03-09-2022, 08:20 PM | #21 | ||
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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03-09-2022, 11:16 PM | #22 |
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
1d(2) pi and 2d pi- cause the same amount of injury. The reason the larger bullet is armor piercing is because it's a hard projectile that doesn't expand on impact.
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03-10-2022, 04:17 PM | #23 |
Join Date: Aug 2004
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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. |
03-10-2022, 04:17 PM | #24 | |
Join Date: Jun 2013
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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In a case of pi vs pi-, the former leaves a wider wound channel. That's the whole reason there's a difference between the two. In cases where that doesn't matter, 1d(2) pi vs 2d pi- are indeed indistinguishable. In cases where it does matter, however, the two are different. I'd argue that, in a case where the the bullet is blowing through such that it can strike something behind the target, the difference between the two is significant - in either case, the target has a hole all the way through it, but pi results in a wound channel that's roughly twice as wide as pi-.
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03-10-2022, 04:22 PM | #25 |
Join Date: Aug 2004
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
Here's how twenty-step logST lifting compares to Basic Set ST lifting in the range of 1 to 30:
ST 1: 3548% ST 2: 995% ST 3: 496% ST 4: 313% ST 5: 225% ST 6: 175% ST 7: 144% ST 8: 124% ST 9: 110% ST 10: 100% ST 11: 93% ST 12: 87% ST 13: 84% ST 14: 81% ST 15: 79% ST 16: 78% ST 17: 77% ST 18: 78% ST 19: 78% ST 20: 79% ST 21: 80% ST 22: 82% ST 23: 84% ST 24: 87% ST 25: 90% ST 26: 93% ST 27: 97% ST 28: 101% ST 29: 106% ST 30: 111% There's a bubble from ST 11 to ST 27 where Basic Set ST outperforms 20-step logarithmic ST by a much as 29%; outside of that range, logarithmic ST gradually comes to vastly outperform Basic Set ST. One of the difficulties in terms of matching damage is that the standard system is kind of weird: ST 2=0.00 dmg ST 4=0.16 dmg ST 6=0.50 dmg ST 8=1.00 dmg ST 10=1.67 dmg ST 12=2.5 dmg ST 14=3.5 dmg ST 16=4.5 dmg ST 18=5.5 dmg ST 20=6 dmg ST 22=7 dmg ST 24=8 dmg ST 26=9 dmg ST 28=9.5 dmg ST 30=10.5 dmg ST 32=11.5 dmg ST 34=12.5 dmg ST 36=13 dmg ST 38=14 dmg ST 40=15 dmg ST 42=16 dmg ...and so on. If we were to convert these directly to WP according to the table I worked up earlier, we'd get: ST 2=-∞ WP ST 4=-11 WP ST 6=-1 WP ST 8=5 WP ST 10=10 WP ST 12=13 WP ST 14=16 WP ST 16=18 WP ST 18=20 WP ST 20=21 WP ST 22=22 WP ST 24=23 WP ST 26=24 WP ST 28=25 WP ST 32=26 WP ST 34=27 WP ST 38=28 WP ST 42=29 WP ST 46=30 WP ST 50=31 WP ST 54=32 WP ST 60=33 WP ST 66=34 WP ST 72=35 WP ST 80=36 WP ST 90=37 WP ST 100=38 WP ST 110=39 WP ST 122=40 WP After that, each increase in WP corresponds to an escalating increase in Basic Set ST. Not surprising, considering that WP represents a geometric growth while BS ST represents a linear growth. Put another way, here's what you'd have to buy in Basic Set to get the rough equivalent of each of these 20-step logarithmic ST scores: ST -30 [-400]=Lifting ST 1 [-27], Striking ST 1 [-45], 0 HP [-20]: [-92] ST -18 [-280]=Lifting ST 2 [-27], Striking ST 2 [-40], 0 HP [-20]: [-87] ST -16 [-260]=Lifting ST 2 [-24], Striking ST 3 [-35], 1 HP [-18]: [-77] ST -11 [-210]=Lifting ST 3 [-21], Striking ST 4 [-30], 1 HP [-18]: [-69] ST -6 [-160]=Lifting ST 4 [-18], Striking ST 4 [-30], 2 HP [-16]: [-64] ST -2 [-120]=Lifting ST 5 [-15], Striking ST 5 [-25], 3 HP [-14]: [-54] ST -1 [-110]=Lifting ST 5 [-15], Striking ST 6 [-20], 3 HP [-14]: [-49] ST 1 [-90]=Lifting ST 6 [-12], Striking ST 6 [-20], 4 HP [-12]: [-44] ST 4 [-60]=Lifting ST 7 [-9], Striking ST 7 [-15], 4 HP [-12]: [-36] ST 5 [-50]=Lifting ST 7 [-9], Striking ST 8 [-10], 4 HP [-12]: [-31] ST 6 [-40]=Lifting ST 8 [-6], Striking ST 8 [-10], 5 HP [-10]: [-26] ST 7 [-30]=Lifting ST 8 [-6], Striking ST 8 [-10], 6 HP [-8]: [-24] ST 8 [-20]=Lifting ST 9 [-3], Striking ST 8 [-10], 8 HP [-4]: [-17] ST 9 [-10]=Lifting ST 9 [-3], Striking ST 9 [-5], 9 HP [-2]: [-10] ST 10 [0]=Lifting ST 10 [0], Striking ST 10 [0], 10 HP [0]: [0] ST 11 [10]=Lifting ST 10 [0], Striking ST 10 [0], 11 HP [2]: [2] ST 12 [20]=Lifting ST 11 [3], Striking ST 11 [5], 13 HP [6]: [14] ST 13 [30]=Lifting ST 12 [6], Striking ST 12 [10], 14 HP [8]: [24] ST 14 [40]=Lifting ST 13 [9], Striking ST 12 [10], 16 HP [12]: [31] ST 15 [50]=Lifting ST 13 [9], Striking ST 13 [15], 18 HP [16]: [40] ST 16 [60]=Lifting ST 14 [12], Striking ST 14 [20], 20 HP [20]: [52] ST 17 [70]=Lifting ST 15 [15], Striking ST 15 [25], 22 HP [24]: [64] ST 18 [80]=Lifting ST 16 [18], Striking ST 16 [30], 25 HP [30]: [78] ST 19 [90]=Lifting ST 17 [21], Striking ST 17 [35], 28 HP [36]: [92] ST 20 [100]=Lifting ST 18 [24], Striking ST 18 [40], 32 HP [44]: [108] ST 