It's not exactly revolutionary, though :P
Unlike other stat rolling methods, this one cannot be be done in any practical fashion using dice. It requires computer assistance.
The method is actually quite simple though it might be biased in favour of certain combinations. I haven't yet verified it mathematically.
It generates at first a list of all possible descending arrays of stats you can purchase for a given point buy. It returns one of these at random.
The result is
1: What you get is random
2: It matches, perfectly, any given point buy
My current implementation is as a java application. I'm planning on writing a javascript implementation and putting it somewhere online.
Of course there are still "dud" rolls. For example: 13, 13, 13, 12, 12, 12 and 14, 13, 13, 12, 11, 11 :P
I made this back in the day. HERE.
My current Favourite system for stat generation is the focus/ foible system used by the way of the wicked campaign. Your focus gets an 18, your foible a 8, all other stats are rolled in order with a 1d10+7.
So you get your good stat, you get a bad stat, then the others are random, which leads to some interesting characters that never end up completely gimped. So you end up with a Ranger with High Str and Int, and bad con who became a bookworm due to a childhood illness or the sorcerer who got 16 str who occasionally beats things when he gets bored. And if you want to avoid dealing with the horrible luck of rolling all ones, just say the GM can let someone re-roll if their initial roll sucked.
There are in total 11^6 = 1771561 ordered sets of six numbers ranged 7-18.
My "algorithm" counts 32448 of those sets as meeting the requirement of a 15 point buy.
Out of these 9630 contain at least one 17 or 18. That's roughly 29% chance of getting a 17 or 18.
Now the big thing for players is not having an abundance of odd numbers.
I mean a dump stat is a dump stat, but unless you're making a character 4th level or above you probably aren't going to go with a bunch of 11s,13s,15s or 17s in your stat block.
thejeff:
I just thought of a way how to reason about the probabilities.
The higher a particular value is, the more points have to be spent on that particular ability. That means less points for other abilities. The fewer points we have to spend on other abilities, the fewer combinations we can generate with that particular array.
As an extreme example, if it cost us so many points to buy an 18 in one ability that we had to dump the others to all 7, we'd have a total of six possible arrays with an 18
18, 7, 7, 7, 7, 7
7, 18, 7, 7, 7, 7,
7, 7, 18, 7, 7, 7,
7, 7, 7, 18, 7, 7,
7, 7, 7, 7, 18, 7,
7, 7, 7, 7, 7, 18.
This encompasses ALL arrays with an eighteen.
If a value of 17 was 4 pts cheaper than 18, then an array like [17, 8, 7, 7, 7, 7] can be formed. Such an array can be formed in 30 different ways.
What I'm trying to argue here is that, as a randomizing algorithm picks one of these combinations at random, it's more likely to pick an array with a lower maximum value, because those are more frequently occuring thanks to the point-buy bias.
Karlgamer:
Yes. This is why, ideally, dud arrays should be removed entirely. Perhaps by removing all arrays with 15 or lower as their highest value.