Conditional Injury with Knowing Your Own Strength

[Anthony]

Originally Posted by Raekai

[*]How do I make it work with ×10 is +20?

You'll need to remake the tables based on 20xlog10 instead of 30xlog10 (easy with a spreadsheet, otherwise requires you to remember values). Also need to redo the addition and subtraction table and wound thresholds.

[RyanW]

Regarding armor, my thoughts were along these lines. Given that +1 Wound Potential is about +50% damage, that means that armor stops all of WP X allows through about 1/3 of X+1, 1/2 of X+2, 2/3 of X+3, and 4/5 of X+4. On this scale:

1/3 = -3
1/2 = -2
1/3 = -1
4/5 is between -1 and -0. As long as you're consistent, you could round it up or down.

Regarding +3 ST = +1 WP, I assumed damage scaled with the square root of BL (roughly the same as RAW, but I did some figuring involving force, mass, and distance over which acceleration occurs to make sure the number wasn't unreasonable). On a logarithmic scale, taking a root becomes dividing, so the square root of damage means half the WP. +3 ST = ×2 BL, therefore +3 ST = ×1.5 damage = +1 WP.

Edit: I don't have access to the original KYOS right now. It occurs to me that I may have made modifications to it.

[dataweaver]

Here's an alternative to the Robustness Threshold and Wound Potential Tables that's based on +20=×10 instead of the current +6=×10:

HP/dmg: RT/WP |
1: 0
2: 6
3: 9
4: 12
5: 14
6: 16
7: 17
8: 18
9: 19
10: 20
11: 21
–13: 22
–15: 23
–17: 24
–19: 25
–21: 26
–24: 27
–27: 28
–30: 29
–34: 30
–38: 31
–42: 32
–47: 33
–53: 34
–59: 35
–65: 36
–75: 37
–85: 38
–95: 39
–105: 40
–115: 41
–135: 42
–150: 43
–170: 44
–190: 45
–210: 46
–240: 47
–270: 48
–300: 49
–340: 50
–380: 51
–420: 52
–470: 53
–530: 54
–590: 55
–650: 56
–750: 57
–850: 58
–950: 59

Entries starting with a – are ranges that start one higher than the previous entry: so “–13” is actually “12–13”, and “–950” is actually “851–950”. You can extend this table further by multiplying HP/dmg by 10 and adding 20 to RT/WP.

The rule for applying DR (actually, log-subtraction) is:
WP vs. LogDR: WP modifier
0 or less: no damage
+1: -21
+2: -13
+3: -10
+4: -8
+5: -7
+6: -6
+7: -5
+8: -4
+9–+10: -3
+11–+13: -2
+14–+19: -1
+20 or more: -0

That is, find out how much the WP exceeds the “LogDR”, and reduce the effective WP by an amount based on the difference. LogDR comes from DR the same way that RT comes from HP.

Damage ranges (e.g., 1d, 2d, 2d×10, etc.) have a 16-point spread: 1d goes from WP0 to WP16; 2d goes from WP6 to WP22; 3d6 goes from WP9 to WP25; 4d goes from WP12 to WP27; 5d goes from WP14 to WP29; 6d goes from WP16 to WP31; 7d goes from WP17 to WP32; 8d goes from WP18 to WP34; and so on. That is, the maximum WP you can achieve is 15 higher than the minimum you can achieve.

Meanwhile, the average damage you can roll always translates to a WP that's 11 higher than the minimum, and 4 less than the maximum. You can get a reasonable approximation of this by rolling 5d, adding the top three dice to the average WP of the attack, and subtracting 14 from the result. That's your damage roll.

[Raekai]

Originally Posted by Anthony

You'll need to remake the tables based on 20xlog10 instead of 30xlog10 (easy with a spreadsheet, otherwise requires you to remember values). Also need to redo the addition and subtraction table and wound thresholds.

That makes sense. Thanks!

Originally Posted by RyanW

Regarding armor, my thoughts were along these lines. Given that +1 Wound Potential is about +50% damage, that means that armor stops all of WP X allows through about 1/3 of X+1, 1/2 of X+2, 2/3 of X+3, and 4/5 of X+4. On this scale:

1/3 = -3
1/2 = -2
1/3 = -1
4/5 is between -1 and -0. As long as you're consistent, you could round it up or down.

