Well of course it is a matter of subjectivity and how you lay your starting hypothesis. If you feel that only a handful of people from each thousand will have a specific characteristic at +3, then yes. But again that's the fruit of an assumption, and not exactly the first one we have to make to come this far into the model. And that's even easy to argue by considering that characteristics aren't independent to each other, because investing in a +3 in one of them will have quite an impact on the values of the others.
The more we talk about this, the more I feel comfortable with ditching the normal distribution away and work with characteristics' sets!
That is based on the assumption that designer characters for the story (PCs) follow the same rules as random characters from the world. That is certainly not the first assumption I would have made.
But sure. It all boils down to our lives South of the Screen ... my life and comfort is rather incompatible with large random tables, but apparently yours is.
If that seems large to you you should see the 3000 random names in latin one!
Sure, but I wasn't interested in generating every combination of characteristics of every set. As I said I just wanted the row of values, and then I could assign them on the fly to a given NPC.
But now that you mention it, if there are 8 combinations for the first one (8! / 7!) and 8! / (4! * 3!) for the second one, then how many combinations are there for all of them? By multiplying the factorial of the count of every different number in every combination (...and checking that this is actually 8 and 280 for these two cases) and then dividing 8! by that, I get a total of 176464 different combinations. And there are 4 rows with 6 different values (from a total of five) that only have two values repeated twice (two 3s and two 1s, two 3s and two 0s, two 2s and two 1s, and two 1s and two 0s), and each of these gets 10080 combinations.
Well, I came from a time where half of the names I could come up with were Pijus Magnificus, so I really needed that one. It just went somehow out of hand.
The last official method of stat generation was 3rd edition, which used 1d10-1d10 and divide the result between two 'related' stats .
Obviously this results in a distribution of -9 to 9 with a median of 0. Then you made the top characteristics into mages and companions and the rest were grogs.
come 5th edition even grogs get 7 points standard in charateristics, same as companions and mages, which implies a certain statistical equivalence between the three groups for characteristics. Now given that mages are 1 in 100,000 people, and companions nearly as rare, simply deciding that all playable grogs are above average and the typical scores are simply (1d10-1d10)/2 or similar would be a valid approach. The other way to read it is that 7 points in characteristics is a global standard in which case the average will be between 0 and 1.
The excel formula can be adapted to whichever weighting you want for your world, and as I said allows for mass production of populations. But making assumptions is inherent to the process given the lack of information. The other side of that coin is that you can be assured that whatever assumptions you make will be correct for your own saga.
Now you sound like an old-school economist, ignoring all the evidence for bounded rationality.
What yuo can know is that whatever mistakes and inconsistencies you have in your own saga, you have chosen them yourself. And that is possibly a comfort.
On the other hand we are trying to apply statistical analysis and advanced mathematics to a game system which has as an implied rule in game, the "fact" that 2 cubed=10.
