|Something Like This.|
Useful Books For This Discussion
Questions That Should Be Answered
- How many elements exist in the system? The more elements that exist, the thinner we spread the points, the bigger a limitation discount we can apply to an elemental susceptibility meta-trait.
- Are elements compulsory? Can a being opt out of being strong and weak against anything? Does everyone need to have a strength and weakness? Elements might be especially mandatory in a game where players all play non-human races. Elements might be especially optional in a game with mundane races.
- Are Elements Balanced? Do all x elemental types have y weaknesses and z resistances? Are particular elements more susceptible to more types than others?
- Should elemental types multiplex? An important consideration in Pokemon means that some characters can have extraordinary resistances or weaknesses if they have multiple elemental typings.
- Is resistance tiered? In some games, elemental resistances can come in levels like doubled damage, halved damage, zero damage, and absorption.
Simple Rock Paper Scissors
- We have three elements
- Elements are compulsory
- Elements are balanced
- Resistance is not tiered
- Looking up the discount amount for Resistances/Total Elements and Weaknesses/Total Elements. Let's call the first value Resistance discount, and the second Weakness discount.
- Using the following formula:
(1-Resistance Discount) * 50 - (1-Weakness Discount) *50
In our symmetrical example we have
(.85*50) - (.75*50) = 42.5-37.5 = 5Altogether, it is a small advantage. We might consider something like this part of the racial template as well so it doesn't interfere with our disadvantage limits.
Wrench: Null Element
(.75*50) - (.70*50) = 37.5-35 = 2.5, round up to 3.So as a matter of fact, this doesn't make things much harder to calculate.
Wrench: Asymmetric Elements
(.70*50)-(0*50) = 35.Normal is now a 35 point meta-trait, that solely contains elemental resistance to "deity."
The other pretty symmetric elements have 2/5 weaknesses, and 2/5 resistances. 40% is a 25% discount for both... which interestingly means:
(.75*50)-(.75*50) = 37.5-37.5 = 0Our nominal elements have turned into 0 point meta-traits. Finally, our "deity" element that is strong against 3/5 (15% discount) and weak against 1/5 (30% discount) we get:
(.85*50)-(.70*50) = 42.5-35 = 7.5, rounded up to 8.Interestingly, with these asymmetric elements, our conventional rock scissors paper group is the cheapest, and normal turns into our strongest.
Wrench: MultiplexingThe cost of receiving 1/4 damage is exactly double the cost of receiving 1/2 damage, so this syncs up fine. The cost of receiving quadruple damage for mixed elements is also double. and something that is 1/2 * 2 = 1 is -50 + 50 = 0, so that cancels out as well. Mathematically speaking, we do not break down if we give a character two different elemental meta-traits. So for example, using our five element system from before, a character with all the benefits/drawbacks of being a fire element  and all the benefits/drawbacks of being normal  would cost 0+35 = 35 points. A hybrid deity/normal would be 43 points.
Wrench: Multi-TierThis does not work easily in GURPS without extra math. The math is actually a pretty simple extrapolation of the existing equation, but some important differences. First we need to add an absorption factor (Number of elements absorbed/Number of existent elements in the system) and multiply that by the cost of absorptive DR that can only be used for that element... let's try to get close to our 50 point benchmark like the other two factors, just for symmetry's sake. absorptive DR that can only heal HP is an 80% enhancement. Meaning we can have 5 absorption DR for 45 points. We can add this number times the accessibility discount for the amount of elements absorbed. It's not 100% absorption, but 5 DR that recovers is substantial.
The other category is 0 damage, which similarly we do with DR limited by elemental source. Because I like the number 50, again we are going to go with 10 DR.
So the adjusted algorithm for this level of complexity is:
- Find the number of total elements.
- For each element:
- Calculate the ratio of Elements Resisted, Elemental Weaknesses, Elements Absorbed, and Elements nullified to the total number of elements
- Look up the discounts for each ratio. Let's call them the Resistance Discount, Weakness Discount, Absorption Discount, and Nullification Discount
- Run through the following formula:
(1-Resistance Discount) * 50 + (1-Absorption Discount)*45 + (1-Nullification Discount)*50 - (1-Weakness Discount) *50This formula is probably annoying to type run over and over, but it is simple enough that it is easy to run with a spreadsheet program if you want to get into a complex 15 or so elemental system with multiple tiers of damage. For one worked example of the above formula, let's go back to our five element system: Fire, Plant, Water, Normal, Deity. Let's change Fire to instead nullify Fire instead of just being resistant to fire. That means it is resistant to 1/5, weak to 2/5, absorbs 0/5, and nullifies 1/5. The discount for 1/5 is 30%, the discount for 2/5 is 25%. The worked formula would look like:
0.70* 50 + 0*45 + 0.70*50 - .75*50 = 35+0+35-37.5 = 32.5, rounded up to 33.The math for multiplexing elements becomes a little complicated. So it is kinda easier to choose between having a multi-elemental typing system, or a multi-tier elemental typing system, but there is one slightly easy band-aid that allows both. It is easier to create a brand new element in the element list for a multi-typed element, and then calculate the advantage cost as if this is a brand new element. So, for example, if we went with our five element system from before, Fire, Plant, Water, Normal, Deity, and wanted to add in a Plant/Deity hybrid character, it would be easiest to just make "Plant/Deity" a sixth type, and count overlapping weaknesses or strengths twice. So since a plant/Deity would be strong against water for being a plant, and strong against water for being a deity, we would count that twice. This means we can get a wonky ratio of greater than 100%. As long as the ratio stays below 100%, this math coincidentally gets us the right number of points.
What if somehow we get above 100%? The multiplier is a little complicated, but basically, you do a bit of modulo division. Say we got a ratio of 120%; This divides by 100% once, with a remainder of 20%. If this were for resistance which is multiplied by 50 points, we would then need 1* 50 points + 50 * (1-Discount factor for 20%), so for every complete 100% we get, we add 100% of the base cost to the total for the modifier, and you will get a reasonable approximation for the complicated interaction of quadruple weaknesses or quadruple resistances. Absorptive DR and Nullfying DR will be additive though, however.
This is, indeed, a bit complicated, so I'd recommend not going this far if you don't like crunching complicated numbers. It might be trivial to automate this though with a bit of simple code, but at this point, it stops being simple enough for a spreadsheet.