Regarding +3 ST = +1 WP, I assumed damage scaled with the square root of BL (roughly the same as RAW, but I did some figuring involving force, mass, and distance over which acceleration occurs to make sure the number wasn't unreasonable). On a logarithmic scale, taking a root becomes dividing, so the square root of damage means half the WP. +3 ST = ×2 BL, therefore +3 ST = ×1.5 damage = +1 WP.

Edit: I don't have access to the original KYOS right now. It occurs to me that I may have made modifications to it.

This looks interesting. It's a bit easier for me to understand, which is always a plus! And this all lines up with your thread, right? You did mention using a "variant on the KYOS system". How does the variant differ? And how much would have to be done for it to work with KYOS as-is? (Your "+3 ST = ×2 BL" checks out. Though, KYOS says, "Extending the “thrust = swing-2” found at ST 10 across the board implies that swinging multiplies force by about 1.5", so I would assume that +2 ST = ×1.5 damage, but I could be very wrong. Of course, it could be the other way around, and we could then say that, with your math, thrust = swing-3.)

Originally Posted by dataweaver

Here's an alternative to the Robustness Threshold and Wound Potential Tables that's based on +20=×10 instead of the current +6=×10:

[...]

Damage ranges (e.g., 1d, 2d, 2d×10, etc.) have a 16-point spread: 1d goes from WP0 to WP16; 2d goes from WP6 to WP22; 3d6 goes from WP9 to WP25; 4d goes from WP12 to WP27; 5d goes from WP14 to WP29; 6d goes from WP16 to WP31; 7d goes from WP17 to WP32; 8d goes from WP18 to WP34; and so on. That is, the maximum WP you can achieve is 15 higher than the minimum you can achieve.

Meanwhile, the average damage you can roll always translates to a WP that's 11 higher than the minimum, and 4 less than the maximum. You can get a reasonable approximation of this by rolling 5d, adding the top three dice to the average WP of the attack, and subtracting 14 from the result. That's your damage roll.

Awesome! Just to clarify, are the alternative to the Robustness Threshold Table and Wound Potential Table based off of standard HP or logarithmic HP (as in, HP = ST from KYOS)? It's hard for me to keep track of who's doing what where. I ask because I was surprised that the bands would balloon so much if based on logarithmic HP. Of course, that's just my intuition—again, math is not my strong suit—because RyanW uses +3 ST = +1 WP, so I'd imagine that +3 HP = +1 RT (again, assuming that HP has been converted like ST in KYOS).

Actually, it seems like my guess is correct. HP 34 is RT 30, and [20 × log(34)] is ~30. Just in case I found a one-off coincidence, I checked with other values. HP 190 is RT 45, and [20 × log(190)] is ~45. I don't understand what I did, but I did it. So, it almost seems like, if you converted HP with the KYOS ST formula, then ~RT would just be HP + 10. Then, at that point, couldn't you just knock the +10 off of each side? Unless I'm just making stuff up, which is very possible.

Also, would it be beneficial to also switch the Conditional Effects Table over to ×10 = +20? Or does it really matter?

[Anthony]

Originally Posted by Raekai

Actually, it seems like my guess is correct. HP 34 is RT 30, and [20 × log(34)] is ~30. Just in case I found a one-off coincidence, I checked with other values. HP 190 is RT 45, and [20 × log(190)] is ~45. I don't understand what I did, but I did it. So, it almost seems like, if you converted HP with the KYOS ST formula, then ~RT would just be HP + 10. Then, at that point, couldn't you just knock the +10 off of each side? Unless I'm just making stuff up, which is very possible.

It's kinda useful to have the zero point be at 1 hp. Otherwise there is no particular reason not to do it.

[dataweaver]

I'm operating on the premise that HP increase roughly at the same rate as damage, on the notion that maintaining a parity between damage and HP will avoid obvious problems of disparities between what you can dish out and what you can take. Thing is, I'm not assuming that damage increases linearly with ST; that's kind of the whole point of Conditional Injury, to put damage and HP on a geometric progression with respect to ST.

Remember that weight is also being recalibrated (by KYOS) to be on an exponential scale; so the relationship between weight and HP is still something to the effect of HP=weight^n; I'm just not sure off the top of my head what n is. I think it's ½.

On the other hand, I'm trying to keep RT, WP, and the equivalent counterpart to DR directly proportional to ST; and as much as possible, I'm trying to get all of the mechanics to work with them instead of dmg, HP, and DR: if I can do that, then I can render moot
the HP-to-RT and dmg-to-WP tables, except for the purpose of converting existing material to RT and WP.

