Converting Enhancements to Limitations and Vice Versa

[Curmudgeon]

This has been bothering me for a long time. Changing the sign in front of the percentage value to convert a Limitation into an Enhancement or vice versa, doesn’t yield the results it should.

The following snippet is from PK’s post #1 in the Either/Or Limitation thread.

Originally Posted by PK

<snip>
Let's take the Jumper example. Since it's 100 points, it makes the percentages really easy to follow. Jumper (Naked, -30%) costs 70 points. Not arriving naked every time is effective a +30% enhancement (cancelling out the limitation).
< snip>

Well, it makes it obvious to me that those values don’t work as they should. The two endpoints are the really important thing here. Jumper (not naked) is worth 100 points and Jumper (naked) is worth 70 points. The absolute difference between the two conditions is 30 points. If we start with Jumper (not naked) the value of the Limitation (naked) has to get us to a final cost of 70 point. Limitation: naked (-30%) does that.

Now if instead, we were to start with Jumper (naked) for 70 points our value for Enhancement (not naked) has to get us to 100 points because that’s our agreed upon value for Jumper (not naked). I’ve been told elsewhere that Jumper (naked) isn’t a 70 point advantage, it’s a 100 point advantage with a -30% Limitation, and that means exactly nothing to this argument. If you start from the opposite end, the value as an enhancement has to get you back to the beginning, which in this case is 100 points.

If we go with Enhancement: not naked (+30%), we get the following result. Jumper (not naked) = Jumper (naked) + Enhancement (not naked) = 70 + 30% x 70 = 70 +21 = 91 points. We’re 9 points, almost 10% short, of where our value should be (100 points).

Putting it another way: Enhancement (not naked) = [Jumper (not naked) – Jumper (naked)]/Jumper (naked) = [100-70]/70 = 30/70 = 3/7 = +42.86% or 43%. If you’re willing to accept 2 points of slop in the value, you could even it out to 40% (final value 98 points) or 45% (final value 101.5 points).

Let’s consider an Innate Attack with 10 levels of Corrosive (10d damage) and one level of the Explosion Enhancement. The basic Innate Attack is worth 100 points and the Explosion Enhancement is +50%, giving the whole thing a value of 150 points.

If we say that (not explosive) is a -50% Limitation, then working backward, 150 points with a -50% Limitation would give us an Innate Attack (Corrosive) (10d) for 75 points. That’s 25 fewer points or a 25% difference from its established worth.

To get an Innate Attack (Corrosive 10d) for 100 points, the value of the Limitation is [Innate Attack – Innate Attack (explosive)]/Innate Attack (Explosive) = [100-150]/150 = -50/150 = -1/3 = -33%.

In short, when converting a Limitation to an Enhancement, changing the sign undervalues its worth as an Enhancement. Likewise, when converting an Enhancement to a Limitation, just changing the sign overvalues its worth as a Limitation.

Note: the differences in the two examples aren’t fiddly little point or two errors. They’re whoppers.

Painful as it may be, I think it’s necessary to do the maths on this one.

For a future edition of GURPS, I’m not sure what a better solution would be. Giving Enhancements and Limitations an absolute cost in points might work but it might be too cheap for costly advantages and too costly for cheap ones.

Maybe if Limitations and Enhancements were given as simple fractions rather than percentages, you could use plug-in formulas to convert back and forth between Limitations and Enhancements.

If a Limitation is worth A, then it’s value as an Enhancement = (1/[1+A]) -1.
If an Enhancement is worth A, then its value as a Limitation is (1/[1+A]) -1.

For example, a 33% Limitation is a -1/3 Limitation. As an Enhancement, it’s worth (1 / [1 - 1/3]) - 1 = (1 / [2/3]) -1 = (3/2) – 1 = +1/2 or +50%.

A +50% Enhancement is a +1/2 Enhancement. As a Limitation, it’s worth (1 / [1 + 1/2]) – 1 = (1 / [3/2]) – 1 = (2/3) -1 = -1/3 or -33%.

[finn]

Originally Posted by Curmudgeon

Well, it makes it obvious to me that those values don’t work as they should.

Actually, it works as it should.

Originally Posted by Curmudgeon

The two endpoints are the really important thing here.

Actually, the "endpoints" are not important at all.

Originally Posted by Curmudgeon

I’ve been told elsewhere that Jumper (naked) isn’t a 70 point advantage, it’s a 100 point advantage with a -30% Limitation, and that means exactly nothing to this argument.

Yes, it does. It is extremely important to this argument.

Originally Posted by Curmudgeon

If you start from the opposite end, the value as an enhancement has to get you back to the beginning, which in this case is 100 points.

