Random ability score method

Happy holidays everyone. What follows in an attempt at a random ability score method that (hopefully) fixes some of the problems with the 4d6-L method. You roll percentile dice and cross reference to get the ability score. (Using percentile dice allows for jury-rigging the bell curve to exact specifications).

Percentile result               Ability score
01-03                                    8
04-09                                    9
10-21                                    10
22-34                                    11
35-50                                    12
51-70                                    13
71-88                                    14
89-00                                    15

Obviously the biggest change is eliminating anything below 8 or above 15, leaving plenty of room to grow at the higher end. Using the 4d6-L method you've got about an 80% chance of getting at least one score above 14 in a given array, compared with only 54% chance of getting at least one 15 with the table. But you've also got about a 30% chance of at least one score below 8 in 4d6-L and there's zero chance of that with the table. Plus the percentage of getting an 8 or 9 is lower with the table, whereas the percentage of getting every other score is higher compared to 4d6-L, so all in all I think it works out to a slight advantage.

Both methods are about the same when it comes to an array with no score above 13 (8% with the table and 7% with 4d6-L). The biggest difference is on the other end of the scale. With 4d6-L, about 1 in 25 arrays will be a super array worth PB 36 or above, compared to only about 1 in 500 arrays using the table. So there's significantly less chance of one player in the group rolling a super array which overshadows everyone else's character.

Thoughts, opinions, corrections of my math all welcome if you're so inclined.
Children believe what we tell them, they have complete faith in us. I ask of you a little of this childlike simplicity, and to bring us luck, let me speak four truly magic words: "A long time ago...." (Jean Cocteau's Beauty and the Beast) Winner of You Build the Character #12, YbtC #22, YbtC #24, YbtC #28 and YbtC #35 Winner of You Make the... Contest #8
I'm of the opinion that either you play with random abilities and risk the disproportionate distribution of stats between characters or everyone starts with the same amount of either points to spend or stats to place.  Your way seems to be a compromise that takes away from both paths.  Here you don't allow characters to have "outstanding" stats but you still allow characters to be uneven (if you roll poorly in the random method you can still roll poorly with this method).  Granted the disparity isn't as potentially great as random rolls but it's still there.  In other words, to me, it seems like you've taken the worst of both paths and placed them together in that you've lowered the reward and still allow for risk. 

I hope you take this as honest opinion/criticism and not being mean or disparaging.


I hope you take this as honest opinion/criticism and not being mean or disparaging.



I'll follow suit and agree with Leo's summary, rather then try to write my own identical summary. It was a good idea, and I for one can appreciate the amount of effort you no doubt put into this, so don't feel discouraged and keep on trying! Happy Holiday too you as well!
I always appreciate honest criticism. Thanks for the replies.
Children believe what we tell them, they have complete faith in us. I ask of you a little of this childlike simplicity, and to bring us luck, let me speak four truly magic words: "A long time ago...." (Jean Cocteau's Beauty and the Beast) Winner of You Build the Character #12, YbtC #22, YbtC #24, YbtC #28 and YbtC #35 Winner of You Make the... Contest #8
The "compromise" solution I'd use between random rolling and point buy is to use the 4d6 drop lowest method for five ability scores and use those raw scores to determine how many points are left to "buy" the last score.  If you roll to well you'll end up with a low score to compensate and via-versa granted rolling too poorly may still leave you "reroll" eligable.
What would you do if the person rolled well enough that they were over your limit?  Would you make them take an 8 or less if they rolled too well?  For example if they rolled an equivalent of 32 points in a 28 point buy would they then start with a 4 or an 8?
What would you do if the person rolled well enough that they were over your limit?  Would you make them take an 8 or less if they rolled too well?  For example if they rolled an equivalent of 32 points in a 28 point buy would they then start with a 4 or an 8?


I go back an forth over what to do when someone "over rolls" their five ability scores but generally figure that getting a score lower than 8 should be possible.

