Tom's Hero Games Blog

Reading the bulletin boards at rpg.net makes me very sad. They talk about the Hero System as if the math in it is very hard. People, the most complicated math (dividing by fractions) I learned in 3rd grade. Some point to the "logarithmic" scale of the Strength Chart, for example, and say, "See! MATHS IS HARD!"

First of all, doubling Lifting for every +5 Strength is "hard?" And since the Strength Chart is there to eliminate that problem (it has the lifting capacity listed right there so you don't have to do the math yourself), this is a spurious argument, at best.

So that leaves the fractions part. So let's go over what it means when we say that Explosion is a +1/2.

First, before we continue (and to satisfy the pedant in me), we must define some terms.

1. The "Base Cost" of a Power is the cost of that Power before any Advantages or Limitations are applied. For example, the Base Cost of a 10d6 EB Explosion (+1/2) Activation 13- (-3/4) is 50 pts.
2. The "Active Cost" of a Power is the cost of that Power after Advantages are applied, but before Limitations are applied. For example, the Active Cost of the Power above would be 75 pts. (50 (The Base Cost) * 1 1/2 = 75)
3. The "Real Cost" is the final cost of the Power after Advantages and Limitations. The Real Cost of the Power above is 43 pts. This is also the amount of pts the character actually pays for the Power.

Also, I should explain the decimal equivalents of fractions:

• 1/4 = 0.25
• 1/2 = 0.5
• 3/4 = 0.75

With that out of the way (and we'll see why those definitions will become important), we will finally (finally!) get to what we mean by that +1/2 and -3/4.

The Explosion (+1/2) means that the Advantage Explosion is worth 1/2 the Base Cost of the Energy Blast. Thus, in the example given above, the Explosion part of the EB is worth 25 pts (50 * 0.5). This is why the Active Cost is 75:

50 + (50 * 0.5) = 75 pts.

Mathematically (through the Distributive Property of Multiplication and Addition), this is equivalent to saying:

Active Cost = 50 x (1 + 0.5) = 75 pts.

Now, that wasn't so bad, was it?

Now, to the fun part, and where my explanation above may fall apart around my ears. The value of a Limitation (such as the (-3/4) above) essentially asks the opposite question as the Advantage does above. In my example further up, I give "Activation 13- (-3/4)" as a Limitation to the EB Explosion Power, and 43 pts as the Real Cost.

Let's reverse this for a second, and say that the Base Cost of the Power is 43 and we have just placed a +3/4 Advantage on it. We would then have:

43 * (1+ 0.75) = ~75 pts.

So that means that what we're looking for when we're evaluating a Limitation is the number which we multiply 1.75 by to get 75 pts. Algebraically, we could write it like this:

Code:

1.75x = 75

Then, we have to divide each side of the equation by 1.75 and round off:

Code:

1.75x = 75
----   ----
1.75   1.75

x = 43

Okay, let's do some more elementary algebra to put this into a form we can use correctly. "r" below is the Real Cost, "l" is the sum of all fractional values of the Limitations on a Power, and "a" is its Active Cost. We must solve for r:

Code:

r(l + 1) = a

r(l + 1) =    a
--------   -------
(l + 1)    (l + 1)

r= a / (l + 1)

If you have any questions, corrections, tomatoes, please feel free to PM me or comment here.