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Old 08-26-2019, 06:13 PM   #31
Anthony
 
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Default Re: Conditional Injury with Knowing Your Own Strength

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Originally Posted by dataweaver View Post
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.
It's logarithms, square and cube are just multiply by 2 or 3 regardless of base. Yes, you don't get a nice result on the cube root of x10 (it's 3.33 on dB, +4 on +12/x10), but you make up for that by getting a nice result for the cube root of x2 (+1, vs +1.2).
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Old 08-26-2019, 07:38 PM   #32
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Default Re: Conditional Injury with Knowing Your Own Strength

Again, having exact values (other than “+x=×10”) isn't that important, since we're using these for ranges; and having an “exact” value for the cube root of 2 isn't really that big of a deal.

Conversely, both squares and cubes have shorter lists if x is a multiple of 6, and continue to hit ×10: if x=12 then the sequence for squares is six steps to ×10 and the sequence for cubes is four steps to ×10. By contrast, the sequence for squares if x=10 is five steps to ×10 and the sequence for cubes is ten steps to ×1000, and misses both ×10 and ×100. (Admittedly, it does do a reasonable job of approximating a ×2 per step pattern; but again, that's not all that important.)
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Old 08-26-2019, 07:51 PM   #33
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Default Re: Conditional Injury with Knowing Your Own Strength

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Again, having exact values (other than “+x=×10”) isn't that important, since we're using these for ranges; and having an “exact” value for the cube root of 2 isn't really that big of a deal.

Conversely, both squares and cubes have shorter lists if x is a multiple of 6
Only if you actually care about multiples of ten. If you don't care about other exact values, why care about multiple of 10?
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Old 08-26-2019, 08:06 PM   #34
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Default Re: Conditional Injury with Knowing Your Own Strength

Because we use a decimal number system, you need to precisely hit a power of ten after a whole number of steps, or else you won't have a pattern that repeats. Ever.

(And if you have a pattern that hits a power of ten in a whole number of steps, you can rearrange them to produce a pattern that hits ten in the same number of steps or less.)
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Old 08-26-2019, 09:20 PM   #35
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Default Re: Conditional Injury with Knowing Your Own Strength

This makes me think of people discussing which base/radix is most useful. 10 for ten fingers? 12 for divisibility? 16 for being a power of 2? 20 for ten fingers and ten toes? 60 for even more divisibility? I stand by 12 and 16, but that's not really important. It just helps me feel like I'm still relevant in this math-heavy conversation.

Maybe I should start a new thread about switching all of GURPS over to a duodecimal system... Hmm...

Anyway, it seems like there are a few major proposals:
  1. +10 = ×20
  2. +10 = ×24
  3. +10 = ×30
I'll attempt to sum up what's been said and done alongside my own personal feelings below.


+10 = ×20 System

The +10 = ×20 system feels the best to me. It seems like it would take the least work to digest alongside Knowing Your Own Strength, especially because KYOS lifting is +10 = ×10. Because it already converts standard ST to KYOS ST using this kind of scale, it seems like it would be a natural fit to KYOS, especially because RT would just be KYOS HP + 10 (assuming my math was correct). dataweaver gives a conversion from standard HP/damage to +10 = ×20 here.

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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.
As far as I can tell, KYOS uses weight-based HP that's in-line with determining HP for objects. HP = 2 × weight^(1/3). That's supposed to keep HP "the same" as it was before. Alternatively, it gives ST = 10 × log(weight/6) with up to a -4 penalty for beings with fine dexterity (e.g., humans), which could theoretically determine logHP from weight. That might suggest that KYOS HP should be KYOS ST + 4 for humans, or it might suggest that KYOS HP should be KYOS ST - 4 for other beings.

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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.
Also, is there a more intuitive/streamlined way of doing this? Even if it's a bit less of a "reasonable approximation". It seems like this would add quite a bit of extra math in play.