I should point out that I would be basing the remaining PB on the raw scores rolled and NOT their PBequivalents.  If the PB option was 28 points then the "random" option would begin at 68 points (base 8x5 +28 points) and each of the five scores rolled would reduce that value directly so rolling a 17, 14, 13, 10, & 8 will leave you with 6 points to "buy" your last score.  Now that would leave you with a PBe = 32 as I'm not "penalizing" a high roll so maybe it needs to be tweeked a bit but the general idea would be to not "penalize" a single high score so much while trying to prevent the across the board great array.

The problem I would guess with roll 5, PB the sixth is that with above average rolls that sixth stat just becomes your dump stat anyway. It might be a little lower than you otherwise would have it but it's still a dump stat and so doesn't really make a lot of difference. That would sort of negate the balancing factor. It would be different if all six ability scores were useful for all characters. (This is a good argument for something like tri-stat where you trim the ability scores down to an array where every score is valuable, but I digress. )

Point-buy stats just look a little too neat and optimized once everyone gets used to doing it a certain way. So I was thinking either a standard array, or some kind of "controlled" rolling method where the variance isn't so great but isn't perfectly uniform either. There's the minimum wage/salary cap approach, where you roll 4d6-L and reroll if the PB value of the array is less than X or greater than Y. The table is sort of an attempt to do that without the need for some of the rerolling that would otherwise be likely. But I guess it might be better just to set specific high and low values and roll normally.

Children believe what we tell them, they have complete faith in us. I ask of you a little of this childlike simplicity, and to bring us luck, let me speak four truly magic words: "A long time ago...." (Jean Cocteau's Beauty and the Beast) Winner of You Build the Character #12, YbtC #22, YbtC #24, YbtC #28 and YbtC #35 Winner of You Make the... Contest #8
Why do you want to penalize players for rolling high?  I understand that you want to keep things on as even a keel as possible but it just seems wrong to go after the top of the scale.  (It's too "Harrison Bergeron" like [a short story by Kurt Vonnegaut]).  If it really bothers you move up the minimum and leave the upper end to whatever the dice roll.
I also can see where you want to avoid the "superman" problem but if you're going to roll then it will happen occasionally.

All the groups I have played with over the years have used the 4d6-L method. We've never looked at PB or any other method for stat generation. We've always had a mutual understanding that somebody most likely will have really good stats and someone will most likely have really horrible stats, but it's a mutual understanding amongst players and GM, so there are no ill feelings and disappointments on either side. As long as the GM and the players can reach that understanding, I don't think it really matteers what score generation method you use.

Personally I don't have a problem with differences in power level as long as it fits the concept. But when you start with a solid concept and then use a wide variance method like 4d6-L, you often end up with stat arrays that simply don't match the concept. And yes, that can include too high as well as too low, or too great a discrepancy between high and low stats. Star Wars heroic characters usually have decent stats across the board. You don't have D&D types where there's a place for a wide discrepancy of say 18 high and 5 low (weakling wizards, dumb barbarians, etc). Point buy is the usual answer to this, but has its own problems.

But then again, I might just be getting tired of the traditional point buy. Maybe Pathfinder's point buy system would be better. Or just going with a standard array.

Children believe what we tell them, they have complete faith in us. I ask of you a little of this childlike simplicity, and to bring us luck, let me speak four truly magic words: "A long time ago...." (Jean Cocteau's Beauty and the Beast) Winner of You Build the Character #12, YbtC #22, YbtC #24, YbtC #28 and YbtC #35 Winner of You Make the... Contest #8
If you're looking for equality amongst the players then either some sort of point buy or a standard array is the way to go.  If you really want to knock yourself out then you could come up for a "cost" for the different races and factor that into your point buy (like GURPS).

If you're worried about a concept that is bent out by stats being too high the solution is simple allow the player to voluntarily lower the offending stat.  If you're feeling generous allow him to add some of the value of the lowered stat to another stat.

If you're worried about a concept being broken because the stats rolled were too low then you can do any of the following:
     Allow the character a reroll on that stat;
     Reroll the entire character;
     Just give the character the stat he wants or come to some determination of the minimum he       
     should have or;
     In our group when we roll stats by whatever method we allow the numbers to be placed in 
     whatever order we want ( basically it is a randomly generated stat array).

Whatever you decide to do good luck with it.