Multiplicative Modifiers

different concept:
*apply enhancements, record final value as new trait
*apply limitations to that new trait
Example:
*Warp costs 100
*+100% enhancements final cost 200
*-50% limitation applied to 200 results in final cost 100
Under original system +100% and -50% is net +50% with final cost 150. So under MM it ends up cheaper. MM basically applies the value of limitations to enhancements in addition to the value of the base ability.
Limited Enhancements work in a similar way, except they ONLY apply the limitation to the enhancement, and not the base ability.
==TRUE multiplication==
===Sums vs Modifiers===
The original system is more like "Multiplicative Modifier Sums" because you're only multiplying the enhancement sum by the limitation sum.
What this does not do however is allow enhancements to multiply the cost of other enhancements.
For example:
*Warp costs 100
*+50% raises to 150 value
*+100% raises to 300 value
ie 100*1.5*2 = 100*3
Using the additive system (enhancements-only in original, or first step of MM prior to limitation application) it would be 100*1.5 + 100*2
:100*(1+.5+1)
:100*2.5
:250
Using TRULY multiplicative modifiers would lead to more expensive enhancement combinations.
It might also lead to exponential costs of leveled traits, like for example Long Range (50/level) being effectively +125% for Long Range 2, instead of +100%
*it also is very problematic for non-linear stagger-tiered traits like Increased Duration or Increased Range
===TRUE division===
One benefit to this system however is that there is no need to apply cutoffs to the sum of limitations to prevent -100% from creating a free ability. Just as enhancements would have increasing costs, limitations would have diminishing returns, which is consistent to what we see in overlapping accessibilites.
Example (assume ability with no enhancements)
*old system -40% and -40% sums -80%
*new system: x0.6 x0.6 = x0.36 reduction to 36% is equal to -73%: diminished return
So instead of reducing a 100 point ability to 20 points, the first -40% reduces it to 60, and then -40% applied to 60 reduces it to 36.
This is similar to how Either/Or Limitations works except rather than multiplying the value of limitations you are multiplying the value of the reduced abilities.
It should be possible to use both systems. Either/Or for two -40% limitations is 0.4x0.4 = 0.16, a -16% limitation which reduces a 100 point ability to 84.
==exceptions==
The only time you would need to deviate from cases like this would be where you have modifiers of -100% or more.
For example: the Succubus in Horror who has "Takes Extra Time 10 -100%".
Solving leveled traits is easy: you just apply each level individually.
Example with 100 point ability:
*TET 1 = 90 points (-10)
*TET 2 = 81 points (-9)
*TET 3 = 73 points (-8) you should technically get -8.1 but it rounds "up" (toward zero) unless GM is okay with CP to 1 decimal in which case the ability costs 72.9
Where there is a problem is when you can't split it into levels. For example: Provides no DR -100% modifier for Damage Resistance used in Sorcery: Protection and Warning Spells designed for pairing with Reflection (+100%) to create a 0-point feature/modifier.
In that case, you should probably just apply the -80% cutoff, but in terms of specific limitations, not the net sum of modifiers.
Another option would be to break that up into "provides less DR". Like for example "provides half DR -50%". Taking two of those would be -75% for 1/4 DR.
-100% is never necessary because you can always just design a small enough % that it leads to a fraction that you would round down anyway.
For example: provides half DR would reduce DR 2 to DR 1, but it would reduce DR 1 to DR 0 (you round down fractional DR under standard rules when armor divisors are applied to them).
For GMs allowing more granuality (example 0.1 increments of DR) you would retain 0.5 DR, and could take a -90% limitation instead of -50% to reduce it to 0.1. Going beyond 90 however would require rounding down a sub-0.1 amount to 0.
Basically whatever % it would take to reduce the final DR below the smallest threshold (where round-down-to-zero occurs) is probably the most you should be allowed to take on it.
Reflection +100% is a x2 to cost. Since ANY limit applied to DR 1 would normally reduce it to zero, you should probably only get the smallest granuality that would save you a point (in this case -20% to save 1 point on a 5 point advantage). -20% applied to 10 points (cost after reflection doubles) is 8. Being able to do 1 damage to anthing that hits you is worth something, look at Spines! But maybe that's too costly. Perhaps it should just be 2 points? Keep in mind that spines only work against melee attacks though, this bounces EVERYTHING, so 8 could be justified...