Which reminds me: another table that needs to be changed is the Conditional Effect Table. The Severity column needs to be rescaled so that what's currently -6 becomes -20, and what's currently +6 becomes +20. That's a simple multiple, though: just divide by 3 and multiply by 10. So ±6 becomes ±20, ±5 becomes ±16, ±4 becomes ±13, ±3 becomes ±10, ±2 becomes ±6, and ±1 becomes ±3. Likewise, all of the Injury and Severity modifiers need to be inflated to for the new scale: e.g., the Target Composition modifiers for Unloving go from -2, -3, and -4 to -6, -10, and -13. Heck, all modifiers need to be recalibrated to the 20-step scale.

[Anthony]

The advantages of +30/x10:

• You can just look up the mass of an object on the KYoS table and convert directly to a toughness rating. A 1 lb unliving object (KYoS -3) has 4 hp (LogD 18). A 1,000 lb unliving object (KYoS 27) has 40 hp (LogD 48).
• It interacts nicely with the range/speed chart. For example, if you want to divide damage by distance, that's just a modifier of -10 + 5x range modifier. If you want to multiply by speed, add 10 - 5x speed modifier (e.g. collision damage for an unliving object in KYoD works out to 3d + Mass - 5xRSM - 23). You can do the same sort thing with the +20/x10, but you wind up multiplying by 10/3, which is annoying.
• In the typical range of PC HP (8-18) you can just add 20 to the linear value and be correct within error margins.

The disadvantage, however, is that GURPS 4e did a lot of things based on quadratic scaling, and in vanilla GURPS lifting ability actually varies with 2/3 power of mass, so a 1,000x heavier creature (with 10x the ST) actually only has 100x the BL (+20). The collision case is particularly inconsistent because you can get 10x damage by either multiplying speed by 10 (100x the energy) or by multiplying mass by 1,000 (1,000x the energy).

The thing this is leaving out is mostly wound width: the 1,000x mass collision might make hole of the same depth as the 10x speed collision, but the hole is much wider. The only attacks in G4e that have a concept of wound with are piercing attacks, but it actually applies to everything. In the case of ST-based attacks, a 1,000x more massive creature might not apply 1,000 the force -- but it probably applies 100x the force over 10x the distance, for a net of x1,000 energy.

[dataweaver]

Personally, Is be more inclined to rework KYOS to use +12=×10, then rework CI to +24=×10. Using a multiple of six gives you easy squares and cubes.

[Anthony]

Originally Posted by dataweaver

Personally, Is be more inclined to rework KYOS to use +12=×10

Problem with that is nasty numbers. On a +10=x10 scale, there are several values that are very close to integer multipliers -- using two significant figures, the values are 1, 1.3, 1.6, 2.0, 2.5, 3.2, 4.0, 5.0, 6.3, 7.9, which gives you x2, x4, and x5 as integer. By comparison, on the +12=x10 scale, the values are 1, 1.2, 1.5, 1.8, 2.2, 2.6, 3.2, 3.8, 4.6, 5.6, 6.8, 8.3, none of which are particularly nice numbers.

If I were making bigger changes, I'd probably switch the range/speed chart to decibel (+10=x10) or 2dB (+5 = x10) rather than changing KYoS away from dB, as converting to dB is generally easier than the RSM -- for example, 1 AU = 1.6e+11 yards, which can be converted to dB by looking up 1.6 and adding 11x10 (112 dB relative to 1 yard). On the RSM, you instead look up 1.6 and add 11x6 (+67 relative to one yard, +65 relative to 2 yards).

[dataweaver]

Originally Posted by Anthony

Problem with that is nasty numbers. On a +10=x10 scale, there are several values that are very close to integer multipliers -- using two significant figures, the values are 1, 1.3, 1.6, 2.0, 2.5, 3.2, 4.0, 5.0, 6.3, 7.9, which gives you x2, x4, and x5 as integer. By comparison, on the +12=x10 scale, the values are 1, 1.2, 1.5, 1.8, 2.2, 2.6, 3.2, 3.8, 4.6, 5.6, 6.8, 8.3, none of which are particularly nice numbers.

That's less of a concern than you might think, since we're actually more interested in ranges of values than exact values. You're not looking at, say, the number 1.21 as you're looking at the range (1.10, 1.33].

And when you're working in an environment where squares and cubes are likely to come up frequently, the fact that squaring a twelve-step pattern gives you a six-step pattern, and coming it gives you a four-step pattern, is much nicer than how the decibel scale behaves in similar conditions.