Looking up Aranaville's defense guide - Werner's curve might be the correct one.
Your equation which was basically Damage/defense, was really Damage/chance to miss
But a 16% defense doesn't result in a 16% chance to miss, at least not according to that guide.
"Base to hit formula is:
NetToHit=Accuracy*(base to hit-defense) "
Which should make the Base to Miss the reciprocal of above and not the defense number.
Or 1/accuracy*(base to hit-defense)
Werner has already admitted my method is correct. Compare what each mitigates, pick the one that mitigates the most.
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The problem is that his method requires additional information - information not included in this thread. Hence why he has to test using his own character. He has to add more numbers in any attempt to solve the situation. He cannot actually answer this without using more info (ie: his own characters information).|
Well, let's say you're at 50% resistance, with 100 DPS being put out by the enemy: With no defense you are taking 25 DPS. With 16% defense you are taking 17 DPS. You've mitigated 8 DPS instead of 16 DPS, so only 8% of the enemy damage output. So if you have 50% resistance, if 8% of enemy damage output > the regen amount, you should take the defense. |
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cares about the percentage increase in the number of bosses you can survive 0% defense = 1.00 bosses = NA 5% defense = 1.11 bosses = +11.1% more bosses 10% defense = 1.25 bosses = +12.5% more bosses 15% defense = 1.43 bosses = +14.9% more bosses 20% defense = 1.67 bosses = +16.7% more bosses 25% defense = 2.00 bosses = +20.0% more bosses 30% defense = 2.50 bosses = +25.0% more bosses 35% defense = 3.33 bosses = +33.3% more bosses 40% defense = 5.00 bosses = +50.0% more bosses 45% defense = 10.00 bosses = +100.0% more bosses |
thinking on it - it is going to be a curve not a straight line.
Look at the soft cap
If we say only 50% of the original damage gets through due to minion accuracy
And then we claim that 45% of THAT damage gets mitigated by defense-
The the softcap wouldn't mitigate 95% of all damage. it would only mitigate
(using 1000 to save me algebra)
1000 damage /2 = 500 damage * 45% = 225 damage
225 out of 1000 is only 77.5% of the damage.
Anyone who had played at the softcap knows you aren't getting hit 22% of the time.
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Apparently he doesn't read the fundamental point of the thread so I don't know how else to highlight the fact that he hasn't compared anything to regen yet.|
Originally Posted by all_hell
The larger the font, the more correct you must be. One thing that could make you more right would be if you used all caps.
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If you have a way to get it through to him that I don't care that survivability increases with defence and that he has to make a choice between regen & defence, let me know.
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No.|
Originally Posted by Hai Jinx
thinking on it - it is going to be a curve not a straight line.
Look at the soft cap If we say only 50% of the original damage gets through due to minion accuracy And then we claim that 45% of THAT damage gets mitigated by defense- The the softcap wouldn't mitigate 95% of all damage. it would only mitigate (using 1000 to save me algebra) 1000 damage /2 = 500 damage * 45% = 225 damage 225 out of 1000 is only 77.5% of the damage. Anyone who had played at the softcap knows you aren't getting hit 22% of the time. |
You mitigate 45% of the ORIGINAL damage.
Simply put: 100 incoming, 45% defence.
50dps misses because of 50% miss chance.
45dps is mitigated because of 45% defence.
Damage received: 5dps.
Now you see that 45% defence mitigates 45% of the initial damage. It is a linear relationship for mitigation.
Don't be tricked by his graph. He is not graphing mitigation, he is graphing survivability.
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Oh, I've stopped trying to convince you of anything. That wasn't the point at all. I've realized that you can read the post and say with a straight face, "No, surviving a lieutenant is just as good as surviving two bosses, two lieutenants and one minion." I've realize that you can look at that graph with its obvious curve and say with a straight face, "No, a straight line is the best model of what defense is doing for us here." I cannot pretend to understand what's going on in your brain that lets you do so, but it no longer surprises me.|
Originally Posted by BunnyAnomaly
You can't tell the OP which is better. Instead you ran a useless test that examined only your own survivability vs defence. Not only did your test in any way do anything to do with the numbers provided, they used your own. All they did was test your defence.
You have done absolutely no calculation to determine if the regen was better than the defence. |
No, it's for other people. People who are interested in survivability in terms of what you can actually survive in the game. The post lets those people know, if they were doubtful, that the standard model of survivability DOES correspond very closely to what you observe in the game.
