I remember for 2nd edition, I read a statistical breakdown of the average expected score from each stat generation method -- roll 3d6, roll 4d6 drop lowest, point buy, etc.
Anybody have something similar for Pathfinder?
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... I read a statistical breakdown of the average expected score from each stat generation method ... roll 4d6 drop lowest
I like fiddling with math problems, kinda' like little puzzles, but for the life of me I've never been able to figure out what the formula would be for getting the average on 4d6 drop the lowest. How the hell do you model that?
Ahh, I should have a file somewhere where I calculated probabilities with several different methods...if I can find it, I'll post info off it tomorrow.
I already did this in "Welcome to the Design Forums" sticky thread. I have graphs of stat distribution and everything, but they are on a different computer that I can't get to untill the weekend. If anyone wants more detailed information I can get it for them then (ie percent of getting an 18 etc).
First off, I think Classic needs to mention that it is markedly underpowered in comparison to the other methods and the way the rest of the game is designed.
I don't know if anyone cares, but I was in the mood for fiddling with excel, and did some analysis on the different rolling methods outlined in beta. AVG=average score for a stat, STDEV=standard deviation for that method, NINTYSIX= 96% of all stats rolled will be between these values. Numbers rounded to three decimals.
Classic
AVG(10.5), STDEV(2.965), NINTYSIX(4.570,16.430)
Modern
AVG(12.245), STDEV(1.708), NINTYSIX(8.828,15.662)
Heroic
AVG(13), STDEV(2.449), NINTYSIX(8.101,17.899)I think it would be cool to add a sentence for each method.
Classic: The average score is 10 with most scores between 5 and 16.
Modern: The average score is 12 with most scores between 9 and 16.
Heroic: The average score is 13 with all scores between 8 and 18
yeah, noticed that afterwards...I did calculate also some other ways of rolling, like 2d8+2, 4d4+2, 5d6 drop two lowest...but unfortunately couldn't find the file. So no info about those. More dice -> smaller deviation.
@Mosaic
The trick is to go with statistics instead of probabilities. Since its quite easy to generate all the possible outcome on a speadsheet, you end up with the whole population of outcome instead of a sample. So the numbers are exact.
for 4d6 drop lowest, here are the % of getting said score
18 21 0.016203704
17 75 0.041666667
16 169 0.072530864
15 300 0.101080247
14 460 0.12345679
13 632 0.132716049
12 799 0.128858025
11 947 0.114197531
10 1069 0.094135802
9 1160 0.070216049
8 1222 0.047839506
7 1260 0.029320988
6 1281 0.016203704
5 1291 0.007716049
4 1295 0.00308642
3 1296 0.000771605
middle colomn being the number of added occurences (21 out of 1296 throws give you 18, 75 give you 17 or 18 [so 75-21 is the 17 outcome], etc.)
last colomn is the probability of getting said score.
You can, from there, generate the statistical spread of the added 6 ability scores, or convert it into bonuses if you want. So you have in a quick glance the position of the added ability scores compared to the "expected" total. I've done this ages ago. I'll see if I can dig it up.
Oh, and JBScroeds...I'd say 96% is not particularly helpful figure here, it covers too large area...
I'd say "25% of values exceed XX, 75% of values exceed X" beside that average and STDEV are more informative pointers to compare rolling methods...
Oh, and JBScroeds...I'd say 96% is not particularly helpful figure here, it covers too large area...
I'd say "25% of values exceed XX, 75% of values exceed X" beside that average and STDEV are more informative pointers to compare rolling methods...
I just did the two standard deviations range because it was what I remembered off the top of my head. I never took a stats class, I'm an engineer and took linear algebra instead of stats because its way more useful for things like Finite Element Analysis. I just remembered 96% for two std-dev range. I could do up a percent over X if I had that spreadsheet on me, but I don't feel like redoing the whole thing...but I may anyways because I'm obsesive like that.
Oh, and JBScroeds...I'd say 96% is not particularly helpful figure here, it covers too large area...
I'd say "25% of values exceed XX, 75% of values exceed X" beside that average and STDEV are more informative pointers to compare rolling methods...
