Many games use 3d6 to decide character stats. Zedeck Siew posted an interesting discussion regarding how to interpret ability scores. This made me ponder the question: what happens when we take the statistics of ability scores literally? Let's look at the odds of rolling each possibility on a 3d6:
| 3d6 | Number of ways to roll | % chance |
| 3 | 1 | 0.46% |
| 4 | 3 | 1.39% |
| 5 | 6 | 2.78% |
| 6 | 10 | 4.63% |
| 7 | 15 | 6.94% |
| 8 | 21 | 9.72% |
| 9 | 25 | 11.57% |
| 10 | 27 | 12.50% |
| 11 | 27 | 12.50% |
| 12 | 25 | 11.57% |
| 13 | 21 | 9.72% |
| 14 | 15 | 6.94% |
| 15 | 10 | 4.63% |
| 16 | 6 | 2.78% |
| 17 | 3 | 1.39% |
| 18 | 1 | 0.46% |
If we interpret these percentages literally, it means that one out of every 216 people have an 18 strength, one out of every 216 people have 3 strength, ect. To put that in perspective, check out this video of the CA weightlifting championships. If we assume that the contestants you see in that video are the 300 strongest people in CA, then those guys are in the top 0.0008% for human strength, making them far stronger than merely being in the top 0.46% of human strength implied by someone with 3d6=18 strength. So (if we choose to interpret this literally) a person with a score of 3 or 18 would most likely not be obviously different from a normal person. There's probably a few dozen guys at your local weight room who have the statistical equivalent of 18 strength.
On a personal note, when I got tested for ADHD I found out my capacity for visual and auditory attention is in the bottom 1%. So if that was a D&D stat, my stat would be 4. I finished a graduate degree and had a whole career without anyone noticing something was off about my attentional abilities.
In conclusion, if we look at stats from a statistical perspective, all possible stats rolled on a 3d6 represent fairly normal people. We'd probably need to roll stats on a 3d100 to accurately reflect the full range of human ability. To be clear, I don't actually endorse this, overly literal interpretations of game numbers leads to absurd results most of the time. My overall point is, there's no need to roleplay your stat numbers because all possible stat numbers could easily represent a fairly average person.
