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Old 05-21-2017, 01:31 AM   #1
Curmudgeon
 
Join Date: Sep 2011
Default Converting Enhancements to Limitations and Vice Versa

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.

Quote:
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%.
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