Yes, I am indeed obsesive and redid the sheet for 4d6-drop-lowest. The first column is the stat value, the second is the percent of the stats that will be greater than or equal to that stat value, and the third column is the percent chance of getting exactly that value.
3, 100.00%, 0.08%
4, 99.92%, 0.31%
5, 99.61%, 0.77%
6, 98.84%, 1.62%
7, 97.22%, 2.93%
8, 94.29%, 4.78%
9, 89.51%, 7.02%
10, 82.48%, 9.41%
11, 73.07%, 11.42%
12, 61.65%, 12.89%
13, 48.77%, 13.27%
14, 35.49%, 12.35%
15, 23.15%, 10.11%
16, 13.04%, 7.25%
17, 5.79%, 4.17%
18, 1.62%, 1.62%
So that means you have a 1.62% chance of getting an 18, 23.15% of a 15 or higher, and a 73.07% chance of getting an 11 or higher, and 13 is the most common single value, while 12.2446 is the average roll.
Yes, I am indeed obsesive and redid the sheet for 4d6-drop-lowest.
People who do these things tend to be a bit obsessive...good work :)
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The trick is to go with statistics instead of probabilities. Since its quite easy to generate all the possible outcome on a speadsheet, you end up with the whole population of outcome instead of a sample. So the numbers are exact.
That's funny, when I couldn't figure out a probability formula I just started listing out all the possible outcomes of 4d6 drop the lowest by hand. Obviously it got out of hand quickly. I was in the Peace Corps at the time so I had some free time, but not that much!
Thanks to all the math/excel wizzes for the mathmagics show.
What about the point buys? Is there a way to find an average for them for comparison purposes?
What about the point buys? Is there a way to find an average for them for comparison purposes?
Point buys are tricky unless you consider the average to be the same as whatever stat (amount of points)/6 would buy...
Longer option would be to take all the different spreads set amount of points can buy, and get an average of them, though that does not really model real world where some of the spreads are more common/popular/sensible than others.
What are the statistics for 2d6+6?
What are the statistics for 2d6+6?
Why? WHY? You people just made me redo another sheet. Its not right to take advantage of an obsessive like this. As before, the first column is the stat value, the second is the percent of the stats that will be greater than or equal to that stat value, and the third column is the percent chance of getting exactly that value.
8, 100.00%, 2.78%
9, 97.22%, 5.56%
10, 91.67%, 8.33%
11, 83.33%, 11.11%
12, 72.22%, 13.89%
13, 58.33%, 16.67%
14, 41.67%, 13.89%
15, 27.78%, 11.11%
16, 16.67%, 8.33%
17, 8.33%, 5.56%
18, 2.78%, 2.78%
As you can see, the range of possible values is reduced from the 4d6-drop type. Also, the mean, median, and mode are all 13. You also have the exact same chance of rolling above a 13 as you do below (the distribution is a triangle rather than a bell curve).
5d4 - 2 then? :)
Any ideas on how to get averages for point buys for comparison?
5d4 - 2 then? :)
Any ideas on how to get averages for point buys for comparison?
You had to ask. The first column is the stat value, the second is the percent chance of getting exactly that value, and the third column is the percent chance that the stat will be greater than or equal to that stat value.
3, 0.10%, 100.00%
4, 0.49%, 99.90%
5, 1.46%, 99.41%
6, 3.42%, 97.95%
7, 6.35%, 94.53%
8, 9.86%, 88.18%
9, 13.18%, 78.32%
10, 15.14%, 65.14%
11, 15.14%, 50.00%
12, 13.18%, 34.86%
13, 9.86%, 21.68%
14, 6.35%, 11.82%
15, 3.42%, 5.47%
16, 1.46%, 2.05%
17, 0.49%, 0.59%
18, 0.10%, 0.10%
The mean and median are 10.5, while the mode is 10. As for point buy, I could make a program to do it, and probably will since it seems to be a popular requst. Matlab, here I come.
EDIT: I just looked at pathfinder pointbuy, and its inclusion of negative points makes programing a pointbuy solver much more complicated and it really isn't worth my time.