An Alternative Method for Multiplying Modifiers [Powers]

[AlexanderHowl]

I have become dissatisfied with the additive and multiplicative methods of making abilities, so I offer a third choice. The formula is as follows:

CP = ((Base value × ((1 plus (Total Enhancement Value/100))/(1 minus (Total Limitation Value/100)))), rounded up).

For example, imagine that you have Crushing Attack 10d with Cosmic, Ignore DR, +300%, and Melee Attack, 1-2, -20%. The additive system would have you paying 190 CP while the multiplicative system would have you paying 160 CP. The new system would have you paying (50 × (4/1.2)) or 167 CP. While it is more complicated, I believe that it ends up being fairer, especially with abilities that have lots of modifiers.

[Anthony]

Congratulations on reinventing the Hero system.

[AlexanderHowl]

A little less complex because there are no adders and you round once rather than twice, but I see the similarities (I have never actually bothered to play Heroes, as there was always something more interesting to play).

[ericthered]

As a note, the "minus" in the equation cancels out with the negative value on limitations?

This is a notable nerf on large limitations. -100% is now effectively -50%. I think its a good scheme, but I also think that far enough away from the way points were balanced in the first place to cause issues.

[AlexanderHowl]

Yes, negatives cancel. This is so that the limitations can act as an effective divisor, which means that -100% of total limitation value would only effectively halve the overall cost of an ability, which is an issue for highly limited abilities. I am thinking of putting in a rule that if Enhancements are less than or equal to Limitations, use the normal additive modifier rules instead. The end result would be the normal additive rules for abilities where Enhancements <= Limitations, but the new rule for abilities where Enhancement > Limitations.

[Anaraxes]

Originally Posted by ericthered

t I also think that far enough away from the way points were balanced in the first place to cause issues.

Yes. If you change the math, you also have to create a replacement list for all the published traits and modifiers. Using the same numbers in new equations won't work (even to the extent that the existing ones do).

It's easy to have one's sense of mathematical elegance and what constitutes and equal-and-opposite modifier to cancel out its complement and invent prettier math. But the real work is in balancing the numbers you put in. GIGO, no matter how pretty the algorithm is.

[AlexanderHowl]

Its easy enough to create an Excel sheet since you only have a rule, formula, and three variables. You would have to do the same thing if you used the multiplicative modifier rule, except that the new rule is only used when Enhancements > Limitations. If Enhancements <= Limitations, you use the normal additive rules.

For example, Banestorm gives us the Petrifying Gaze of the Medusa. It is a heavily modified Affliction, so the base cost is 10 CP, the enhancements are +670% (× 7.7), and the limitations are -20% (/1.2). The previous cost was 75 CP, the new cost would be 65 CP, so you end up saving 10 CP, reflecting the loss of utility caused by the limitation.

Of course, limitations produce diminishing returns, and the end result is that the new rule never reduces that cost of an ability below the base cost of the underlying advantage (the normal additive rules kick in when that would occur). An ability with +500% in enhancements and -400% in limitations would cost 20% more than the base cost of the underlying advantage. Of course, it does not offer the massive point breaks of the multiplicative modifier rule, but it does mean that every limitation matters.

[dataweaver]

My own preference is to use a 50-step exponential table, with ±5% of modifiers translating to one step up or down the list:

1     1.05  1.1   1.15  1.2
1.25  1.3   1.4   1.45  1.5
1.6   1.65  1.7   1.8   1.9
2     2.1   2.2   2.3   2.4
2.5   2.6   2.7   2.8   3
3.1   3.3   3.5   3.6   3.8
4     4.2   4.4   4.6   4.8
5     5.2   5.5   5.7   6
6.3   6.7   7      7.3   7.7
8     8.3   8.7   9      9.5
10    10.5  11    11.5  12
12.5  13    14    14.5  15
16    16.5  17    18    19
20    21    22    23    24
25    26    27    28    30
31    33    35    36    38
40    42    44    46    48
50    52    55    57    60
63    67    70    73    77
80    83    87    90    95
100   105   110   115   120
125   130   140   145   150
160   165   170   180   190
200   210   220   230   240
250   260   270   280   300
310   330   350   360   380
400   420   440   460   480
500   520   550   570   600
630   670   700   730   770
800   830   870   900   950
1000

You can extrapolate both up and down in this list. To use this chart, find the point cost of your Advantage and then move up or down the appropriate number of steps: +50% becomes ten steps forward, and -20% becomes four steps backward.

There's no -80% cap on limitations, though I'm inclined to impose a minimum cost of 1 point no matter what. That said, it takes the equivalent of -175% worth of limitations to reduce an initial cost of 100 points to 20 points, and another -75% worth of limitations to get it down to 10 points.

Finally, if you have a cost that falls between two on the list, treat it as if it was the higher of the two.

The benefits of this system are: (1) ability builds can be black boxes: it doesn't matter how you arrived at an ability's cost, applying modifiers to it works the same regardless. (2) as mentioned above, there's no need to impose a limitation cap.

The drawbacks of this system are: (1) fractional point accounting, which shouldn't be too much of a headache (I've kept it at 20ths of a point); removing fractional accounting leaves voids at the lower end that require multiple steps to overcome, though that's arguably no worse than the current system. (2) price inflation: what would have been a -80% price break is now only slightly better than half off, and what would have been +100% is now closer to +150%. This can be mitigated (but not eliminated) with a more nuanced translation from old-style percentage modifiers to this system's steps, which would require a separate table. At the lower end, -5% would still be “one step down”; but +50% would become “nine steps up” instead of “ten steps up”, and -50% would become “fifteen steps down” instead of “ten steps down”.

As well, because of the rounding on the table, what would have been, say, a 75-point Ability is now a 77-point Ability. At the upper end of the chart, this can be as much as a four-point increase.