+10 = ×24 System

This would be best to use if KYOS was converted to be +10 = ×12. It's a bit of extra work, but it could be done. Plus, dataweaver mentioned that it "gives you easy squares and cubes", but the importance is beyond what I can safely guess. Anthony argues that it gives "nasty numbers", and dataweaver argues that it's "less of a concern than you might think, since we're actually more interested in ranges of values than exact values". Earlier in the thread, dataweaver detailed these values.


+10 = ×30 System

Anthony already listed the advantages of this scale. I'm inclined to believe that what Anthony wrote must be true. Also, Anthony fleshed this out as Know Your Own Damage. I'm fairly certain that RyanW is also working in this scale, but I don't want to be flat-out wrong.


Notes

Please, please, please let me know if I got anything wrong. I'm sorry about the excessive hedging—that's a lot of "seem" and "think" and "feel". Because I know so little about what I'm talking about, I just want to make it clear that I'm never trying to step on anyone's toes. Also, thank you to everyone who has participated in this discussion so far. Not only do I have a much better idea of how to merge KYOS and CI, I have learned a bit about math as well!
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Old 08-26-2019, 11:18 PM   #36
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Default Re: Conditional Injury with Knowing Your Own Strength

Note that you can sensibly combine +20 ST = x10 damage and +30 LogD = x10 damage:

Let Mass = (LogST required to lift an object as 1x BL).

It's convenient to say Wound Threshold = Mass±X. Using the tables in Basic and the KYoD tables, the level 0 wound threshold works out to Mass-8 for living, Mass+1 for unliving, Mass+10 for homogeneous (a 125 lb/mass 18 object has 10/20/40 hp, corresponding to 30/39/48 on the LogD table, and level 0 wound threshold is at -20).

However, the problem we find is that the formula for ST in Basic is not actually Mass+X -- it actually resolves as Mass*2/3 - 2 (a 125 lb/Mass 18 creature has ST 10, BL 20, logST 10, a 1,000 lb/Mass 27 creature has ST 20, BL 80, LogST 16). Thus, if we compute HP based on Mass and damage based on ST, the two values don't align. Either we have to wound threshold on something other than Mass, or we have to increase damage faster than ST.

It turns out there's a pretty easy way of doing this: add a term for weapon weight. If damage scales with ST + (weapon Mass/3), the x8 more massive creature likely has 8x heavier natural weapons (+9 Mass) and thus even though it has only 6 higher ST, it would have 9 higher damage.
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Old 08-26-2019, 11:21 PM   #37
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Default Re: Conditional Injury with Knowing Your Own Strength

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Originally Posted by Raekai View Post
This makes me think of people discussing which base/radix is most useful. 10 for ten fingers? 12 for divisibility? 16 for being a power of 2? 20 for ten fingers and ten toes? 60 for even more divisibility? I stand by 12 and 16, but that's not really important. It just helps me feel like I'm still relevant in this math-heavy conversation.
You're actually dead on with this: while I've been talking about squares and cubes, Anthony is right that when you convert to a lot system, these become doubling and tripling — or halves and thirds, making it an issue of divisibility. Meanwhile, the main arguments for the decibel system is that we use base 10: the one's place gives you numbers based on the ten digits, while the tens etc. represent orders of magnitude. It's not that far removed from “10, because we have ten fingers”.

Quote:
Originally Posted by Raekai View Post
Anyway, it seems like there are a few major proposals:
  1. +10 = ×20
  2. +10 = ×24
  3. +10 = ×30
I'll attempt to sum up what's been said and done alongside my own personal feelings below.


+10 = ×20 System

The +10 = ×20 system feels the best to me. It seems like it would take the least work to digest alongside Knowing Your Own Strength, especially because KYOS lifting is +10 = ×10. Because it already converts standard ST to KYOS ST using this kind of scale, it seems like it would be a natural fit to KYOS, especially because RT would just be KYOS HP + 10 (assuming my math was correct). dataweaver gives a conversion from standard HP/damage to +10 = ×20 here.
If you're going to leave KYOS as decibel-based, then yes, this is your best option IMHO. Going with 24 steps for CI implies going with 12 steps for KYOS.


