(Discussion) Character Points Change Issue

[Knight Otu]

As it happens, I made a spreadsheet earlier today, using 6*5000 rolls for 4d6, drop the lowest. The average for stats is 12,25something, which translates into five 12s and a 13 (more of a 13.5), which would be a 25 point buy.

The average point buy cost, assuming that stats below 8 are 0 points, however, works out to be 29.1x.

The reroll parameters, of course, would increase this further.

That said, I have already voted no.

Edit - After a tweak in my spreadsheet, I also have the average point buy cost with taking "rerolls" into account (to be honest, it ignores "illegal" rolls). It works out to bo 30.5.

 

[Pbartender]

But the average *points* per character isn't 4.24*6=25.4, it's somewhat higher.

That depends on how you word your statistic...

The point buy value for characters with average ability scores using the 4d6-L system is about 25 points.

The average point buy value for characters with ability scores using the 4d6-L system is about 30 points... Or something there-abouts due to the reasons you stated above.

Do you want an average set of abilities, or do you want an average group of characters?

 

[orsal]

That depends on how you word your statistic...

The point buy value for characters with average ability scores using the 4d6-L system is about 25 points.

The average point buy value for characters with ability scores using the 4d6-L system is about 30 points... Or something there-abouts due to the reasons you stated above.

Do you want an average set of abilities, or do you want an average group of characters?

Well, a character with all 12s and 13s is a middling character *in the extreme*. That isn't what I would consider average. The average character neither has all middling abilities, nor all extreme abilities. Something like 8,10,12,13,14,16 in some order would seem more average to me for a 4d6 method -- the character's best and worst ability aren't the best and worst possible, but nor are they abnormally mediocre. 13 as a highest score is very low, and 12 as a lowest score is very high.

The appropriate average to consider, IMHO, is the mean of all characters created by a given method. That's 29 point something.

 

[Pbartender]

Well, a character with all 12s and 13s is a middling character *in the extreme*. That isn't what I would consider average. The average character neither has all middling abilities, nor all extreme abilities. Something like 8,10,12,13,14,16 in some order would seem more average to me for a 4d6 method -- the character's best and worst ability aren't the best and worst possible, but nor are they abnormally mediocre. 13 as a highest score is very low, and 12 as a lowest score is very high.

The appropriate average to consider, IMHO, is the mean of all characters created by a given method. That's 29 point something.

Oh, I agree.

You're making precisely the same point I was... That there is a distinct difference between a character with 'average' abilities, and an 'average' character.

 

[Creamsteak]

Each ability score generated by 4d6-L gives you 1296 different rolls (6 to the 4th power) possible. Each possible result (3 to 18) occurs a certain % of the time.

One easy method that I used to generate the average points value of all ability score arrays (6 sets of 4d6-L) was to use those %s as the occurence factor of each set of each ability. There are 6^24 different ways the dice could fall, many of which are the same. The very least common result would be 24 1's, which occurs 1 time out of the 6^24 total.

Using a computer, I can run a program that tests all 6^24 different rolls. It's not entirely accurate though, since I am using a certain degree of floating decimals.

If you accept all sets of 24 six sided dice, subtracting the lowest die from each set of 4 generated, you get an average points value of around 28, give or take a little.

Using all of the sets of dice, you get roughly 30.5 using my method, but I do believe someone did a more accurate method (testing all 6^24 comparisons), and came up with something closer to 31.5.

I'm not sure how much that means to anyone, but my bet would have been to vote on a change to 31 point buy. 31 seems just slightly more accurate, and it's odd. I'm also ameniable to 32... but 33 seems out of place to me.

 

[orsal]

Using all of the sets of dice, you get roughly 30.5 using my method, but I do believe someone did a more accurate method (testing all 6^24 comparisons), and came up with something closer to 31.5.

I very much doubt that anybody ever ran a program on all 6^24 possible sets of die rolls. If you could check a million every second, you'd have to run the computer nonstop for 150 thousand years to do that. Neither D&D nor high-speed computing have been around that long.

However, for a straight 4d6, drop lowest, no exchanges or refunds, you don't need to consider 6 ability scores at once. Just consider a single ability score. There are only 1296 combinations, and very crude programs can handle that. (That's how I did the spreadsheet I mentioned earlier.) You can then get a distribution for either score on the 3-18 scale or point buy count for a single ability; find its average, and multiply by 6 to get the average for a whole character. The average points come out to 29.13 if you count everything less than 8 as 0 points, 28.71 if you count negative points (between -1 and -5) for lower scores.

If you get into a "reroll the whole character if you don't get something at least this good overall" formula, it becomes more complicated, because you can't consider each of the six attributes in isolation anymore. That's when you need to know a little mathematics. It would be fairly simple to tweak the spreadsheet to calculate averages for a "reroll if no attribute is above X" rule, but rather harder for a "total must be at least Y" rule if you want to be exact. (An approximation, however, shouldn't be too difficult with a little basic statistics, which I sometimes teach so I should be able to do it.)

 

[Thomas Hobbes]

Is anyone else getting the Charlie Brown grown-up voice (mwa mwa mwa mwa mwa mwa mwa) in their heads when they read the statistical discussion?

 

[Pbartender]

Is anyone else getting the Charlie Brown grown-up voice (mwa mwa mwa mwa mwa mwa mwa) in their heads when they read the statistical discussion?

For me it's getting to be something more like...

BLAH BLAH BLAH BLAH BLAH BLAH 31 point buy. BLAH BLAH BLAH BLAH BLAH BLAH BLAH. BLAH BLAH BLAH. BLAH BLAH BLAH BLAH BLAH BLAH.

33 point buy BLAH BLAH BLAH. BLAH BLAH BLAH BLAH BLAH. BLAH BLAH. BLAH BLAH 31 point buy BLAH BLAH. BLAH BLAH BLAH BLAH.

BLAH BLAH BLAH BLAH. BLAH BLAH. No change BLAH BLAH BLAH. BLAH BLAH BLAH.

 

[Creamsteak]

I very much doubt that anybody ever ran a program on all 6^24 possible sets of die rolls. If you could check a million every second, you'd have to run the computer nonstop for 150 thousand years to do that. Neither D&D nor high-speed computing have been around that long.

No, your missing the elegance of a simpler program design. You don't need to run 6^24 binary comparisons to check each total, you need to run 15^6 by simplifying the algorithm. And you only need a few kilobytes of memory to run it as well. Look at the equation from the end result (6 different sets with 3 to 18 listed) and you can simplify it based on that. That's what I've done, but a more precise language can do the same thing only vastly more precise. If I took something to the second double precision instead of the first, I could technically calculate it with less than a billionth of error.

And taking just 1 ability scores average points value for all results will not yield you the results for two reasons. 1) You can't take criteria like "one ability must be greater than 13" into consideration, and 2) Since point buy is non-differential, you can't break it down into a linear equation that breaks up evenly, so since 18s and 17s are worth more than 14s and 9s, you get a total which is related to the most common values 12-14 that will dominate the single instance, but not all instances that exist for 6 arrays.

Now, the only speculation left is what to do with abilities less than 8? Do you factor them in as 0s or as negative scores?

 

[crueldespot]

If 33 point buy is better than 30 point buy, then why stop there? Why not 36 point buy? Why not 50 point buy?

I am being sarcastic. As long as everyone has the same number of points, what does it matter? The only difference I see is this: With less points, characters are more likely to have a flaw (a low score) which makes them more interesting. With a lot of points, they are more likely to be average or above average in everything- which makes them less distinctive from each other.