My weekend D&D group has a different way of rolling attributes for characters, and it's probability has been bothering me mathematically for a couple of weeks now.  First, I should show how the regular rolls work for comparison.  Normally when you create a D&D character, you roll 3 six-sided dice (also known as 3d6) and add them up to get a total.  You do this 6 times and apply each totaled value to one of six character attributes.  A higher character attribute is better.  10 is average, while 18 is the best you can roll.  Anything below a 9 is below-average for a human, so a character with an intelligence of 6 isn't so great.  The numbers in each attribute are used to determine attribute bonuses.  Attribute bonuses are used inthe game to affect certain skills.  For example, a character with an Intelligence rating of 18 receives a bonus of +4 to all skills related to intelligence.  A character with a Strength of 18 receives a bonus of +4 to all melee attacks and to damage.  This factors into the game significantly.  For every two points in an attribute, the bonus changes by one.  A single bonus point is an effective 5% bump in chance to succeed.  So a character with a Strength of 18 has a 5% better chance of hitting a creature than a character with a Strength of 16, and the stronger character also does at least one more point of damage when he hits.  Ok, so now I will describe our in-house rolling system, and you can see how horribly broken it is. 
The extra little bit that we've added is to re-roll 1s and 2s.  So if you rolled 1-2-3-4, you would roll those two dice again until they were not a 1 or a 2.  The possible range of the roll is now from 9 to 18, since you can't roll 1s or 2s to bring the total lower.  See what's going on here?  Essentially, that reduces the number of possible roll combinations to 256.  7 in every 20 rolls will result in an attribute bonus of +3 or higher - that's 35% of all rolls, meaning two of your six attributes will have +3 or greater bonuses.  72% of all rolls will result in at least a +2 bonus.  So with this rolling method, you've basically got a character that is usually at least 10% better at every skill than the baseline, and probably 15%-20% better at what he specializes in than an average character specializing in the same thing.  Statistically it's extremely improbable (1 in 24 million rolls) that your character will have a +0 in all attributes - an average character.  Now when you factor in that all monsters challenge ratings are based on being fought by a party of average characters, you start to see real cracks in this rolling method.  Mind that it's not even just one character having a 10% advantage, it's a whole party of superior characters.  The solution is certainly not to employ more difficult monsters or adjust challenge ratings.  The solution is to use a normal method for rolling attributes that celebrates extraordinary character abilities.  Alternatively, setting character attributes diretly based on a point system would also work.  I would suggest starting all six character attributes at 8, and then letting players allocate 14 points to any attributes they choose. 

Comments

I could see using your modified roll technique on one attribute as a way to compensate for the fact that nobody wants to role play an "average" character.

That lets you choose your class, and get a big stat in one key area, which should result in a better balance for your party.

More interesting would be to allow players to use one more enhanced roll at the cost of an inverse enhanced roll (discard 5's and 6's, ignore highest dice)

Or, you could maybe not discard 2's, just ones, so the effect is softened quite a bit.

I dunno - I haven't played D&D in 15 years or more, so I'm just spewing ideas out there.

Part of the game concept is that PCs are not average people in the game world. If they were, they wouldn't be adventurers. By definition, PCs are extraordinary and the game system is geared toward interacting with them.

Better systems would simply enforce a fair allocation of points. I keep concluding that all of these contrived random attribute generators are worthless if people keep nudging the system to get what they want anyway.

If attribute points were a bit easier to come by during the game then I would be quite happy to accept an average start up roll. But attributes don't come easy, like additional hit points so the leap that takes you from being a farmer with a sharpend stick to a dragon slaying Uber Hero becomes impossibly distant.

Personally I like the process of allocating attribute points up to a total. GURPS does this nicely by making the higher values more expensive to buy and balancing out a super attribute with a corresponding weakness.

It also allows you to tweak your character suit your vision.

--nick

When we play, we've tried 2 methods:
1) Point buy-in system. This is much as you suggested... we start at 8, get a certain number of points at creation, and then some per level. This is nice because it allows you to make a character that fits your needs, but it takes the randomness out of it. Alot better when you're trying to create a specific character without allowing people to create overly powerful characters.

2) We roll a pool of 7 attribute values by doing a 4d6 and throwing away the lowest, then assign them to whatever attribute you want (leaving 1 extra roll). It's a further tweak on the optional rules. If you die as much as we tend to, then you'll be happy for whatever you can get. :)

I like the 2nd one above, because it's somewhat random, but you can still customize your character so that you don't get screwed with a low value value in the main class atrribute.

Brian was telling me that his group's system is simply to allocate the same numbers to every character: 18 16 15 14 12 11

That's 39 points to allocate on a base of 8. That doesn't seem too bad. We did a 40-point allocation once that wasn't horrible.

Maybe next time.

I'm kinda' obsessed with statistics... I can give you all sorts of data on percentages of the various rolling systems if you (or anyone else is interested).

Regarding this thread, I had these thoughts:
1) 3d6 is not (at least not for many years) a normal way to roll attributes. First, because it does create average characters in a game that is designed for above average ones. Second, because it is too random. Using 3d6 only instead of 4d6 minus the lowest die, you are more likely to have one player way stronger than another.
2) 4d6 minus the lowest is the official way now. (Has been for a few versions, no?) Anyway, this is less random, because throwing away the lowest compresses the range upward. I prefer this method with the official reroll rule added as a safety net.
3) The official reroll rule goes a long way toward fixing this... Instead of throwing away more low dice, which just raises the average while still leaving it common for there to be weak characters mixed with strong ones, it simply says that if you got one of the weak ones, you go make a new one (entirely... I.e. you don't get to keep that one 17 you rolled... You throw it all out and start over until you get at least a minimum. FYI, the official rule is that if you have no single attribute of 14 or more, or if the sum of your modifiers is not 1 or more, you get to reroll.

The attribute allocation system a DM friend of mine uses is that you start with 8 for all attributes. Then you get 25 points to spend. Except that attributes up to and including 14 cost 1. Above 14 cost 2 per point gain. (You can also sell scores down below 8 to get morepoints for other scores)

Rolling 4d6 has about a 60% chance of giving you more points than this allocation system. But of course there is also about a 30% chance of going below.

Sorry for rambling... Cheers!

Call me old school, but what's wrong with the original system? Human confirmation of original rolls determines whether a character lasts or not. Granted it's been a very long time since I've actually played, but that was the thing, you roll for specific attributes, and whoa, "I think that could be an awesome ranger...".

Or not, and they maybe they make it to level 7-8, and finally you retire them, and start over. Or has the game evolved past me?

They are applying more game science to games these days. Where in the old days, the stats were good for a starting point and weren't really used too often, they're nearly essential to everything now.

Plus, characters are more oriented toward having an average score of 10 or 11 now - the game is actually aware of this and accounts for it.

But I completely agree: If you roll a poor character you should either play it or re-roll, not complain about statistics.

I'm confused. If you're re-rolling the bad 1 and 2 outcomes then obviously you're going to get attributes that are higher than if you didn't. So it can't be too much of a surprise then that your characters will have better stats.

It is definitely frustrating to have bad luck and roll a crappy character and be stuck with it. I do like the point allocation scheme that videogames sometimes use, although it gets rid of a lot of the uncertainty that can make games like this fun...

Yeah, I know. That's what my whole post here is complaining about - that we use a broken way of creating characters.

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