Power Limitation Formula Question

[gamerchick]

Ok, I've looked at it for a long time, and I keep coming up with the same conclusion. I've discussed it with a physics major/math minor and one other math person (as I'm somewhat a math person myself), and I have a question. And before you tell me to search, I've searched the forums every way I can think of and have come up with nothing in these forums, so I'll just ask and you can flame me if I've missed something obvious.

So here's the explanation of my question.

Ok, in the Power Limitations section of the book, the formula for determining the cost of a power is:
Real Cost = Active Cost/(1+Total Bonus from all Limitations)

Now, we'll say (for ease of understanding) that the active cost of a power is 60 points. Now, we want to put a 1/4 limitation on it.

The formula in the book states that we should divide the Active Cost (60) by 1 + the limitation bonus. So the formula we get is:
60/(1 + 1/4) or 60/1.25

It's easier to demonstrate my point in fractions, so let's convert. 1.25 is equal to 125/100 which simplifies to 5/4. So our new equation is 60 / (5/4). Since dividing by a fraction is equivalent to multiplying by it's inverse, this is the same as saying 60 x (4/5).

So, 60 x 4/5 = 48 (which if you use 60/1.25 it comes out the same, check your calculators if you don't believe me).

Here's where the actual question comes into play. We all know that 1/4 of 60 is 15 (60/4 if you want to test it). So it would seem that by putting a 1/4 limitation bonus on a power, we'd get 1/4 of the points back for it, so that a 60 pt power with a 1/4 limitation would cost 45 points (or 60 - [60 x (1/4)]). Now, obviously the more a power costs, the more pronounced this difference will be (at 60, the difference is 3, at 100 it's 5, etc). But, instead we only get 12 points back for it instead of 15. So, for a 1/4 limitation on a power, we actually only get a 1/5 bonus. Of course, this is *exactly* what the chart in the book describes which is what leads me to my question.

Following me here or have I lost people? I tend to think anyone that plays Hero System is pretty decent at math to begin with, so my apologies if this is too basic for some of you or over anyone's head.

So finally, I'll get to my question:
Was this done on purpose so that limitations were more of a penalty than the equivalent bonuses are a bonus (as the chart in the book would indicate), or was this a mistake in a formula?

I can certainly understand how it could be on purpose to ensure that the limitations truly were limitations, and to thwart power gaming a bit, but the way the limitation bonuses are described, it just seems like a mistake. I apologize for even bringing this up, but it's been driving me nuts wanting to know the truth behind the formula, and I certainly don't want to bring it up in my gaming group until I know for sure one way or the other. Thank you for your time :o)

- Gamerchick

[Steve Long]

Since you addressed this to "people," I'm guessing you'd like to hear responses from gamers other than me, so I've moved your question.

As for me, my usual answer in these situations is "I generally don't answer rules design/philosophy questions."

[Killer Shrike]

I think you are being too literal minded. A -1/4 Limitation isnt the same thing as a 25% rebate.

It's just a balancing mechanic with it's own internal rules/logic.

[Doug Limmer]

You calculated the costs correctly.

If a -1/4 limitation meant you actually took 25% off the price of the power, then a -2 limitation (such as 1 charge) would mean you took 200% off the price of the power, thus not only giving you the power for free, but actually giving you bonus points back!

[Nevenall]

What Doug said.

The formula is designed to make sure limitations cannot reduce a power to a cost of 0 points (or less).

A simple and elegant solution to huge range of game balance issues. IMHO .

[gamerchick]

Actually, I thought people would refer to the game designers as well, which is who my question was directed to, since only the game designers themselves would know the actual answer as to the intention of the formula. And I know I calculated the formula correctly. That wasn't my question either. I simply wanted to make sure this wasn't a math mistake on the designer's since the text infers a different method to the formula presented. Especially since the 1/4 increments are exact for the power advantages. It seems to me there should be a method to balance out advantages and limitations on powers, but because of this formula, that would take at least 4 of one and 5 of the other to balance out the cost.

So the question stands-- is this a mistake, or was this done on purpose? And I was indeed asking the designers, not other gamers, since, in a nutshell, other gamers would simply have opinions on the matter where the designers would have the actual answer (which is what I'm looking for).

[Gary]

It seems pretty obvious to me that the system was designed so that equal advantages and limitations would cancel out (a +1/2 and a -1/2 would leave the power at exactly the same cost), and that diminishing returns are built into limitations so that all powers would cost a positive number of points.

[Killer Shrike]

Actually, I thought people would refer to the game designers as well, which is who my question was directed to, since only the game designers themselves would know the actual answer as to the intention of the formula. And I know I calculated the formula correctly. That wasn't my question either. I simply wanted to make sure this wasn't a math mistake on the designer's since the text infers a different method to the formula presented. Especially since the 1/4 increments are exact for the power advantages. It seems to me there should be a method to balance out advantages and limitations on powers, but because of this formula, that would take at least 4 of one and 5 of the other to balance out the cost.

