Conditional Injury with Knowing Your Own Strength

[dataweaver]

A quick tutorial on how to determine the Log subtraction, using decibels as an example.

First, remember that we're dealing with ranges: 0 dB isn't ×1; it's ×0.89 to ×1.12, centering on ×1.

0dB: ×1 (×0.89 to ×1.12)
1dB: ×1.26 (×1.12 to ×1.41)
2dB: ×1.58 (×1.41 to ×1.78)
3dB: ×2.00 (×1.78 to ×2.24)
4dB: ×2.51 (×2.24 to ×2.82)
5dB: ×3.16 (×2.82 to ×3.55)
6dB: ×3.98 (×3.55 to ×4.47)
7dB: ×5.01 (×4.47 to ×5.62)
8dB: ×6.31 (×5.62 to ×7.08)
9dB: ×7.94 (×7.08 to ×8.91)
10dB: ×10 (×8.91 to ×11.22)

(I got these numbers as 10^(x/10), with x being the number of steps for the “center numbers” and x being “half steps” like 0.5 or 1.5 for the “border numbers”. The “/10” comes from there being ten steps from ×1 to ×10. Anything within the range of one border number to the next is acceptable; the closer it is to the center number, the more precise it is. All numbers on the above chart are accurate to two decimal places, except ×1 and ×10 which are exact. Note that +3dB is only approximately ×2, though you'd need another digit to see the discrepancy: +3dB≈×1.995, which rounds up to ×2.00.)

Traditionally, the decibel scale uses numbers picked from each range which are easy to use and to remember rather than being precise: thus, we get ×1, ×1.25, ×1.6, ×2, ×2.5, ×3, ×4, ×5, ×6, ×8, ×10. The more steps you have to ×10, the narrower the ranges are and the more precise your “good enough” numbers have to be.

When subtracting, you actually want to look at the negative decibels, which can be found be subtracting 10 from the dB figures and dividing the factors by 10:

-10dB: ×0.1 (×0.089 to ×0.112)
-9dB: ×0.126 (×0.112 to ×0.141)
-8dB: ×0.158 (×0.141 to ×0.178)
-7dB: ×0.200 (×0.178 to ×0.224)
-6dB: ×0.251 (×0.224 to ×0.282)
-5dB: ×0.316 (×0.282 to ×0.355)
-4dB: ×0.398 (×0.355 to ×0.447)
-3dB: ×0.501 (×0.447 to ×0.562)
-2dB: ×0.631 (×0.562 to ×0.708)
-1dB: ×0.794 (×0.708 to ×0.891)
0dB: ×1 (×0.891 to ×1.122)

What matters is how many steps below the higher number the lower number is. Subtract the center numbers, then find the range that fits in. So:

-0dB: 1-1=0, or -∞dB
-1dB: 1-0.794=0.206, or -7dB
-2dB: 1-0.631=0.399, or -4dB
-3dB: 1-0.501=0.499, or -3dB
-4dB: 1-0.398=0.602, or -2dB
-5dB: 1-0.316=0.684, or -2dB
-6dB: 1-0.251=0.749, or -1dB
-7dB: 1-0.200=0.800, or -1dB
-8dB: 1-0.158=0.842, or -1dB
-9dB: 1-0.126=0.874, or -1dB
-10dB: 1-0.1=0.9, or -0dB.

[RyanW]

Originally Posted by Raekai

This also seems like a great idea, but I don't think I quite understand it. Would you mind giving an example?

Say you are hit by a WP 10 hit (that would be ~100 damage in GURPS RAW terms).

If you have Prot 10 armor (~100 DR), it absorbs it entirely.
If you have Prot 9 armor (~70 DR), it lets through 7 WP (~30).
If you have Prot 8 armor (~50 DR), it lets through 8 WP (~50).
If you have Prot 7 armor (~30 DR), it lets through 9 WP (~70).
At Prot 6 (~20 DR), it would let through more than 9 WP, but not enough that you couldn't justify rounding to 9 if you preferred.
At Prot 5 (~15 DR) or less, it would let through much more than 9 WP. Rounding to 9 would be harder to justify. At this point, there isn't enough DR to make a meaningful difference at the scale I was using.

[RyanW]

Originally Posted by Raekai

You could probably add intermediate steps to DR (because it's a bit weird after multiplying by 3 and leaving as-is).

• Exceeded by 0: Reduce by 12 (or negate all WP?).
• Exceeded by 1: Reduce by 11.
• Exceeded by 2: Reduce by 10.
• Exceeded by 3: Reduce by 9.
• Exceeded by 4: Reduce by 8.
• Exceeded by 5: Reduce by 7.
• Exceeded by 6: Reduce by 6.
• etc.

It would actually look more like:

• Exceeded by 1: Reduce by 19
• Exceeded by 2: Reduce by 14
• Exceeded by 3: Reduce by 11
• Exceeded by 4: Reduce by 9
• Exceeded by 5: Reduce by 7
• Exceeded by 6: Reduce by 6
• Exceeded by 7: Reduce by 5
• Exceeded by 8-9: Reduce by 4
• Exceeded by 10-12: Reduce by 3
• Exceeded by 13-15: Reduce by 2
• Exceeded by 16-25: Reduce by 1
• Exceeded by 26+: No reduction

I assumed matching protection would always stop damage, but included the +/- 1 roll for cases where armor might stop an attack.

