## 12 May 2021

### Worse than Even - more on probability descriptions

Following up to this post on what do DC should certain descriptions have, I found the original posts I was thinking of and so revisit this and convert to the 5e bounded accuracy system.

I was recalling the data visualisations done by u/zonination in 2015 on reddit which was building from government research by Sherman for the CIA. Pulling apart the 2019 survey data we can show the percentage probability that respondents assigned to various words. I have re-ranked them most to least probable.

Here the range on each bar is the inter quartile range - 50% of responses fall within this range. Some words are narrowly understood - about even means 50% with no range for most people. Some have a broad range meaning they are less clear - we believe and we doubt being to good examples with a 20% range.

Taking these and combining with the guidance from the 5e DMG that the DC of a 'about even' task should be DC15 we end up scaling all this to have a maximum at DC 30. This fits exactly to the bounded accuracy system.

What is very interesting to me is the steady trend of probability descriptions from 'certain' to 'even chance' and then a jump to 'probably not'. All is well until you hit 50-50, then once things go past that it immediately jumps to 1-in-3 and gets worse from there. Here are the ranges expressed as DC for 5e.

Probability Word High DC Mid DC Low DC
Almost No Chance 31 30 29
Highly Unlikely 29 29 28
Little Chance 29 28 26
Improbable 29 27 24
Chances are Slight 28 26 25
Unlikely 28 25 22
We Doubt 28 25 22
Probably Not 26 24 22
About Even 16 15 15
Better than Even 14 13 13
Probable 13 11 8
Probably 13 11 8
Likely 11 10 8
We Believe 11 8 5
Very Good Chance 8 6 4
Highly Likely 7 5 2
Almost Certain 4 3 2

I am not convinced this is more useful than our previous example so for comparison, here is that rescaled for 5e also.

Descriptor % span d20 span DC
Almost no chance / remote 1 to 5 1 30
Very unlikely / highly improbable 5 to 20 4 25
Unlikely / improbable (improbably) 20 to 45 9 18
Roughly even chance / roughly even odds 45 to 55 11 15
Likely / probable (probably) 55 to 80 16 7
Very likely / highly probable 80 to 95 19 3
Almost certain(ly) / nearly certain 95 to 99 20 1