Post/Author/DateTime	Post
#1 nabuchadnezzar Oct 13, 2008 1:32:01	Hello to all! I managed to calculate how many points (per the point buy system) are needed to correctly generate a "4d6" character. Short answer: 30 points. Long answer: First, I calculated the probability for each stat to appear, from 3 to 18 (sum all four dices and subtract the lowest). There are 6^4 = 1296 cases, then I associated each stat to its point cost (I used empirical values for 3-7 stats, but as you can see by editing those very values in the analysis sheet at the end, it doesn't really matter much).
#2 fallen-angle Oct 13, 2008 13:56:49	I had always wondered how many points the average 4d6 roll was worth. But I think the real question is, what is the deviation from that mean. What are the chances that you will generate a character well above 32 points. Also, assuming rerolls are permissable for low rolls would that change the average mean (if #
#3 yawar Oct 13, 2008 17:02:01	Thank you very much for this great piece of work. Here, have a Humbly yours, Solely Yawar
#4 tshern Oct 13, 2008 17:11:43	Mad mathematics skills, I say. Thanks for this piece of information, I am sure this will come to use at some point...
#5 17flyingaxes Oct 13, 2008 17:18:10	Nice work! Of course, I'd argue that this is no more powerful than a 25-pt buy, because in a point buy you have more control over how stats are distributed. But of course that's not really mathematically quantifiable.
#6 surreal Oct 13, 2008 17:37:24	Hmm, the file doesn't work for me. My computer says it is an invalid zip.
#7 nabuchadnezzar Oct 13, 2008 18:00:51	Thanks for the answers :D and the ! @Fallen-angle: It's hard to choose an "average" set (but I can tell you that the most common is [15 14 13 12 11 10], just search for the highest probability) and calculate the deviation from that, but one can calculate the deviation from the "average" point cost (30 in the example). It's not hard, you need only to add a column or two and make the sheet calculate your standard deviation. I've just done it and the result is that the "average" point cost is 29.9 + 8.3 The chances that a rolled character's stats will be between 22 and 38 point buy are about 68% per the mathematical definition of standard deviation. I can tell you that without rerolls, the average point cost would be around 28 (just reduce the minimum mod to, say, -30 and the minimum max to 0 to see it): 27.8 + 9.8 @17flyingaxes: Of course, bought stats are superior to rolled stats, because chaos always works against the player. With the point buy you can choose every aspect of your character, while rolling 4d6 you might have some bad surprises (or some good ones). It's like choosing between rolling for the hit points or taking the average... It's generally better to take the average, because having more hp's isn't as crucial as having less hp's. EDIT: @Surreal: I just downloaded it but I found no problems. It might be due to the "à" in the name... I'll upload the updated (with standard deviation) uncompressed sheet with a neat name. It's 27.2 MB though... Uploading udated sheet anyway... it will take some time
#8 tshern Oct 13, 2008 18:07:03	Hmm, my WinRAR opened it with no troubles...
#9 nabuchadnezzar Oct 13, 2008 19:05:13	Here is the updated version of the sheet. It's uncompressed and it calculates the standard deviation too. EDIT: You could also make a hystogram with the point buy and the probability for that point buy to come. I did that and here are the results for the 4d6 rolls (with rerolls for low sets): Download latest analysis, compressed zip
#10 surreal Oct 14, 2008 13:17:35	Strange, my computer only downloads a 5mb file... I'll try again when I get home.
#11 nabuchadnezzar Oct 14, 2008 13:59:27	Try to download the latest analysis
#12 BloodDragon Oct 15, 2008 15:12:34	Bravo... I can make much use of this.
#13 lo77o Jul 27, 2009 8:10:00	This is a very nice reference post, ill be sure to point this out next time we make characters. Gracias
#14 awaken_D_M_golem Jul 30, 2009 17:03:53	Very nice. So the old standard of 28 point buy, is slightly weak. Could do a: 20 + d20 = point buy value Would still have some variability, and would "err" in the other direction by half ... ;)
#15 nabuchadnezzar Jul 31, 2009 6:43:42	You could also use 20+3d6 to make sure that "average" (n)pc's are more common than "extremes" ;) I think that the "standard" 28 point buy was set because one didn't think about "rerolls". Without rerolls, the average is indeed 28 points. With rerolls, the average raises to 30 points.