[Raekai]

Originally Posted by dataweaver

A quick tutorial on how to determine the Log subtraction, using decibels as an example [...].

I appreciate this a lot and will study it.

Originally Posted by RyanW

Say you are hit by a WP 10 hit (that would be ~100 damage in GURPS RAW terms).

If you have Prot 10 armor (~100 DR), it absorbs it entirely.
If you have Prot 9 armor (~70 DR), it lets through 7 WP (~30).
If you have Prot 8 armor (~50 DR), it lets through 8 WP (~50).
If you have Prot 7 armor (~30 DR), it lets through 9 WP (~70).
At Prot 6 (~20 DR), it would let through more than 9 WP, but not enough that you couldn't justify rounding to 9 if you preferred.
At Prot 5 (~15 DR) or less, it would let through much more than 9 WP. Rounding to 9 would be harder to justify. At this point, there isn't enough DR to make a meaningful difference at the scale I was using.

Excellent. This definitely makes more sense now. Do you like this method or your previous method more?

Originally Posted by RyanW

It would actually look more like:

• Exceeded by 1: Reduce by 19
• Exceeded by 2: Reduce by 14
• Exceeded by 3: Reduce by 11
• Exceeded by 4: Reduce by 9
• Exceeded by 5: Reduce by 7
• Exceeded by 6: Reduce by 6
• Exceeded by 7: Reduce by 5
• Exceeded by 8-9: Reduce by 4
• Exceeded by 10-12: Reduce by 3
• Exceeded by 13-15: Reduce by 2
• Exceeded by 16-25: Reduce by 1
• Exceeded by 26+: No reduction

I assumed matching protection would always stop damage, but included the +/- 1 roll for cases where armor might stop an attack.

Excellent. Thank you for that. It saved me a lot of hurt in trying to figure it out myself.

Speaking of which, how do you convert DR to Protection? I realized that I don't actually know that. Also, would you use BS DR values or convert them to KYOS first?

[dataweaver]

DR becomes Prot the same way HP become RT.

[Anthony]

Note that the Subtraction table in Know Your Own Damage is the same thing being described above, though the finer granularity means more steps (1 point difference is -34, 2 is -25).

[RyanW]

Originally Posted by Raekai

Excellent. This definitely makes more sense now. Do you like this method or your previous method more?

That's the method I came up with from the very beginning. I just added in what RAW damage and DRs would be equivalent.

Originally Posted by Raekai

Speaking of which, how do you convert DR to Protection? I realized that I don't actually know that. Also, would you use BS DR values or convert them to KYOS first?

I don't think DR would be affected by KYOS. I just use the published DR value and convert them just as I would convert damage to WP.

[dataweaver]

I may have said before, but I'll say it again: KYOS is about matters involving mass; CI is about matters involving damage. Whatever KYOS has to say about damage should take a back seat to what CI has to say about it.

[Raekai]

EDIT: Also, I merged the old information from the second post in this thread into the first post in this thread and made the second post into the information about each system so no one had to go digging.

Originally Posted by Anthony

Note that the Subtraction table in Know Your Own Damage is the same thing being described above, though the finer granularity means more steps (1 point difference is -34, 2 is -25).

Upon looking at them at the same time, I see it! It makes sense, but that's pretty neat to me nonetheless. And good to know!

Originally Posted by RyanW

That's the method I came up with from the very beginning. I just added in what RAW damage and DRs would be equivalent.

I don't think DR would be affected by KYOS. I just use the published DR value and convert them just as I would convert damage to WP.

Ah, okay! I misunderstood. I thought it was maybe a different way to tackle it in play, though it did seem like that would require knowing how much DR should stop damage.

And excellent. That makes sense, but I wanted to be sure.

Originally Posted by dataweaver

I may have said before, but I'll say it again: KYOS is about matters involving mass; CI is about matters involving damage. Whatever KYOS has to say about damage should take a back seat to what CI has to say about it.

That's good to make clear. However, my brain is definitely not working at full power today—it's been a mentally-draining day—, so I'm struggling to figure out how to best utilize that information. What does CI say about damage that would overwrite KYOS?

This makes me think of my idea to use KYOS ST and BL progression but to use equivalent BS damage for KYOS ST.

Originally Posted by Raekai

A MESSY SOLUTION

Everything is calculated per BS except for ST, which is the default assumption of KYOS. However, for this, damage is reverted to how it was before for calculating reasonable WP.

• ST 10 = BL 20 = 1d-2/1d damage = HP 10 = 125 lb.
• ST 16 = BL 80 = 2d-1/3d+2 damage = HP 20 = 1000 lb.
• ST 20 = BL 200 = 3d+1/6d-1 damage = HP 32 = 4096 lb.
• All of this is input in CI as normal.

If this is what KYOS taking a back seat means, I'm sure there'd be a better way to do it, but, again, my brain's a bit fried right now.

[RyanW]

Originally Posted by Raekai

Ah, okay! I misunderstood. I thought it was maybe a different way to tackle it in play, though it did seem like that would require knowing how much DR should stop damage.

I try my best not to convert "at the table" by having most relevant information precalculated. Character sheets and NPC cards have the damage, HP, and DR replaced with WP, RT, and Protection.