Ability Levels - or, Fun With Statistics!

[The Shadow]

I had the thought that True20 ability modifiers might be readily interpreted as the number of standard deviations from the mean. (For example, an ability of +2 would really be the range +1.5 to +2.5.)

I got curious and checked it out, and the results work surprisingly well. The following data might be handy for designing campaign worlds - ie, to answer the question, "Just how many people in a given town are likely to have a +4 Str or more?"

Odds of a given character having an exact score in a given ability:

+0: 38% of the population
+1: 24% - call it 1 in 4.
+2: 6% - 1 in 16.5
+3: 1 in 167
+4: 1 in 4400
+5: 1 in 296 thousand
+6: 1 in 53 million
+7: 1 in 25 billion - best in the world
+8: 1 in 32 trillion - best who ever lived, by far
+9 and up: You ain't human no more.

The negative values have the same odds to the degree of accuracy listed - the fact that -5 is the minimum has negligible effect.

Odds that a given character has *better* than a given value in a given ability:

-5: 100% (close enough)
-4: 99.98%
-3: 99%
-2: 93%
-1: 69%
+0: 31%
+1: 1 in 15
+2: 1 in 161
+3: 1 in 4300
+4: 1 in 294 thousand
+5: 1 in 53 million - and the rest match the previous list too.

Just how special are PC's in this system of interpretation? It really depends on how you spread your points out. If you have +1 in everything, "only" 1 in 11 million people are better than you in every respect. "Only" 1 in 168 are better than you in 3 ability scores. But 34% are better than you in *something*.

On the other hand, if you have one +6 and 5 +0's, only 1 in 9 trillion outclass you in everything (ie, nobody). Though 1 in 25 billion will outclass you in your best stat - maybe one other person in the world. (There's a 23% chance that such a person exists, given a population of 6.5 billion. Only a 1% chance at a more medieval population level of 250 million.) On the other hand, 1 in 358 will outclass you in every single one of your blah scores.

Odds that Joe Random Character will have at least one score above a given value:

-1: 99.9%
+0: 89%
+1: 34%
+2: 3.4% (1 in 27)
+3: 1 in 717
+4: 1 in 49000
+5: 1 in 8.8 million
+6: 1 in 4.2 billion
+7: 1 in 5.2 trillion
+8: Ludicrously small.

[FickleGM]

As I am beginning to create a new homebrew and am going to be running True20 again soon, I thank you for this.

I like to use demographic guidelines and think that I can get some use out of this.

I think this would be nice if added to my GM sheets and used when PCs enter a community.

Nice job Shadow...