This standard model then allows us to answer many questions, such as the OPs question about whether defense or regen is better. Better here is expressed in terms of what the new build options will allow you to survive. The build that can survive the more dangerous group is the better build. These survivability calculations were done four posts above the one you focused on.
But that post won't show you anything either, as it is trivial to demonstrate that it's the wrong answer in cases where the incoming damage is far lower than would actually challenge the build, cases where it's pointless to worry about such questions. It's trivial to point out that my calculation has many more variables than yours, and that I merely guessed at some of those variables since I haven't seen all hell's actual build options. I'm sure you think that somehow proves it's wrong. That's fine. I just expect everyone else to see through your confusion by this point, and thought they might want a little more information.
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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Of course I'm graphing survivability. Nice to finally see you admit that. So, you concede that defense has a non-linear effect on survivability?
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Originally Posted by BunnyAnomaly
Don't be tricked by his graph. He is not graphing mitigation, he is graphing survivability.
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"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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Until you graph 6.7 hp/s regen on a survivability curve you have answered nothing.|
Originally Posted by Werner
Oh, I've stopped trying to convince you of anything. That wasn't the point at all. I've realized that you can read the post and say with a straight face, "No, surviving a lieutenant is just as good as surviving two bosses, two lieutenants and one minion." I've realize that you can look at that graph with its obvious curve and say with a straight face, "No, a straight line is the best model of what defense is doing for us here." I cannot pretend to understand what's going on in your brain that lets you do so, but it no longer surprises me.
No, it's for other people. People who are interested in survivability in terms of what you can actually survive in the game. The post lets those people know, if they were doubtful, that the standard model of survivability DOES correspond very closely to what you observe in the game. This standard model then allows us to answer many questions, such as the OPs question about whether defense or regen is better. Better here is expressed in terms of what the new build options will allow you to survive. The build that can survive the more dangerous group is the better build. These survivability calculations were done four posts above the one you focused on. But that post won't show you anything either, as it is trivial to demonstrate that it's the wrong answer in cases where the incoming damage is far lower than would actually challenge the build, cases where it's pointless to worry about such questions. It's trivial to point out that my calculation has many more variables than yours, and that I merely guessed at some of those variables since I haven't seen all hell's actual build options. I'm sure you think that somehow proves it's wrong. That's fine. I just expect everyone else to see through your confusion by this point, and thought they might want a little more information. |
The problem is that a survivability curve is pointless in deciding. You'd need to draw another survivability curve for the regen and then compare the two. That is going to be an absolute nightmare.
You should be comparing what they mitigate and choose the one that is highest. Failure to do anything else is a failure of maths.
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That's not a concession, that just shows you don't get it. My entire point is that you compare mitigation, not survivability,and that survivability is an extremely poor metric because now drawing "6.7 hp/s" on a survivability curve is, as above, a nightmare.
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Originally Posted by Werner
Of course I'm graphing survivability. Nice to finally see you admit that. So, you concede that defense has a non-linear effect on survivability?
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To say that you have increasing survivability when defence goes up says nothing about whether it's better than defence. I have total agreement that this is the case. My point is that it is an exceptionally difficult metric to use.
Why is that so?
Because to decide, which is the point of this thread, between two choices, you're now going to have to graph regeneration on the same graph. Now other than it being rife with all kinds of experimental errors it also takes an eternity. Oh, and then you're STILL not able to solve the question without adding in your own numbers.
Or you could just determine which mitigates more and do that.
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Right, there's nothing wrong with the math Bunny highlighted. To quote the conclusion, "So if you have 50% resistance, if 8% of enemy damage output > the regen amount, you should take the defense."|
Originally Posted by BunnyAnomaly
Werner has already admitted my method is correct. Compare what each mitigates, pick the one that mitigates the most.
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Unfortunately, that isn't an answer - it's a decision procedure.
To apply that procedure, you need to plug in a value for the variable - enemy damage output. This is unknown. Yes, we could create a graph of enemy damage output and compare our horizontal line of regeneration vs. our upward sloping line of mitigation from defense. Yes, line. Mitigation of a given increment of defense vs. damage output is indeed linear. I'm not arguing that. You do have a point where the two lines cross. Above this point, choose the defense. Below this point, choose the regeneration. But again, all we've done is graphed the decision procedure. We STILL need to choose a number for enemy damage output. Only then can we actually know which is better.
