Post/Author/DateTime	Post
Peter Lee 10-04-04, 08:29 PM	What would be the average stats for someone using the normal 3d6 rules? (not 4d6 dropping the lowest -- straight up 3d6.) Mentally, I guess I'm asking to roll up an infinite number of characters, sort the resulting rolls from highest to lowest, and determine the average value for each stat. It must be symetric around the 10.5 value, something like 12, 11, 11, 10, 10 and 9. (where if you average the top and bottom number you get 10.5) Does anyone have the exact values? (I think the Elite Array of 15, 14, 13, 12, 10 and 8 is calculated in a similar way but with the 4d6 - lowest method.)
Finley DaDum 10-04-04, 09:12 PM	Well if you want the most likely outcome of 3d6 rolled 6 times: 11,11,11,10,10,10 is the most likely outcome but the likely hood of that result versus something like 13,12,11,10,9,8 both these results have a very similiar likelyhood. Im not gonna do the math someone else certainly can if you want a good array I would recommend using the 2nd for NPCs if you want to make them a little more unique but still average.
Isthramir 10-04-04, 10:02 PM	The "Most Likely" result is not that meaningful as it's not terribly likely. 10,10,10,11,11,11 will occur more often in the 6^18th number set of all possible die results on 18 dice ... and each of those results is equally likely with fair dice. But well over half of possible results will yield one stat over 11, and well over half will have a stat under 10. A "standard distribution" as defined in statistics would lead us to predict a set of stats that looked like 6, 8, 10, 11, 13, 15 which is a more interesting thing to look at, but is also very easy to draw false conclusions from if you don't understand how these numbers were generated.
eudas 10-05-04, 10:19 AM	If you want a discussion of statistics, I'm not your guy right now; I'm at work. But, if you'd like a dice roller I do have a link for you: http://www.irony.com/igroll.html It works pretty well and you can make it roll however many times you want, to help you develop statistics or get a feel for the averages. eudas
Captain Casualty 10-06-04, 10:05 AM	Pure stats here. The best way of determining an average or expected score on a die is to do an expected outcome calculation. This is expressed as E(x) where x is the expected outcome. So who cares? What you need to know is how to work it out. Thankfully there is a simple way of doing it in circumstances where there is a smooth linear number progression over a fixed interval (ie on a dice). Simply take the highest value roll and the lowest value roll then add them together and divide by 2. For a D6 this comes out to 3.5 (the number not the editon) so the expected outcome of 3 dice is 10.5 What this means is that if youa add all your stats up an exactly "normal" character would have 63 points of attributes. Like most stats of very little relation to the real world!
eudas 10-06-04, 11:47 PM	heh so your "average" character would have six stats of value 10.5 each. that's equivalent to three of 11 and three of 10 each, giving us a point-buy of 3*3 + 3*2 = 9 + 6 = 15 point buy. Woo! Something to tell people next time they ***** about 25-28 point buy or whatnot. :) eudas
was_fired 10-07-04, 03:50 AM	Eudas, your a bit off. This is true when each number has only it's value counter. Point buy uses a non-linear value increase. Counting every result under 8 as a point value of zero we get an 18 point point buy (if all abilities under 8 defaulted to 8). If you reroll anything under 8 you get 21 point buy. Using 4d6 drop the lowest you end up with around a 30 point point buy (don't have time to do the math to check though. The standard distribution for a 3d6 is: 3: 1 .46% 4: 3 1.4% 5: 6 2.8% 6: 10 4.6% 7: 15 6.9% 8: 21 9.7% 9: 25 12% 10: 27 13% 11: 27 13% 12: 25 12% 13: 21 9.7% 14: 15 6.9% 15: 10 4.6% 16: 6 2.8% 17: 3 1.4% 18: 1 .46%
eudas 10-07-04, 02:25 PM	well, i guess this is why i'm not a math major. i stand corrected! :) eudas