Quote:
Originally Posted by Raekai View Post
As far as I can tell, KYOS uses weight-based HP that's in-line with determining HP for objects. HP = 2 × weight^(1/3). That's supposed to keep HP "the same" as it was before. Alternatively, it gives ST = 10 × log(weight/6) with up to a -4 penalty for beings with fine dexterity (e.g., humans), which could theoretically determine logHP from weight. That might suggest that KYOS HP should be KYOS ST + 4 for humans, or it might suggest that KYOS HP should be KYOS ST - 4 for other beings.
IMHO, KYOS is primarily about the relationship between ST and weight, while CI is primarily about the relationship between ST and damage. HP is a “damage” thing, so you should take your cues for it from CI rather than KYOS, where they conflict. Since both are based on ST, that will imply a relationship between weight and HP; but IMHO, that's not as important as the relationship between damage and HP: Those should be kept in sync with each other, else you end up with high-ST characters having far more ability to dish out damage than to take it, while low-ST characters end up being exceptionally good at taking damage in comparison to their ability to dish it out.

That's why I'm suggesting that HP (or its log-counterpart, RT) should be designed to parallel damage-dishing capability, and letting the relationship between weight and HP fall where it may.

Quote:
Originally Posted by Raekai View Post
Also, is there a more intuitive/streamlined way of doing this? Even if it's a bit less of a "reasonable approximation". It seems like this would add quite a bit of extra math in play.
A major motivation behind using a log scale for damage is to reduce the math: it lets you replace multiplication and division with addition and subtraction, and it lets you replace powers with multiplication and division. Every ± modifier found in CI has an existing multiplier or divisor in the standard rules: things like Unliving applying a divisor to damage become simply levying a straight subtraction penalty in the CI system.

+10 = ×24 System

This would be best to use if KYOS was converted to be +10 = ×12. It's a bit of extra work, but it could be done. Plus, dataweaver mentioned that it "gives you easy squares and cubes", but the importance is beyond what I can safely guess. Anthony argues that it gives "nasty numbers", and dataweaver argues that it's "less of a concern than you might think, since we're actually more interested in ranges of values than exact values". Earlier in the thread, dataweaver detailed these values.[/QUOTE] That's an accurate summary.

Quote:
Originally Posted by Raekai View Post
+10 = ×30 System

Anthony already listed the advantages of this scale. I'm inclined to believe that what Anthony wrote must be true. Also, Anthony fleshed this out as Know Your Own Damage. I'm fairly certain that RyanW is also working in this scale, but I don't want to be flat-out wrong.
IMHO, the primary benefit of the 30-step scale is that it embeds both the decibel scale (every third step matches up with a decibel number) and the Speed/Range scale (every five steps matches up with an entry from the Speed/Range Table). It's also the smallest number of steps that does this.

Quote:
Originally Posted by Raekai View Post
Please, please, please let me know if I got anything wrong. I'm sorry about the excessive hedging—that's a lot of "seem" and "think" and "feel". Because I know so little about what I'm talking about, I just want to make it clear that I'm never trying to step on anyone's toes. Also, thank you to everyone who has participated in this discussion so far. Not only do I have a much better idea of how to merge KYOS and CI, I have learned a bit about math as well!
Yeah; log scales can be very useful; but they're also something of a dying/lost art.
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Old 08-27-2019, 10:05 AM   #38
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Default Re: Conditional Injury with Knowing Your Own Strength

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Every ± modifier found in CI has an existing multiplier or divisor in the standard rules: things like Unliving applying a divisor to damage become simply levying a straight subtraction penalty in the CI system.
I've been watching this thread with much interest; I don't use KYOS but I am firmly in the camp that having a scale that's well behaved from "a tiny amount of ST" to "moves planets" - which requires a log scale - is something extremely useful for GURPS.