You don't start form the other end. You start from the original cost of the advantage.

"Naked" is a limitation worth -30%, which is worth -30 points.

"Not Naked" is a enhancement worth +30%, which is worth +30 point. The 30% is multiplied against the the original 100 point. Not against the 70 points you call the "other end".

So, a Jumper advantage with a "Naked" and "Not Naked" is worth

100 - 30 +30 = 100

That's how GURPS math works as written.

This math has it's own set of problems, but not the issue you mentioned.

[Curmudgeon]

Originally Posted by finn

Actually, it works as it should.



Actually, the "endpoints" are not important at all.



Yes, it does. It is extremely important to this argument.



You don't start form the other end. You start from the original cost of the advantage.

"Naked" is a limitation worth -30%, which is worth -30 points.

"Not Naked" is a enhancement worth +30%, which is worth +30 point. The 30% is multiplied against the the original 100 point. Not against the 70 points you call the "other end".So, a Jumper advantage with a "Naked" and "Not Naked" is worth

100 - 30 +30 = 100

That's how GURPS math works as written.

This math has it's own set of problems, but not the issue you mentioned.

No, that's not how it works as written. GURPS math isn't a different thing from regular math.

PK's calculation as written in the snippet isn't actually RAW. It's an argument following the principles of other examples that are RAW about calculating unknown values.

For example, and I'm doing this from memory, there was a calculation for an Enhancement where the effects against Blondes were doubled, which wasn't a standard enhancement. The argument for valuing it ran roughly as follows: We do have an limitation for halving the effect. Affects only Blondes is a 30% Limitation. If the population is 100%, then Affects Non-Blondes is 100% - 30% = 70% because any individual in the population is either blonde or not-blonde. (Mathematically, the conditions are exhaustive and mutually exclusive, i.e., there can be no one is both blond and non-blond nor anyone who is neither blond or non-blond). We can apply the limitation halving the effect to the 70% non-blondes. We now have a power that has half its effectiveness against non-blondes and a proper price for the value of that Limitation. But a Limitation halving the effectiveness of the power vs. non-blonds gives exactly the same effect as an enhancement that doubles the effectiveness of the power against blonds. All we need to do is buy the power at the level we want Blonds to be affected at, apply the Limitation: halved effect against non-blonds, and call it doubled effect against blonds. Done.

Now look at PK's argument and the fallacy contained therein. He says that it's a 30% Enhancement because adding 30% to 70% gives 100% cancelling the Limitation and getting us back to our original value.

The fallacy in the argument is that he's not adding a +30% Enhancement to get us back to the original 100 points which is what an Enhancement needs to do. He's simply cancelling the original -30% Limitation and calling it an Enhancement.

Here's why doing that is a problem. Adding the 30% back is adding back the 30% calculated from the 100 point original advantage. In a sense, that's okay because we're adding back 30 points to get 100 points. But that's the nub of the problem.

We want to add those 30 points back to our limited advantage! Those 30 points are exactly what the Enhancement negating the 30 point Limitation is worth. The problem with it as a % Enhancement is that it's 30% of the Advantage without the Limitation. The reason we presumably want its value as an enhancement is to apply to an advantage where arriving naked is a built-in part of the advantage and we don't know what the price of that advantage would be when enhanced.

The only way we can get the value of it as an enhancement is to find what those 30 points are worth as a % enhancement to the 70 point Advantage with the Limitation and as I mentioned previously, its an inconvenient +43%. When you are Enhancing an advantage to not arrive naked, you need to add 43% of the value of arriving naked.

For example, if you want to go from Jumper (naked) at 70 points to Jumper (not naked); it's a 43% Enhancement. 43% of 70 is 30 points, so for 100 points (the original 70 points plus the 30 point enhancement), you can have Jumper (not naked).

100 points -30 points +30 points = 100 points is fine.

100%-30%+30% =100% is fine, too.

However: If I have 100 jellybeans and lose 30% of them, what percentage of the remaining jelly beans do I have to find to have 100 jelly beans again? The answer isn't 30%, but it's what you're insisting on.

[kdtipa]

Very long posts. My short reply is that I agree with Curmudgeon. With Jumper (not naked) being the default condition, there's no need at all for a "not naked" enhancement. And if you call Jumper (naked) the default at 70 points, a "not naked" enhancement would have to be the ~42% enhancement to bring it back to 100 points instead of 91 if it were a 30% enhancement.

[David Johnston2]

Originally Posted by kdtipa

Very long posts. My short reply is that I agree with Curmudgeon. With Jumper (not naked) being the default condition, there's no need at all for a "not naked" enhancement. And if you call Jumper (naked) the default at 70 points, a "not naked" enhancement would have to be the ~42% enhancement to bring it back to 100 points instead of 91 if it were a 30% enhancement.

