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Old 03-10-2022, 04:17 PM   #23
dataweaver
 
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Default Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!

For reference purposes, here's what I worked up a while back when I was asked by Raekai for help in combining Conditional Injury and Know Your Own Strength.

The first thing to note is that the two systems use very different logarithmic progressions: Conditional Injury is built around the Speed/Range table, which operates at six steps from ×1 to ×10; whereas KYOS uses a decibel scale, which operates at ten steps from ×1 to ×10.

Meanwhile, Basic Set operates on a ST^2 scale for Basic Lift (meaning that ST 20 can lift four times as much as ST 10) and has a kinda sorta linear progression for damage (from ST 9 to ST 27, +4 ST=+1d6 Swing and +8 ST=+1d6 Thrust; starting at ST 27, +8 ST=+1d6 for both; and from ST 1 to ST 9, you get massive distortion based on the fact that you're forced to work with a single damage die).

Neither CI nor KYOS align very well with this. To bring KYOS more into line with the “ST 20 can lift four times as much as ST 10”, Raekai and I decided to try out a 20-step progression from ×1 to ×10. That actually places ST 20 at only 3.16 times ST 10, which is a tad on the weak side; but not bad in comparison to KYOS's “ST 20 has ten times the basic lift as ST 10”. (The closest match in the vicinity of ST 10 would come from seventeen steps from ×1 to ×10; but that's a really ugly number to work with. And anything less than that is too fast.)

For reference the raw 20-step scale goes like this:

+0=×1.00
+1=×1.12
+2=×1.26
+3=×1.41
+4=×1.58
+5=×1.78
+6=×2.00
+7=×2.24
+8=×2.51
+9=×2.82
+10=×3.16
+11=×3.55
+12=×3.98
+13=×4.47
+14=×5.01
+15=×5.62
+16=×6.31
+17=×7.08
+18=×7.94
+19=×8.91
+20=×10

---

Once the +20=×10 baseline was established, the next step was to rework the Conditional Effects Table from CI to work with that instead of the +6=×10 progression that it was originally designed for. My logic in doing so was as follows:

If we were to set +0 to 1 point of damage, then 1d-2 would fall somewhere between +3 and +6 — in fact, its mean value falls almost precisely between +4 and +5. For simplicity, I'm going to assume that +5 corresponds to 1d-2. With that in mind, here's the map of WP to Basic Set damage:

0 WP: 0.562 dmg
1 WP: 0.631 dmg
2 WP: 0.708 dmg
3 WP: 0.794 dmg
4 WP: 0.891 dmg
5 WP: 1.00 dmg
6 WP: 1.12 dmg
7 WP: 1.26 dmg
8 WP: 1.41 dmg
9 WP: 1.58 dmg
10 WP: 1.78 dmg
11 WP: 2.00 dmg
12 WP: 2.24 dmg
13 WP: 2.51 dmg
14 WP: 2.82 dmg
15 WP: 3.16 dmg
16 WP: 3.55 dmg
17 WP: 3.98 dmg
18 WP: 4.47 dmg
19 WP: 5.01 dmg
20 WP: 5.62 dmg
+20 WP: ×10 dmg

Using a similar approach, here's how RT should map to HP:

0 RT: 3.16 HP
1 RT: 3.55 HP
2 RT: 3.98 HP
3 RT: 4.47 HP
4 RT: 5.01 HP
5 RT: 5.62 HP
6 RT: 6.31 HP
7 RT: 7.08 HP
8 RT: 7.94 HP
9 RT: 8.91 HP
10 RT: 10 HP
11 RT: 11.2 HP
12 RT: 12.6 HP
13 RT: 14.1 HP
14 RT: 15.8 HP
15 RT: 17.8 HP
16 RT: 20.0 HP
17 RT: 22.4 HP
18 RT: 25.1 HP
19 RT: 28.2 HP
20 RT: 31.6 HP
+20 RT: ×10 HP

According to B420, a Major Wound is any single injury of greater than ½ your HP. Since 19 WP is 5.01 damage and 10 RT is 10 HP, Major Wounds begin at Wound Severity +9. I figure that Minor Wounds begin at 1/10 of your HP, which would result in Minor Wounds starting at Wound Severity -5. Would Severity -6 or less would be a Scratch, or None. For the sake of nice, round numbers, let's say that a Scratch starts at Wound Severity -10; that would be roughly equivalent to a little over half a point of damage in the standard system. (-11 would be almost precisely half a point.)

