There was a post on reddit about moderating the player vs. player randomness when rolling ability scores. There was some sentiment that if you want players to be evenly matched, don’t roll; only roll if you’re okay with some players having better abilities.

I initially agreed with that assessment, and posted some stats about the expected variability. But then I realized that it is valid to want different levels of variability, so I went through my list of ways to roll abilities, and did some simulations to try and find a range of possibilities with different variability between players.

The results are in the table below, and all the columns/rows are explained after the table. The key metric is the Q2 column, which is the median/2nd quartile of the difference in the total ability scores between the best roller and the worst roller. The simulations were done for 100,000 trials, with five players in each trial.

Name | Q1 | Q2 | Q3 | Median Set | >=18 | <=3 |
---|---|---|---|---|---|---|

1d6 ad +9 hi/lo | 5 | 6 | 8 | 18, 15, 14, 13, 12, 8 | 100% | 0% |

1d6 ad +9 | 6 | 8 | 10 | 15, 15, 14, 13, 13, 11 | 0% | 0% |

3d6 dl +4 x6 dl hi/lo | 6 | 8 | 10 | 18, 15, 14, 13, 12, 8 | 100% | 0% |

3d6 dl +4 hi/lo | 8 | 10 | 13 | 18, 15, 13, 12, 10, 8 | 100% | 0% |

3d6 dl +4 | 9 | 12 | 16 | 15, 14, 13, 12, 11, 10 | 0% | 0% |

3d6 w4 dl | 10 | 13 | 16 | 15, 14, 13, 12, 11, 10 | 2.7% | 0% |

3d6 ad | 10 | 13 | 17 | 15, 14, 13, 12, 11, 9 | 5.3% | 0.01% |

5d6 dl | 11 | 14 | 18 | 17, 15, 14, 13, 12, 10 | 19.4% | 0.08% |

4d6 dl | 12 | 16 | 20 | 16, 14, 13, 12, 10, 9 | 9.3% | 0.46% |

2d8 +3 | 14 | 18 | 23 | 16, 14, 13, 11, 10, 8 | 25.1% | 0% |

2d10 | 17 | 23 | 29 | 16, 14, 12, 10, 8, 6 | 30.1% | 16.7% |

d20 ad | 20 | 26 | 33 | 19, 18, 16, 13, 11, 7 | 85.6% | 12.9% |

1d20 | 24 | 32 | 41 | 18, 15, 12, 9, 6, 3 | 62.1% | 6.3% |

### Rows/Ways to Roll

If you look at my list of ways to roll abilities, there’s all sorts of weird stuff in there. I tried to stick to things similar to 3d6 or 4d6 drop lowest. I maybe got a bit silly with the last few rolls, but I thought someone might want more variance between players.

- 1d6 ad +9 hi/lo: Roll 2d6, keep the higher one, add 9. Do this four times, and the DM gives a set high and low value (18 and 8 were used in the simulation).
- 1d6 ad +9: Roll 2d6, keep the higher one, add 9.
- 3d6 dl +4 x6 dl hi/lo: Roll 3d6, drop the lowest, add 4. Do this six times, keeping the four highest rolls. The DM gives a set high and low value (18 and 8 were used in the simulation).
- 3d6 dl +4 hi/lo: Roll 3d6, drop the lowest, add 4. Do this four times. The DM gives a set high and low value (18 and 8 were used in the simulation).
- 3d6 dl +4: Roll 3d6, drop the lowest, add 4.
- 3d6 w4 dl: Roll 3d6, add a die equal to 4, then drop the lowest.
- 3d6 ad: Roll 3d6 twice for each ability, keeping the higher roll.
- 5d6 dl: Roll 5d6 and drop the two lowest dice.
- 4d6 dl: Roll 4d6 and drop the lowest die.
- 2d8 +3: Roll 2d8 and add 3.
- 2d10: Roll 2d10.
- d20 ad: Roll 2d20 and drop the lowest die.
- 1d20: Roll 1d20.

### Columns

- Q1: The first quartile of the difference in the total abilities of the best and worst rollers. 25% of the time, the difference will be this low or lower.
- Q2: The median (or second quartile) of the difference in the total abilities of the best and worst rollers. 50% of the time, the difference will be this low or lower.
- Q3: The third quartile of the difference in the total abilities of the best and worst rollers. 75% of the time, the difference will be this low or lower.
- Median Set: This is the median set of abilities. It was calculated by taking the median of the best roll, the median of the second best roll, and so on.
- >=18: The probability that one or more of the abilities will be 18 or higher.
- <=3: The probability that one or more of the abilities will be 3 or less.