So the question stands-- is this a mistake, or was this done on purpose? And I was indeed asking the designers, not other gamers, since, in a nutshell, other gamers would simply have opinions on the matter where the designers would have the actual answer (which is what I'm looking for).

Well for starters the current designers of the game are not the original designers. There's an entire section in the back of the current edition that gives a basic 411 on the history of the game.

For seconders the current designers have a policy of not answering direct game design questions such as you are asking.

For thirders your basic operating assumption is false and your various conclusions stemming from that assumption are subsequently also false.

Limitations function just as they are described as functioning, and that function is intentional.

If you have a specific passage in the book which seems confusing to you in this regard, then please post a page reference and explain what passage is causing your confusion and why.

[Gary]

It seems to me there should be a method to balance out advantages and limitations on powers, but because of this formula, that would take at least 4 of one and 5 of the other to balance out the cost.

Nope, a single 1/4 advantage will exactly cancel out a 1/4 limitation. I don't know why you think it takes 4 of one and 5 of the other to balance out the cost.

[gamerchick]

All I'm asking for is a response of either "It was intentional," or "It was a mistake." I don't see how that's a "philosophical" question.

[Hugh Neilson]

All I'm asking for is a response of either "It was intentional," or "It was a mistake." I don't see how that's a "philosophical" question.

Steve is very careful not to get involved in any design philosophy question (I'm sure he could spend his life on those discussions and debates), and probably errs heavily on the side of caution.

I'd say that the mechanics are intentional in that the advantage/limitations formuli are unchanged since the first edition of Champions in the early 1980's.

[Mark Taylor]

So finally, I'll get to my question:
Was this done on purpose so that limitations were more of a penalty than the equivalent bonuses are a bonus (as the chart in the book would indicate), or was this a mistake in a formula?

Whether obvious or not, limitations pretty much have to work the way they do to be viable. If they worked the way you suggest they should, -1 or more of limitations would reduce a power, no matter how expensive, to a cost of 1 (the minimum cost for any power). Now even if limitations were worth less and came in much more finely grained values, this would be a nonsense simply because a 100 active point power with -1 of disadvantages, however severe these limitations might be, is obviously going to be worth more than a 50 active point power with the same limitations.

As Gary pointed out, the system is balanced so that advantages and limitations of equal value cancel each other out, and so that increasing values of limitations give diminishing returns. That's quite necessary for the system to be balanced at all, and in fact it represents quite well the real value of powers with multiple limitations. You can keep stacking up limitations on a power and its cost continues to represent its value pretty well. If -1/4 was 25% off, -1/2 was 50% off, and so forth, powers would rapidly become far cheaper than their worth even before you hit the problem of reaching a cost of 1 as mentioned above.

Also, it might be worth pointing out that this basic element of the system is over 23 years old now. If it was wrong or somehow "broken" a lot more people would have noticed by now.

[Derek Hiemforth]

All I'm asking for is a response of either "It was intentional," or "It was a mistake." I don't see how that's a "philosophical" question.

It was intentional. For the reason Doug stated above. If it was some kind of percentage rebate as the math would strictly imply if you expanded the 1/4=25% discount concept to other values, then you'd be getting powers for free at a -1 Limitation, and actually getting points back for larger Limitations.

Limitations have to have diminishing returns in order for powers to always have positive costs. It's intentional.

Or look at it this way... it's been this way since the beginning (24 years). Five editions have been done overall. If it wasn't intentional, it would have been changed by now. It hasn't.

[Ben Seeman]

The answer you're looking for implies that your assumption is correct, when it is not.

It's like asking a guy on trial for murder "Are you glad you killed your brother?" He tries to say he didn't kill his brother yet the lawyer says "Just answer the question."

But the entire formula for calculating Real and Active Cost was made that way intentionally. The Limitations may "reduce more number" than advantages gain, but that's just because you calculate Active Points before Real Points. If you calculate from the Limitations (Limited Cost? bleh) first and then Advantages and you'd still get the same Real Cost and it would appear that Advantages provide more of an increase in cost than Limitations lower it.

[gamerchick]

Actually, the answer I was looking for was exactly what Mark & Derek gave me. Thank you both.

I wasn't implying the formula should be any one thing or another, just noting an oddity in the reference. It's unusual to see numbers listed in the way they are in the book without referring to percentages, which is where my question came from.

As a side note, the book I have myself is Champions Deluxe. I know how long the system has been around (and that the formula hasn't changed at all). I'd like to point out, however, that an encyclopedia that has been around about 80 years now still has the word "commonest" in it (which I'm sure you all know is incorrect any way you put it).

Good evening to you all, and best wishes.