"ImYourHuckleberry;c-1625585" wrote:
@crzydroid @Woodroward anyway you can once again summarize your formulas? I'd like to build an excel model.
Sorry to come in late on this, but looks like you found it.
"ImYourHuckleberry;c-1625593" wrote:
Here is @crzydroid version
b Base Offense
z Offense Primary Percent
y flat offense and equipped gear
o Offense from Ingame Bonuses
m Damage Multiplier
c Critical Chance
x total critical damage bonuses from crit damage triangle and in-game abilities
c = (1)/(1.5+2z+(2y/b)-x)
I would clarify this by saying the variable z also includes all % based mod secondaries, not just primaries. So if I had a mod primary of 5.88%, and a secondary of 0.88%, z would be 0.0588+0.0088 = 0.0676.
Keep in mind that this formula is based off the new set bonus of 15%. It should allow for either 5e or 6e (or any other) values. For example, for a 5e crit damage primary and no in-game bonuses, x would be 0.36. For 6e, it would be 0.42. If you are looking at a situation where the Crit Damage Up buff is present, add 0.5 to x, etc.
"Woodroward;c-1625597" wrote:
"crzydroid;c-1625588" wrote:
If an offense set provides a 77% increase in damage 100% of the time compared to an crit damage set that provides 100% damage 77% of the time (because it crit 77% of the time), then they are equal. So the % increase in damage than an offense set provides compared to a crit damage set IS the crit chance breakpoint where a crit damage set becomes better than an offense set. If the result is 1.21, then at 121% crit you'd be better (assuming the damage continued to rise which it doesn't, hence anything over 1 means offense is just better) Anything over 1 means a crit damage set isn't capable of producing more damage than an offense set.
This is where you have a missing component. The offense set provides 77% more damage 100% of the time vs. NO SET BONUS. Likewise, the cd set provides 100% more damage 77% of the time vs. NO SET BONUS. You may claim you are not trying to compare offense to cd, but as soon as you start putting them in the same equation (one over the other and determing break points), then you ARE, by definition, COMPARING them. The offense set then no longer provides 77% increase 100% of the time. It provides a 77% increase 23% of the time. The other 77% of the time, it provides a DECREASE in damage (1.77/2=0.885; 0.885 <1).
This is what you are not taking into account. This is actually quite similar in form to a phenomenon known as Simpson's Paradox, for what it's worth.
So this is what I'm trying to show--when comparing the two sets, you are setting up the values wrong because you are leaving out a component of the puzzle. You say you are not comparing the two sets or averages or whatever--fine. But then you need to be clear about what it is you are comparing and what you mean by "critical damage breaking point" and if your question--whatever it may be--is at all interesting to others.
Because when most people say "critical damage breaking point," they mean that point for which the total damage provided by one set is equal to the total damage provided by the other set, holding all else equal. And that is very much so a question of averages, of both crit and non-crit damage.
No, no. My calculations are not comparing no set bonus. They are ONLY comparing set bonus. I factored out everything EXCEPT the set bonus for comparison.
That's the whole point of comparing only % damage increase for each set bonus. I factored out every single other piece of damage. How could I possibly be comparing the damage without a set bonus when I factored it out before I compared?
The fact that it provides an increase 77% of the time, and a decrease 23% of the time is exactly why it is EVEN. It is the breakpoint. That means even. If it was an increase 77% of the time and equal the rest, it would be an overall increase, but that's not what a breakpoint is. That's where things become even...
When you "factored it out before comparing," that is when you compared it. For example, how did you get that the set bonus provides a 77% increase? By comparing it to the non-set portion. If you were truly comparing just the sets to each other, in your earlier example then you would've never had a cd set increase of 1.156. That's the set bonus over (ie, COMPARING TO) non-set bonus (2.22/1.92). If you were comparing to only the offense set, you would have 2.22/1.92*1.083....but that 1.083 is itself a comparison to no set bonus.
The short of it is, you are "factoring out" components that ought not to be factored out. You are comparing incomplete proportions.
Anyway, it seems from your comments that you are inexperienced with using mathematical expressions, and have some revulsion against even attempting to do so. Instead, you claim that the tools mathematicians have used for centuries to solve problems are "improper math," without explaining why. You claim that algebra is needlessly complicated, vaguely hinting that an increase in variables increases likelihood of computational error, but without pointing out where any errors might have occurred. You've "corrected" a formula of mine, not based on mathematical adjustments, but rather on the basis of some conceptual-seeming arrangement of terms during some other step. You also say things like, "You've added in extra constants which can be left out like we discussed before,"--however, as we discussed before, if those terms truly were constants, it would only affect the scale and not the relationships. When I take a proportion, it should yield the same result. You also seem to perhaps show a lack of understanding of how the depiction of a function, such as f (x) stands in for an entire expression.
I'm trying to point out an omisssion in your set up, but you are refusing to actually have a set up. Instead you are preferring to solve components piecemeal and skip steps as it were in a process that seems to serve your intuition. But in this case, you are supposing you can lop off some chunk that is actually an important piece. I have tried to show you mathematically that you are inadvertantly splitting and combining fractions in an incorrect way by doing this. But you have no interest in looking at math.
So I think this conversation is pretty much finished. I have felt obliged to indulge in this thus far because you have been trying to make arguments that math--which people have been studying since ancient civilizations--somehow does not work. In so much as math is one of the most struggled-with disciplines, I didn't want to leave readers in a place where they didn't know what worked and what didn't.
I feel satisfied, however, that there is now enough in this thread that those who are able and willing to follow the discussion will be well-informed to come up with their own conclusions. Those who cannot follow the conversation will say, "Oh well, stick cd on high crit chance characters and offense otherwise and then just enjoy the game." And that's fine by me.
If there are other questions I will respond in the thread as necessary, but I am done trying to combat false accusations that mathematical problems should not be solved with mathematical tools.
