you are allowed to adjust your stats until they equal 32 on the point buy system.

Seasong:
If both ichabod and myself got the impression that you were trying to duplicate the roll system then I would say there is a 66% chance you were not clear and a 33% chance that you were clear. Please do not take offense at this it is simply flat probabilities based on the number of people who are concerned is all.

Additionally if you like to play around with the stuff why are you not in the die probabilities thread?

 

[seasong]

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

No problem. This looks like the same probabilities as I was working with (my first post in this topic), just done up with a chart? What is this showing, again?

 

[Drawmack]

No problem. This looks like the same probabilities as I was working with (my first post in this topic), just done up with a chart? What is this showing, again?

You calculated the slope wrong.

 

[kenjib]

Seasong:
If both ichabod and myself got the impression that you were trying to duplicate the roll system then I would say there is a 66% chance you were not clear and a 33% chance that you were clear. Please do not take offense at this it is simply flat probabilities based on the number of people who are concerned is all.

I did not think he was in the least bit ambiguous and I understood what he was getting at 100% perfectly the first time. To say that you can simulate a random system using a non-random method just doesn't make any sense. Furthermore, when I follow and understand the mathematics he uses to arrive at his point values, it is completely and pefectly clear what he is trying to achieve just from looking at his calculations and without any of the explanatory text.

Furthormore, from a statistical standpoint, people are more likely to post if they disagree than if they agree, so the fact that two people were confused and posted has very little direct correlation to the total percentage of people that were confused. It's entirely possible that only you Ichabod misunderstood out of 20+ readers.

P.S. I like hybrid roll/point buy too.

 

[seasong]

You calculated the slope wrong.

Our numbers are the same. And I didn't even use the slope of the raw numbers anywhere that I can see. I used the slope of the percent of the population any number is better than or equal to.

For example, a 13 is better than or equal to 64.51% of the population.

Whether or not that's a good measure for how advantageous a given number is, I'm not so sure, but it looks like that's what WotC's numbers were closest to, so I went with it.

 

[seasong]

Additionally if you like to play around with the stuff why are you not in the die probabilities thread?

Didn't see it. Is it in the General Forum, or am I just blind looking at House Rules?

 

[Drawmack]

You are correct WotC's numbers are based on the area under the curve.

I think to improve on this you need to derive a formula that bases it on both the area under the curve and the slope of the curve. This can be easily accomplished with a cumulative system.

Step 1) Assign an arbitrary point value to an arbitrary percentage of the population. Both systems do this, however you are assigning 1 point to 45%, I assume that this was done because (50 - 45) < (64 - 50).

Step 2) At the critical points (all whole numbers) calculate the slope of the curve and base your increase on that. For example

# Slope
9 29
10 31
11 26
12 19
13 5
14 -12
15 -29
16 -37
17 - 40
18 - 33

first step is to |slope|, this will get rid of all negative numbers.
# Slope
9 29
10 31
11 26
12 19
13 5
14 12
15 29
16 37
17 40
18 33

Our lowest slope is 5 so let's make step to to divide all slopes by 5 and round down.
# Result
9 5
10 6
11 5
12 3
13 1
14 2
15 5
16 7
17 8
18 6

Now if we normalize the results around a point, take 13 since it's the lowest.

# Result
9 5
10 4
11 3
12 2
13 1
14 2
15 3
16 4
17 5
18 6

Now we use summation to get our point totals.
# Points
9 1
10 5
11 8
12 10
13 11
14 13
15 16
16 20
17 25
18 31

To use this point buy system you would need to give out a lot of points, however it is a better model because it uses area under the curve and point slope instead of just area under the curve. I.E. It's much easier to jostly around near the mean of 13 then it is to work at either end point.

 

[seasong]

You are correct WotC's numbers are based on the area under the curve.

Or I'm wrong, and their based on an intuitive guess. Without getting them in here, since their numbers don't quite match up, we'll never really be sure .

I think to improve on this you need to derive a formula that bases it on both the area under the curve and the slope of the curve. This can be easily accomplished with a cumulative system.

Why do you think this will improve on it, for purposes of representing the advantage of having a particular ability score?

Step 1) Assign an arbitrary point value to an arbitrary percentage of the population. Both systems do this, however you are assigning 1 point to 45%, I assume that this was done because (50 - 45) < (64 - 50).

I assigned an arbitrary value to the advantage of shifting from an ability score of 3 to a 4. All further points were based on the slope of the population %, as mentioned. Once I had all of the points worked out, I divided them by 100, in order to have usable numbers.

That your assumption above and my method synchronize on most of the curve is an interesting coincidence .

With that said, I like the idea of mixing the effects of the % chance of getting a number with the % population you equal/exceed.

Now if we normalize the results around a point, take 13 since it's the lowest.

# Result
9 5
10 4
11 3
12 2
13 1
14 2
15 3
16 4
17 5
18 6

I'm not sure why you normalized the numbers?

Now we use summation to get our point totals.
# Points
9 1
10 5
11 8
12 10
13 11
14 13
15 16
16 20
17 25
18 31

To use this point buy system you would need to give out a lot of points, however it is a better model because it uses area under the curve and point slope instead of just area under the curve. I.E. It's much easier to jostly around near the mean of 13 then it is to work at either end point.

To get 12, 12, 12, 12, 13, 13 would cost 62 points (28 old).
To get 11, 11, 11, 11, 12, 18 would cost 73 points (34 old).
To get 8, 8, 8, 16, 16, 18 would cost 71 points (36 old).

Note that all three of these are "average" rolls for 4d6/low.

"Old" means the system I put at the beginning of this thread. The new system hovers around "old" x 2 for both middle range and extreme. It seems almost exactly as 'jostly' as mine at the middle range and the extremes.

 

[seasong]

Well, I looked at the die probability thread. It looks more like a programming class to me .

Seriously, it looks like the guy is looking for a program that calculates probabilities, not things to do with the probabilities once he has them. I'll leave it to the real math & CS geeks.

 

[kenjib]

Now we use summation to get our point totals.
# Points
9 1
10 5
11 8
12 10
13 11
14 13
15 16
16 20
17 25
18 31

To use this point buy system you would need to give out a lot of points, however it is a better model because it uses area under the curve and point slope instead of just area under the curve. I.E. It's much easier to jostly around near the mean of 13 then it is to work at either end point.

It depends on what you mean by "easier". If you mean easier in terms of fewer points changing between scores then you are correct. This assumes, however, that gaining and losing points are equally desirable, which is not the case.

i.e. If you get increasing gain from taking a lower score, I would argue that it becomes easier to jostle down in the lower range because you get more returns for it. I think that while it does help to maintain an averaged point spread, it creates an unwanted dynamic that encourages dump-stat behavior. What do you think?