You run quickly into mechanics issues, of course! There's a lot of collateral damage, so to speak, shifting to new scales. ST rolls probably need to die completely - the difference between "what am I lifting" and "what's my lifting power" should be a modifier to a DX or HT roll.

Given the small amount of extra mass that usually makes you go from "doing reps" to "can't budge it" in the real world, scales with many steps actually help you here.

Note that I use a 12-step chart in Technical Grappling as well for the "Grappling Encumbrance Modifier."

No real comment, other than to reply and say "Yes" to the SSR being as close as possible to the "how many HP damage does it take to get to 0, -HP, -NxHP, and finally -10xHP. Plus the various multipliers for stuff.
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Old 08-27-2019, 10:38 AM   #39
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Default Re: Conditional Injury with Knowing Your Own Strength

There are basically three concerns which decide the specific scaling you use
Mass-Based vs ST-Based
HP in G4e is either sqrt(BL*5) or (2, 4, or 8)*mass^(1/3). These work out to the same numbers for critters because BL is set to 0.8 * mass^(2/3).

If you want to figure out toughness and damage based on ST, the formula should be ST/2 + some constant, and objects will have HP (and DR) thresholds based on Mass*2/3.
If you want to figure out toughness and damage based on mass, the formula should be (Mass Rating)/3 + some constant, where mass rating is the ST required to lift the thing, and ST-based damage should be about ST*1.5 plus some bonus (or maybe ST + weapon bonus, where weapon bonus is expected to make up the difference).

KYoS gets around this by making BL linear in mass.
Appropriate damage variance
The difference between minimum and maximum damage in GURPS is a factor of 6 (0.78 on a log10 scale). On 20xlog10, that is 15.6 points, roughly the difference between minimum and maximum on 3d6. However, there are plausible arguments that damage (or at least penetration) differences in GURPS are unrealistically high, or alternately you might prefer something other than 3d.
Convenience
Whatever scale you work with should be easy to use (frankly, the SSR table, at +6 per x10, is a poor design decision, humans much prefer 2, 5, or 10 scales).
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Old 08-27-2019, 11:18 AM   #40
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Default Re: Conditional Injury with Knowing Your Own Strength

So I have a very silly question, as some of the math and conjecture in this thread is above my head:

Why is it that KYOS and CI don't properly work together?

By my understanding, per KYOS - ST is logarithmic as far as lifting capacity, but damage progression remains the same (with the exception of Thrust damage which is raised to match Swing progression, as noted in the OP). So while ST itself may be logarithmic, I don't understand how Damage is all of a sudden logarithmic? In fact, there was a thread on KYOS about this - how damage, at a certain point, lacks comically far behind lifting capacity (i.e. I can lift a tank as easy as my tennis shoe, but I'm not even close to being able to punch it for meaningful damage - just to be clear I don't have a personal issue with this, but it's been mentioned before).

With the assumption that the previous statements are true (they may well not be, please feel more than free to correct me), we must also look at HP as dictated by KYOS: that is, ST is reduced to its new level (20 to 16 for example), then HP is bought back up to its original level (whichever KYOS calculation you use to do that; by default per this example it would be purchased back up to 20 again).

Now, can't that 20 HP simply be plugged into Conditional Injury for the Robustness Threshold? Aside from Thrust becoming more vicious (intended as per KYOS), I don't see why this breaks anything given that damage itself isn't *actually* any more logarithmic than it was before (despite basic lift progression changing)?

I guess I just can't see why the default HP # needs to change, because it doesn't have to change at all per KYOS; the result in my mind being that Conditional Injury should still work exactly as intended, because you're getting the same RT as well as the same WT (again, aside from Thrust).

I'm sure I must be missing something obvious, appreciate any responses.
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