Ability Score Distribution and Population

[Garnfellow]

Knowing Traveller fandom, I've probably only just recreated someone else's work, but I just did a interesting little analysis of ability scores that I want to share. (I am not a statistician, so keep that in mind.)

So I'm new to Traveller, and I needed to create a bad-ass NPC, someone on par with the unnamed agent from the Serenity movie. Being used to d20 NPC creation, I wondered what a Traveller ability array for someone like that would look like. (Ability arrays are just a standard set of scores, useful for quick NPC generation. You could have an average array, elite array, champion array, so on so forth. The base Traveller array would be 777777.)

One of the things I find so refreshing about the Traveller system is that it is the "no special snowflake" game. PCs are not exceptional adventurers, destined from birth for epic greatness. They are pretty normal, with a lot of luck and plenty of pluck.

So with that in mind, I wanted to find an elite array that was good, but not ridiculously improbable. So I built a little spreadsheet that analyzed all possible totals for ability scores and the probability of each. I then summarized that data to develop a series of standard arrays (and the associated MGT point cost) to facilitate future NPC development, including a few crazy good ones just as a thought experiment. I also tried to put these arrays in some sort of context.

At the uppermost and lowermost extremes, the odds of rolling a perfect (CCCCCC) character and a perfectly awful character (222222) are 1/6^12, or 0.000000046%. The odds of this are approximately 1 in 2.2 billion. Vanishingly rare, but you would expect to find at least one example on any world with a population code of 8, and we would expect 3 individuals with these scores right now on Terra; in an Imperium with a population of something like 28 trillion, there might be something like 13,000 perfects and perfectly awfuls running around.

What's more interesting to me is the relative commonality of very good and exceptional scores. The odds of having an average score of 9 is only 1 in 113; an average score of 10 is only 1 in 1,800, and an average score of 10.5 is only 1 in 13,000. (Rarity escalates rapidly from here.)

So for my super-elite agent, I went with an array that averaged out to 10.5. I wouldn't recommend using anything higher, even for exceptional individuals, and I suspect 10.5 may still strike many veteran referees as munchkin territory.

Anyway, food for thought.

 

[spinwardpirate]

That's brilliant!
How would the distribution change if you took it out to F?

 

[Garnfellow]

That's a good question. The probabilities are all based on a roll of 2d6, so I can't expand it out to F. But F is the natural human limit, so these people with these scores do exist.

One way to model this might be to imagine using an exploding die mechanic during character generation. If you roll a 12, you put down a 12 and get to roll another die. If you get a 6, add +1 to your score and roll again; otherwise you're done. If you get a 6, you add another +1 and roll again. Rinse, lather, repeat. I think this suitably captures the rarity of naturally occurring scores above C.

So to get a single 15 you would need to roll a 6 five times in a row. And then you need to do that six more times. This means the odds of rolling a godlike FFFFFF would be 1/6^30, or 4.52337E-24. The odds of this are 1 in 2.21074E+23. You would not expect to see someone like this is all of mapped space, much less the Imperium. You wouldn't expect to see someone like that in the entire history of the Third Imperium!

 

[Garnfellow]

With the exploding die mechanic, the ability score distribution would look something like this:

2 - 2.777778% (1 in 36)
3 - 5.555556% (1 in 18)
4 - 8.333333% (1 in 12)
5 - 11.111111% (1 in 9)
6 - 13.888889% (1 in 7.2)
7 - 16.666667% (1 in 6)
8 - 13.888889% (1 in 7.2)
9 - 11.111111% (1 in 9)
10 - 8.333333% (1 in 12)
11 - 5.555556% (1 in 18)
12 - 2.314815% (1 in 43.2)
13 - 0.385802% (1 in 259.2)
14 - 0.064300% (1 in 1555.2)
15 - 0.012860% (1 in 7776)