Alternative Damage Calculation
Found an interesting artifact of probability recently. I may change how Reliability tests are performed because of it.

If you treat every die rolled as a separate Performance test, then you get from zero to three successes per die. A roll that meets or beats the target nets 1 success, a roll that beats it by 4-7 nets 2, 8+ gives you 3.

If you measure the average result of every die type vs the standard difficulty of 4, you get:

• A d4 has a one-in-four chance of giving one success, so its average is 0.25
• d6 is 0.50
• d8 is 0.75 (because it can produce 2 successes on a roll of 8)
• d10 is 1.00
• d12 is 1.25 (and nets 3 successes on a 12)

The nifty bit is that this exactly matches the cost ratio for buying those dice for skills. A d4 costs 1 point; a d12 costs 5. The ratios match perfectly.

Now if the difficulty drops below 4 (meaning a particularly easy check) then the average favors the d4s. If it goes above 4, then the average favors the d12s (particularly since d4s can never succeed at a check of difficulty 5+).

Now, the way I had been intending to calculate the results of a Reliability test, each die either gave you zero or one successes and could never produce multiple successes. Vs difficulty 4, that looks like:

• d4 0.25
• d6 0.50
• d8 0.625
• d10 0.70
• d12 0.75

The cost-to-average ratio definitely favors low dice here. So it's something of a style-thing. Do I want to always use at most one success per die and skew things so that 3d4 is about as good as 1d12 (despite costing 3 points instead of 5) for Reliability tests, just worse for Performance tests? I dunno... while it's a cute idea to have a dice system where one combo is better than another for certain types of tests, it'll tend to produce weird die pools (get a bunch of d12s and d4s or d6s and ignore the other dice; that's probably the best combo). The Ironclaw-ish "Each die produces one or more successes" style would take longer to resolve, but might give better results, especially if I'm not going to use Reliability tests very often. So far I haven't come up with a lot of tasks where you'd regularly use both Reliability and Performance tests... and if you don't use both then you'll end up favoring one type of die pool (few large or many small) exclusively for that skill.

This particularly applies for damage because I can say that a regular hit against an unarmored opponent is difficulty 4... where all weapons are balanced. Armor might move the difficulty up as high as 8 (and 12 is potentially possible with high-tech powered armor, just really rare) while critical hits might move it down as low as 2... or even lower. Since the number of wounds inflicted is based on the difference between the number rolled and the difficulty, it should support even negative difficulties just fine. If you roll vs a difficulty of -2, you'll get a one success on a 1, two on a result of 2-5 and three on a result of 6-9. I might even extend it to 4 on 10+, whereas the normal system maxes out at 3 successes. I'll probably leave it maxed out at 3 for right now. Negative difficulties will be very rare, anyway.
- posted by Kiz @ 12:00 PM