However if you allowed fractions: you could apply for the -80% if you functionally could have 0.8 DR for only taking -20%.
A GM could still apply a -80% cap, in which case DR 10 could not be reduced to less than DR 2, as an example.
Using a x0.2 multiplier to cost helps with multiplying with other limitations. This could eventually lead to prices APPROACHING zero (example 0.2 x 0.2 = 0.04 or 4% of price).
There is no need for a cutoff of "advantages can't cost less than 1/5 their base price". This isn't strict anyway, three instances relax it: Internal Advantages and Alternative Abilities and Character Point-Powered Abilities allowing three more instances of x0.2 meaning you could reduce things to 1/25 or 1/125 or even 1/625 base cost)
Instead of a "minimum 20%" rounding up to the nearest character point (200 hours of study) or 0.1 CP (20 hours study) or 0.01 CP (2 hours study) or 0.001 CP (12 minutes study) could still represent very hard to use abilities, and allow vast combinations of limitations.
==using math to understand how far the minimums are==
That said, it would be very difficult to reach those lower tiers due to the diminishing discounts limits would apply, since they are applied to the reduced base value created by preceding limitations.
Exponential patterns could calculate how this progresses for same-value limitation stacking. Maybe that's logarithms?
For example if applying y instances of -10% limitations to a 100 point advantage, to determine final value x.
:x=100*(1-0.1)^y
:x=100*(0.9)^y
If we sub a value for X (say perhaps 1, representing a net -99% limitation) so as to calculate how many levels of TET you would need to get there, as an example...
:1 = 100*(0.9)^y
:1/100 = (0.9)^y
:???
need some math help here about how to simplify expressions when the exponent is a variable?
TET could be a bad example though. Namely because it is not a linear limitation. It doubles prep time each time (example: Healing takes 2 seconds, Healing takes 4 seconds...) but +10% for +1 second doesn't become +30% for +3 seconds. So it ALREADY has diminishing returns built into it.
For that reason, it could be okay to allow them to apply in batches, like for example batches of up to 8 for -80%, and then if you wanted the equivalent of TET 16 you would take -80% twice resulting in an ability costing 1/5 of 20% : 4%
Batches of 8 are inelegant though. There's no reason to allow batches up to the classic minimum. You might for example allow a maximum batch of TET 5, which conveniently works out to two batches for the Succubus' Leech, combined they would work like a -75% limitation.
TET 5 changes non-attack abilities (ready or concentrate) from 1>2 then 2>4 then 4>8 then 8>15 (see egs) then 15>30
From the half-minute baseline it's easier to do further math:
:TET 1 = 1 minute
:TET 2 = 2 minutes
:TET 3 = 4 minutes
:TET 4 = 8 minutes
:TET 5 = 15 minutes
This elegance is why batcho-of-five is pretty convenient.
Less so for attack abilities. Attack abilities are weird with TET and seem to come up on top because the first instates a pre-ready and then levels double THAT rather than the total ready+attack 2-second time TET 1 instates.
It's silly and a good house rule is just to double the attack maneuvers. This is similar to what you're effectively doing if you have Decreased Time Rate (and maybe with Springing Attack, though 'nothing but crouch' precludes a step and is more like a Do Nothing) except 2 attacks over 2 seconds gives 2 steps (just as 2 readies would) while DTR would only get 1 step over those 2 seconds.
AOC gives +1 if all you do is AOC the entire time. If partial bonuses mattered in some way, maybe doing AOC once and normal concentrates the other 9 seconds for something requiring 10 seconds prep could give a +0.1 bonus.
It's not clear why that has Move 0 since AOA does not. Cole took a similar approach with All-Out Aim (Move 0) though.
Unclear if an all-out ready should get 1/2 move like AOAttack or 0 move like AOC/AOAim
==discussion==
===2008===
http://forums.sjgames.com/showthread.php?t=37833
http://forums.sjgames.com/showthread.php?p=561177#post561177
Category:Rules