Why is it important to get "back" to 100 points?

[kdtipa]

Originally Posted by David Johnston2

Why is it important to get "back" to 100 points?

100 points is the balanced price for jumper without having to arrive naked.

Originally Posted by evileeyore

And I disagree as Jumper (Naked, -30%) [70] is not the default condition.

Jumper [100] is the default RAW state.

If you alter this for your campaign, then you are setting a house rule, and that's the territory y'all are entering.

You're agreeing with me. I said Jumper (not naked) was the default.

[evileeyore]

Originally Posted by kdtipa

Very long posts. My short reply is that I agree with Curmudgeon. With Jumper (not naked) being the default condition, there's no need at all for a "not naked" enhancement. And if you call Jumper (naked) the default at 70 points, a "not naked" enhancement would have to be the ~42% enhancement to bring it back to 100 points instead of 91 if it were a 30% enhancement.

And I disagree as Jumper (Naked, -30%) [70] is not the default condition.

Jumper [100] is the default RAW state.

If you alter this for your campaign, then you are setting a house rule, and that's the territory y'all are entering.

[Curmudgeon]

Originally Posted by David Johnston2

Why is it important to get "back" to 100 points?

Originally Posted by Ketsuban

Except the post literally demonstrates how it's just an application of RAW.



Not Naked, +30% cancels out Naked, -30% when applied to the same Jumper advantage, because all enhancements and limitations are summed before being applied to the base cost of the advantage (p. B101). Not Naked, +30% is then limited by the Preparation Required limitation (Limited Enhancements box, p. B111).

Originally Posted by evileeyore

And I disagree as Jumper (Naked, -30%) [70] is not the default condition.

Jumper [100] is the default RAW state.

If you alter this for your campaign, then you are setting a house rule, and that's the territory y'all are entering.

OK, got it. For the limited purpose of getting back to the value of your original advantage from your original value adding the reverse sign of your limitation works quickly and simply. Mind you, I think it should just be called cancelling the Limitation rather than an effective Enhancement because it can lead to confusion, (as witnessed here, where it just did).

But when you need to convert a known Limitation into an unknown Enhancement, reversing the sign doesn't work. Admittedly, naked vs. not naked doesn't work very well as an example because there aren't any advantages where naked is the starting point. But there may well be cases where you want to Enhance an Advantage and that Enhancement doesn't exist in its own right in the rules. The proposed Enhancement produces an effect that is the exact opposite of a Limitation that does have a distinct existence in the rules and the Advantage in question doesn't have that Limitation to start with.

In that case you need a fair value for the Enhancement and the calculations I've been talking about will get you that fair value. I haven't been worrying about Limiting Enhancements (or Enhancing Limitations, for that matter). All I've been considering is how you would turn a Limitation into it's equivalent Enhancement and vice versa and that's why it was important to get back to 100 points.

But I don't think the problem I was attempting to address enters house rule territory because I'm not changing what the default condition is. I never intended to change what the actual default condition is. All I was saying was that if you started off knowing the point value of the Limited Advantage and that its value was derived by applying a -30% Limitation to default advantage, but not what the value of the original default advantage was, you couldn't arrive at it by adding 30% of the Limited Advantage's value to itself.

By the by, thanks, kdtipa. Those were my points. You posted while I was writing this up or I'd have let your answers speak for me.

[Varyon]

Originally Posted by Curmudgeon

No, that's not how it works as written. GURPS math isn't a different thing from regular math.

PK's calculation as written in the snippet isn't actually RAW. It's an argument following the principles of other examples that are RAW about calculating unknown values.

Originally Posted by GURPS Basic Set: Characters, page 101

You can apply any number of modifiers to a trait. Total them to find the net modifier, and then apply this modifier to the base cost of the trait. Round the resulting cost up to the next-highest whole number. For example, a +10% enhancement, a +40% enhancement, a -30% limitation, and a -45% limitation would give a net modifier of -25%.

Shockingly, it turns out the GURPS Assistant Line Editor actually has some idea of what he's talking about. Things get different if you use Multiplicative Modifiers, but that's an optional rule, and one that essentially no other rules are based on.

[Donny Brook]

Originally Posted by Varyon

Shockingly, it turns out the GURPS Assistant Line Editor actually has some idea of what he's talking about. Things get different if you use Multiplicative Modifiers, but that's an optional rule, and one that essentially no other rules are based on.

The quote you provide is not germane to his objection.

Mathematically, when you start from 70 points as PK's method has you do at one point, it takes more than +30% to get to 100.