21 [110]=Lifting ST 19 [27], Striking ST 20 [50], 35 HP [50]: [127] ST 22 [120]=Lifting ST 20 [30], Striking ST 22 [60], 40 HP [60]: [150] ST 23 [130]=Lifting ST 21 [33], Striking ST 24 [70], 45 HP [70]: [173] ST 24 [140]=Lifting ST 22 [36], Striking ST 26 [80], 50 HP [80]: [196] ST 25 [150]=Lifting ST 23 [39], Striking ST 28 [90], 56 HP [92]: [221] ST 26 [160]=Lifting ST 25 [45], Striking ST 32 [110], 63 HP [106]: [261] ST 27 [170]=Lifting ST 26 [48], Striking ST 34 [120], 71 HP [122]: [290] ST 28 [180]=Lifting ST 28 [54], Striking ST 38 [140], 79 HP [138]: [332] ST 29 [190]=Lifting ST 30 [60], Striking ST 42 [160], 89 HP [158]: [378] ST 30 [200]=Lifting ST 32 [66], Striking ST 46 [180], 100 HP [180]: [426] ST 31 [210]=Lifting ST 34 [72], Striking ST 50 [200], 112 HP [204]: [476] ST 32 [220]=Lifting ST 36 [78], Striking ST 54 [220], 126 HP [232]: [530] ST 33 [230]=Lifting ST 38 [84], Striking ST 60 [250], 141 HP [262]: [596] ST 34 [240]=Lifting ST 40 [90], Striking ST 66 [280], 158 HP [296]: [666] ST 35 [250]=Lifting ST 42 [96], Striking ST 72 [310], 178 HP [336]: [742] ST 36 [260]=Lifting ST 45 [105], Striking ST 80 [350], 200 HP [380]: [835] ST 37 [270]=Lifting ST 47 [111], Striking ST 90 [400], 224 HP [428]: [939] ST 38 [280]=Lifting ST 50 [120], Striking ST 100 [450], 251 HP [482]: [1052] ST 39 [290]=Lifting ST 53 [129], Striking ST 110 [500], 281 HP [542]: [1171] ST 40 [300]=Lifting ST 56 [138], Striking ST 122 [560], 316 HP [612]: [1310] So between ST 10 and ST 22, there's a mild bubble where Basic Set's ST outperforms logST by the equivalent of one or two points of logST: logST 12, 13, 20, and 21 lose about 10% of their damage dealing effectiveness compared to the regular rules, while logST 14 to 19 lose about 20%. Below 10 and above 22, logST vastly outperforms Basic Set ST. Those bubbles are unavoidable, being the result of trying to match a logarithmic progression to quadratic and semi-linear curves. With that in mind, I doubt one could do much better than that. The drawback to this approach is that it requires re-engineering both Conditional Injury and Knowing Your Own Strength, with a comparatively minor revision to the latter and extensive revisions to the former. In both cases, the overall structure remains more or less the same (with the exception that this approach attempts to remove the standard damage rolls from CI), with the main changes being to the tables. Last edited by dataweaver; 03-10-2022 at 06:32 PM. |
03-10-2022, 05:11 PM | #26 | |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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On the log scale above: there are two fairly natural formulas for ST damage -- +20 = x10, and +30 = x10. The first one does a better job of matching the existing ST damage table. The second has the benefit that it scales well with hit points: if we set Swing damage for ST 10 at 1d6, a single hit will do about 1/3 the HP of an object with weight equal to BL, and throwing an object with weight equal to BL at 9 yards per second will do Swing damage. Last edited by Anthony; 03-10-2022 at 05:24 PM. |
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03-10-2022, 06:55 PM | #27 | |
Join Date: Aug 2004
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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As for HP, I tend to think that scaling them with the cube root of mass gives too few HP; large objects under the cube root system tend to be too fragile. I'd be more inclined to shift that to the square root of mass, at which point +20=×10 tracks with HP as well. That said, I could see keeping it at the cube root; though then we're back to there being a disconnect between lifting and striking: +20=×10 take with lifting reasonably well, and shifting that to +30=×10 would result in a much wider range of ST scores that wouldn't be able to lift as much as they currently can. In fact, ST 10 to ST 20 would track fairly closely with a linear BL rather then the quadratic BL that 4e adopted: of +30=×10, then +10=×2.15. |
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03-10-2022, 09:34 PM | #28 | |
Join Date: Jun 2013
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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If so, I can certainly see some logic to that, but... a part of me really likes armor divisors. They probably aren't strictly realistic, but they add a sort of nuance that seems to... just work.
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03-11-2022, 01:59 AM | #29 |
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
Either that or the 2d pi- weapon should be written as 1d(2) pi. Having a 'damage' value that reflects neither penetration nor wounding is poor design.
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03-12-2022, 02:29 PM | #30 | |
Join Date: Dec 2004
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Re: Heavily modified (logarithmic) damage system for GURPS: feedback wanted!
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