You could choose this number randomly, which is where my magic 8 ball comment comes in. You could choose it based on past experience with the character, but this will be iffy at best unless you run a lot of herostats and the new builds being considered are very close to the current one.
But we don't need to do any of that, because we have a very good way of choosing it - the immortality line. Do an immortality line calculation, plug in that value for enemy damage output, and you ALMOST get the decision you'd make using a survivability analysis. It is almost equivalent at that point.
The difference is that the survivability analysis goes just a little further. It chooses two different damage levels based on the immortality lines of your two options, not a single one. Each build is capable of facing a different amount of incoming damage. Each build may be mitigating from a different base of damage by the time it is facing any challenge to survivability.
But in any case, that's the long way around. The immortality line calculation IS the survivability calculation. Once you know the damage figures to apply to each build option, you're already done. Those damage figures in and of themselves tell you your answer.
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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And still no answer.
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Strange, many of us use this exceptionally difficult metric all the time. Maybe it's easy for me because I can't do maths. No need to draw graphs. Just do a couple quick survivability calculations regarding the two options, one with the regen, one with the defense. Yes, doing this well this requires some numbers that Mids' will give you. Making the right decision based purely on mitigation requires you make a very good guess for what damage output the build will be facing. Either way you need additional variables, but mine are easily supplied. Yours is not, or at least not accurately. It is of course easy to just make one up, "I'll be facing 100 DPS!" Good luck guessing accurately on that one, though.
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Originally Posted by BunnyAnomaly
To say that you have increasing survivability when defence goes up says nothing about whether it's better than defence. I have total agreement that this is the case. My point is that it is an exceptionally difficult metric to use.
Why is that so? Because to decide, which is the point of this thread, between two choices, you're now going to have to graph regeneration on the same graph. Now other than it being rife with all kinds of experimental errors it also takes an eternity. Oh, and then you're STILL not able to solve the question without adding in your own numbers. Or you could just determine which mitigates more and do that. |
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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If you ever could draw your graphs, good luck with that, you'll still find that it is dependant on the damage you face. But because you can't do maths (as shown this whole thread), you still haven't found this conclusion.|
Originally Posted by Werner
Strange, many of us use this exceptionally difficult metric all the time. Maybe it's easy for me because I can't do maths. No need to draw graphs. Just do a couple quick survivability calculations regarding the two options, one with the regen, one with the defense. Yes, doing this well this requires some numbers that Mids' will give you. Making the right decision based purely on mitigation requires you make a very good guess for what damage output the build will be facing. Either way you need additional variables, but mine are easily supplied. Yours is not, or at least not accurately. It is of course easy to just make one up, "I'll be facing 100 DPS!" Good luck guessing accurately on that one, though.
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The reason is simple. More damage = defence is better. There's a point of intersection where they (regen & defence) are equal.
Again, no solution, but I provided one. That's why your method is awful.
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Except that I have. I answered it using a survivability analysis four posts up from the post with the graph, and this being the second time that I've mentioned it. In fact, you've already quoted the more recent post where I said where to find that post.|
Originally Posted by BunnyAnomaly
And still no answer.
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You'll be certain that my answer is wrong, or flawed because I made up variable values (as you must with DPS, though at least mine are easily gathered from Mids'), but you might want to at least stop repeating that I haven't provided an answer at all. Or not. Say whatever you want.
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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Here's another example of why "100% survival" is not good information on which to make a decision.
You can go from 40->45% defence, and gain 100% survival.
You can go from 0-25% defence, and gain 100% survival.
The problem is that the first example will save your life 5 times in 100. The second will save your life 25 times in 100. The second is 5x better at saving your life. But they both are attributed this useless metric of "100% survival improvement".
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Of course the answer depends on the damage faced, but that doesn't mean that damage must be a variable in the calculation, a very significant point.|
Originally Posted by BunnyAnomaly
you'll still find that it is dependant on the damage you face.
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Your method gets as far as showing that the answer is dependent on the damage faced. So far so good. From there, the standard survivability model moves on to step two, providing a way to objectively determine that damage value from more fundamental quantities, and thus to actually SOLVE the original problem instead of just saying "it depends on the damage" or plucking a damage figure out of thin air.
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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Quote:
The problem is that your survivability analysis is sometimes going to say Regen is better.|
Originally Posted by Werner
Except that I have. I answered it using a survivability analysis four posts up from the post with the graph, and this being the second time that I've mentioned it. In fact, you've already quoted the more recent post where I said where to find that post.
