Encounter Table Bell Curve

OK, I admit it.

First off, I'm really happy that last week's post was helpful. However, I do want to apologise for my math error, and for my disdain of bell curves. So let's set things aright...

Frequency vs. Probability

Last week, I proposed breaking down encounter tables by frequency: 40% common, 30% uncommon, 20% rare, and 10% very rare. I went on to say that you didn't have to limit your table results to four entries. If you were building a 1d10 table, for example, you could split up the 1-4 Common range  to populate your table with more than one Common entry.

However, as Roger correctly points out, this alters the probability of Common results when you make your 1d10 roll. My math-deficient brain had to puzzle over this a few times, but Roger is right, and I want point out my error in the hopes that others won't make (or continue to believe in) the same mistake I did. I'll use the same example as in my reply to Roger:

Let’s assume I have a 1d10 table of spells, like this:

1: hold portal (1st-level)
2: light (1st-level)
3: magic missile (1st-level)
4: read magic (1st-level)
5: knock (2nd-level)
6-7: web (2nd-level)
8: dispel magic (3rd-level)
9: fireball (3rd-level)
0: wizard eye (4th-level)

Strictly speaking–looking at the table only–40% of the results give a 1st-level spell, 30% of the results give a 2nd-level spell, 20% give a 3rd-level spell, and 10% give a 4th-level spell. That's frequency.

However, each 1st-level spell has a 1-in-10 chance of coming up; this is no different than the chance of rolling up a 4th-level spell (i.e., 1-in-10). That's probability.

Thanks for bearing with me on that one, and thanks to Roger for patiently pointing it out my mistake in a helpful way.

Bell Curves

Encounter Table bell curve
(1d4 + 1d6)

I suggested (and continue to suggest) using straight-up 1d10, 1d20, or 1d100 tables. They're easier to create, chiefly because it's easier to calculate the frequency and probability ranges you want. That said, there is something to be said for a mixed-die roll that creates a bell curve.

One possibility is rolling 1d6 + 1d4. This presents nine results in a range of 2-10, so the frequency of each result represents roughly 11.1% of the available numerical values on the table.

However, when you roll 1d6 + 1d4, there are 24 possible die combinations. Certain values on the table can result from more than one die combination. As a result, the probability of each result is quite different, as shown below:

Die Roll Value (1d4 + 1d6) Probability Layman's Frequency
2 1/24 (4.2%) Very Rare
3 2/24 (8.3%) Rare
4 3/24 (12.5%) Uncommon
5 4/24 (16.6%) Common
6 4/24 (16.6%) Common
7 4/24 (16.6%) Common
8 3/24 (12.5%) Uncommon
9 2/24 (8.3%) Rare
10 1/24 (4.2%) Very Rare

Put another way, this curve gives the following probabilities of encounter frequency:

  • Common: 12/24 (50%; Chimera guideline is 40%)
  • Uncommon: 6/24 (25%; Chimera guideline is 30%)
  • Rare: 4/24 (17%; Chimera guideline is 20%)
  • Very Rare: 2/24 (8%; Chimera guideline is 10%)

So while this isn't as "neat" as the straight-up 1d10 table, it does provide a workable equivalent. I haven't decided if I want to use this, but thought it might be a good alternative, particular for "end-line" encounter tables that don't have sub-tables (assuming you want to keep weighted probability in the mix).

Final Words

While this isn't what I wanted to talk about this week, I think it's important to get all the table math and formatting out of the way. Trust me, it'll make the next step of turning your encounter tables to 11 that much easier.

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