I’ve been thinking about ability scores.
The ability scores are used to determine the modifiers used for combat bonuses, saving throws, and other checks. Beyond that, though, the scores themselves seem pointless. No one cares that your character’s strength is 14; we just want to know that you get a +1 to hit. If that’s the case, why bother with the score? Why not just roll up the modifier and use that as your score?
The Traditional Way
I’m using the modifiers that first appeared in Tom Moldvay’s 1981 edition of Dungeons & Dragons:
| Score Range |
Modifier | Chance of Rolling |
|---|---|---|
| 3 | -3 | 0.5% |
| 4 – 5 | -2 | 4.2% |
| 6 – 8 | -1 | 21.3% |
| 9 – 12 | ±0 | 48.1% |
| 13 – 15 | +1 | 21.3% |
| 16 – 17 | +2 | 4.2% |
| 18 | +3 | 0.5% |
The Crowfield Way
I wanted a way to generate a random number between -3 and +3, with the odds of getting any particular score close to the traditional way.
My first thought was to simply use three Fudge dice. While this would generate the right range of numbers, the shape of the curve was wrong. Rolling a -3 (or +3) was 7 or 8 times more likely than the traditional way.
Rolling (1d4 - 1d4) was the same: the range was right, but the probabilities were wrong. In fact, they were worse. With only 16 possibilities, the extreme rolls were wend from a 1:216 chance to 1:16.
That’s when it hit me. If I wanted the curve to resemble 3d6, why not just use 3d6?
The Method
It’s simple:
- Roll 3d6
- Treat any die that’s a 1 as -1.
- Treat any die that’s a 6 as +1.
- Treat everything else as a 0.
It takes longer to explain than to do. In practice you just roll the dice, discard anything that’s not a 1 or a 6. Then if there’s both a 1 and a 6 showing, discard the pair (as [+1] + [-1] = 0). Then just count how many dice are left, treating the count as a negative if the remaining die/dice is/are 1’s.
The Curve
It’s not an exact fit, bit I think I’m happy with it. In essence we give up a small amount from the middle to boost the +1 and +2 scores a little. The +3 score is exactly the same percentage chance.
| Modifier | Traditional Chance of Rolling |
Crowfield Chance of Rolling |
|---|---|---|
| -3 | 0.5% | 0.5% |
| -2 | 4.2% | 5.6% |
| -1 | 21.3% | 23.6% |
| ±0 | 48.1% | 40.7% |
| +1 | 21.3% | 23.6% |
| +2 | 4.2% | 5.6% |
| +3 | 0.5% | 0.5% |
Or, in chart form:
That’s it
It’s just an idea I’m floating around. I’m not committed to it yet, but I think it will work. Let me know what you think.
Very interesting! I never considered the superfluous nature of the scores themselves.
ReplyDeleteI do like the idea, as it makes challenges and encounters more fluid (don't need to remember the 'translation' from score to modifier). And it's easier to quickly glance at a character sheet and determine their strong and weak characteristics.