You'll be certain that my answer is wrong, or flawed because I made up variable values (as you must with DPS, though at least mine are easily gathered from Mids'), but you might want to at least stop repeating that I haven't provided an answer at all. Or not. Say whatever you want. |
However there will be a point where you are taking sufficient damage that your defence will become better and you will live longer with the defence. Your explanation gives no heed to this and hence is useless.
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Damage is a variable because defence depends on the incoming damage to determine it's value.|
Originally Posted by Werner
Of course the answer depends on the damage faced, but that doesn't mean that damage must be a variable in the calculation, a very significant point.
Your method gets as far as showing that the answer is dependent on the damage faced. So far so good. From there, the standard survivability model moves on to step two, providing a way to objectively determine that damage value from more fundamental quantities, and thus to actually SOLVE the original problem instead of just saying "it depends on the damage" or plucking a damage figure out of thin air. |
This summarises why you are still unable to answer.
The way you write that also shows you have appalling maths.
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No, the second is not 5x better at saving your life. For either change to be able to save your life, you MUST be approaching the immortality line of damage. For the first person, that number is MUCH higher than for the second person. Smaller percentage of a higher number. Works out the same.
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Originally Posted by BunnyAnomaly
Here's another example of why "100% survival" is not good information on which to make a decision.
You can go from 40->45% defence, and gain 100% survival. You can go from 0-25% defence, and gain 100% survival. The problem is that the first example will save your life 5 times in 100. The second will save your life 25 times in 100. The second is 5x better at saving your life. But they both are attributed this useless metric of "100% survival improvement". |
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
Videos of Other Stupid Scrapper Tricks
Quote:
Correction noted, I have read 'survivability' too many times in this thread and it snuck in.|
Originally Posted by Werner
No, the second is not 5x better at saving your life. For either change to be able to save your life, you MUST be approaching the immortality line of damage. For the first person, that number is MUCH higher than for the second person. Smaller percentage of a higher number. Works out the same.
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It is 5x better because it protects you from 5x as much damage.
If you compare 5% defence to 25% defence to a static regeneration rate, you will get different results, because 5% & 25% mitigate different amounts.
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Indeed, which is why it's so valuable to actually establish the value of this variable in an objective way. You can then replace it with other variables which can simply be looked up.
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Originally Posted by BunnyAnomaly
Damage is a variable because defence depends on the incoming damage to determine it's value.
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"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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Quote:
No, you can't.|
Originally Posted by Werner
Indeed, which is why it's so valuable to actually establish the value of this variable in an objective way. You can then replace it with other variables which can simply be looked up.
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Your survivability assumes you are only interested in determining the answer at which you are invincible.
That is not a useful method because the vast majority of times you are not. It also has potential to give you the wrong answer once you are in danger of dying (ie: defence will at some stage pull ahead every time).
You should use a method that determines which protects you from more damage, and that is dependant on how much damage you are facing.
The answer lies in finding when defence pulls ahead of regen.
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And this is what I think is so amusing. In terms of what you can actually SURVIVE in the game with that mitigation, based on the original table #2:|
Originally Posted by BunnyAnomaly
It is 5x better because it protects you from 5x as much damage.
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0-25%: +1 bossIn a fundamental and obvious sense, going from 40-45% is five times better. In fact, in a fundamental and obvious sense, going from 40-45% protects you from five times as much damage - the damage output of five bosses instead of one. The exact opposite of what you are saying.
40-45%: +5 bosses
Now, I WILL argue against such a simplistic conclusion. It may be fundamental and obvious, but it could be considered a bit misleading. I think it's best to instead view survivability increases in percentage terms, and both of these are double the survivability, or +100%. But I wouldn't go so far as to say that the more extreme view, that surviving 5 bosses is fundamentally and obviously five times better than surviving 1 boss, is actually wrong.
But to conclude the exact opposite, that mitigation is all that really matters, and therefore surviving one more boss is five times BETTER than surviving five more bosses? The mind boggles.
"That's because Werner can't do maths." - BunnyAnomaly
"Four hours in, and I was no longer making mistakes, no longer detoggling. I was a machine." - Werner
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You can't tell the OP which is better. Instead you ran a useless test that examined only your own survivability vs defence. Not only did your test in any way do anything to do with the numbers provided, they used your own. All they did was test your defence.
You have done absolutely no calculation to determine if the regen was better than the defence.