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Power Cost Multiplier, Math Error?


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I couldn’t find a relevant post, but I apologize if this has already been discussed in another thread.

 

According to my understanding of he math for calculating the Real Cost of a power, the formula is as follow: Active Cost / (1 + total value of limitations). 
Example:

Resistant Energy Reduction, Base cost 30

Always On, limitation, -1/2 cost

 

Should the math not work out as (30/(1 - 0.5))=15?

Hero Designer has it coming out as (30/(1 - 0.5))=20 and I find myself very confused.

 

Other examples for the same power/base cost:

+ 0.5 advantage = 37

- 0.5 limitation = 24

- 1.0 limitation = 15

 

The math just isn’t making sense to me for whatever formula HD is using.

 

Am I just missing something super obvious here?

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You'll want to review the rules regarding how Advantages and Limitations work...as well as general math.  30/(1-.5) = 30/.5 = 60...and doesn't really have anything to do with HERO System.

A 30 Active Point Power with -1/2 in total Limitations would calculate as:  30 / (1+1/2) = 30 / (3/2) = 60/3 = 20 points

A 30 Active Point Power with +1/2 in Advantages would calculate as: 30 * (1+1/2) = 30 * (3/2) = 90/2 = 45 points

Apply a -1/2 Limitation to the Advantaged Power above and the calculation follows the same rules: 45 /(1+1/2) = 30 points

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Per the description of the cost calculator, that’s exactly what the math says. I just figured factoring a negative as a multiplier rather than a divisor would make more sense considering the descriptive term is “limitation” and is depicted as being a negative. 

The examples given for additive multipliers shows what I’d expect, where a +1/4 multiplier on a 40 point power becomes 50. That math makes sense to me. How, then, does the inverse calculate differently? Do negative multipliers not follow the same rules as positive?

Can you explain how a multiplier of -0.5 equates to an actual change of -33% while a +0.25 still equates to +25%? This is where I’m lost. 

Sourcing from “Calculating Costs” on page 94 of The Champions PDF.

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Again, please review the rules.  They are not multipliers, they're Advantages and Limitations.  As for a 1/2 Limitation resulting in a net decrease in cost of 33%, that's just math:

The Active Cost of a Power equals its Base Cost * (1+Advantages total)

The Real Cost of a Power equals its Active Cost / (1+Limitations total)

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I'm sorry if the rules aren't making sense to you -- this isn't the place for rules discussion, this is a forum for discussion of HD.  You expressed a concern that HD was not following the rules (math error), and I explained that it was and gave you the relevant rules.

If you would like to discuss those rules, I would suggest posting in the HERO System Discussion forum.

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Maybe it's the typical notation that's throwing you off, BamBam - here's how I think about it:

Advantages are listed as +x : the positive sign reminds you it is a real-cost increasing effect

Limitations are listed as -x : the negative sing reminds you it is a real-cost decreasing effect.

 

However, in their respective formulas, they're both treated as using their absolute value. (Look at many examples in the books to see this in action.)

 

Yes, the formula is stated as Active Cost / (1 + total value of limitations).  And all the individual limitations are listed with negative values like -¼, -½, -1, etc.

 

However when you put them in that "total value of the limitations" use their absolute value: ¼, ½, 1,  etc.   The literal wording of the text in the rules doesn't say absolute value; but it does say "total the Limitations as positive values, even though they’re listed as 'negative' numbers" in the paragraph above the formula.  (6E V1 page 365) 

 

So a power with two -¼ limitations winds up in the formula as "Active Cost / (1 + ½)",  Thus a 60 active point power comes out to a 40 real cost.  Or with a -1 limitation, a 60 active point power comes out to a 30 real cost.   (It has to work this way, or a power with limitations literally totaled as negative values that totaled to less than -1, such as an OAF (-1) with 4 charges (-1), and thus a literal total of -2, would actually cause a power to have a negative real-cost total.)

 

The use of absolute value and structure of the formulae effectively makes limitations have the same proportional effect as advantages with the same value: for example, a +1 advantage doubles the active cost of a power, 20 active points become 40 real; while a -1 limitation halves the cost of a power, 40 active points becomes 20 real.   A  +½ advantage adds "half-again" to the cost of a power, 20 active points becomes 30 real; while a  -½ limitation cuts it by a third, 30 active points become 20 real.  Proportionally, it works. 

 

 

 

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