Reeling corresponds to a single injury that takes you down to less than ⅓ of your HP in the regular system. That would be Wound Severity +12.

Crippled corresponds to losing all your HP in a single hit: Wound Severity +15.

Mortal Wound corresponds to a hit that does twice your HP in one hit: Wound Severity +21.

Instant Death corresponds to an attack that inflicts 6×HP in a single blow: Wound Severity +31.

Total Destruction corresponds to an attack that inflicts 11×HP in a single blow: Wound Severity +36.

So as far as Gross Effects are concerned, this is what the Conditional Effects Table looks like:

-11 or less: None
-10 to -6: Scratch
-5 to +8: Minor Wound
+9 to +11: Major Wound
+12 to +14: Reeling
+15 to +20: Crippled
+21 to +30: Mortal Wound
+31 to +35: Instant Death
+36 or more: Total Destruction

1d damage has a minimum WP of 5, an average WP of 16, and a maximum WP of 21. The minimum is the average -11, and the maximum is the average +5. That's a 16-point spread.

2d damage has a minimum WP of 11, an average WP of 22, and a maximum WP between 26 and 27. The minimum is the average -11 and the maximum is the average +4 or +5.

3d damage has a minimum WP between 14 and 15, an average WP between 25 and 26, and a maximum WP of 30. The minimum is the average -11 and the maximum is the average +4 or +5.

4d damage has a minimum WP of 17, an average WP of 28, and a maximum WP between 32 and 33. Minimum WP is average WP-11, and maximum WP is average WP+4 or +5.

That's pretty consistent. So we want a damage roll with a similar spread: a 15-to-16 point spread, with the average being biased toward the high end. The closest you can get to that with regular dice is to roll five dice, drop the lowest two, and subtract 14 from the result: that gives an average of slightly less than 0, a minimum of -11, and a maximum of +4.

If we assume that this “5d6, drop 2” will always be added to the damage, we can excise having to subtract 14 from it every time we roll by adding 14 to every entry on the Conditional Effects Table that we constructed. You can also achieve a similar result with 4d6, at the cost of the minimum being slightly higher (average -10 instead of average -11) and the maximum being considerably higher (average +10 instead of average +4 or 5). That's a potential doubling of maximum damage. Still, that's an outlier; and 4d is easier than 5d, drop two.

So we replace the dice pools with a flat 4d6 roll. Severity is that plus the Wound Potential minutes the Robustness Threshold:

Where Severity=4d+WP-RT,
Severity 3 or less: None.
Severity 4 to 8: Scratch
Severity 9 to 22: Minor Wound
Severity 23 to 25: Major Wound
Severity 26 to 28: Reeling
Severity 29 to 34: Crippled
Severity 35 to 44: Mortal Wound
Severity 45 to 49: Instant Death
Severity 50 or more: Total Destruction

Now: as I said before, the line between None and Scratch is largely arbitrary. I see no reason not to move it down three steps, so that Scratch starts at Severity 1. I'm also thinking of moving the threshold between Reeling and Crippled up one step, mostly for aesthetic reasons; but it would have the effect of making Crippling injuries slightly less likely. These changes would give us the following Conditional Effects Table:

Severity 0 or less: None
Severity 1 to 8: Scratch
Severity 9 to 22: Minor Wound
Severity 23 to 25: Major Wound
Severity 26 to 29: Reeling
Severity 30 to 34: Crippled
Severity 35 to 44: Mortal Wound
Severity 45 to 49: Instant Death
Severity 50 or more: Total Destruction

And here's a more drastic revision that moves several of the thresholds by up to three steps purely for aesthetic reasons:

Severity -1 or less: None
Severity 0 to 9: Scratch
Severity 10 to 19: Minor Wound
Severity 20 to 24: Major Wound
Severity 25 to 29: Reeling
Severity 30 to 34: Crippled
Severity 35 to 44: Mortal Wound
Severity 45 to 49: Instant Death
Severity 50 or more: Total Destruction

This puts the start of each range at a multiple of 5. Scratches get a slightly broader range; Minor Wounds become slightly less likely (which isn't a problem, considering that they still have the broadest range of all by far); Major Wounds become a bit more likely; and so does Reeling.

Everything else in Conditional Injury needs to be rescaled to twenty steps instead of six; for example, the Natural Healing Table is based on +6 Severity=×10 Time, and would need to be reworked around +20 Severity=×10 Time.
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