The Defence Myth

I'm not sure if you're just not very good at English, or if you're actually very dense, but that's not what I said. I said they seek conditions where their long-term trend is immortality.

There's a name for what you're doing. It's called a strawman argument. You're claiming my position is both something it's not and something that's very easy to prove wrong. Then, disproving this thing (which I didn't say), you claim you win the argument. Doing that is called a logical fallacy, and to be clear, someone who uses it is not winning the argument.

No, that is not what you displayed. You displayed a case when mitigation <<< damage, and you showed that a higher immortality line did not indicate which mitigation source gave the best time to defeat.

There are so many things you're doing here that are confusing the issue.

All critters in the game have hit chances calculated like so.

FinalHitChance = TotalAccuracy * (50% - TargetDefense + AttackerToHit)

There are limits on both the total and the parenthetical expression - they cannot be below 5% or over 95%.

Let's consider an imaginary minion had one attack on a 4-second timer that deals 100 damage. It would have a raw DPS output rate of 100/4 = 25 DPS. Its chance to hit an same-level character with no defense would be 50%, so the character would experience 12.5 DPS from our minion. Without something else in the picture, it's impossible for the character to experience 100 average DPS from this mob. Even if the character were badly defense debuffed the mob's hit chance can't exceed 95%.

But if this was now a +2 boss, its accuracy would jump to 1.56, and it would have a base chance to hit of 0.78, and our defenseless character would experience 19.5 DPS.

Give our character 5% defense, and he mitigates 10% of the average damage he would experience with 0 defense. Why? Because of the formula
above.

Minion Before:
25 DPS * 1.0* (50% - 0%) = 12.5 DPS

Minion After
25 DPS * 1.0* (50% - 5%) = 11.25 DPS

11.25 DPS / 12.5 DPS = 90%

You take 90% of the damage, and so 10% of it must have been avoided.

Boss Before:
25 DPS * 1.56* (50% - 0%) = 19.5 DPS

Boss After
25 DPS * 1.56* (50% - 5%) = 17.55 DPS

17.55 DPS / 19.5 DPS = 90%

So 5% defense allows you to mitigate 10% of the damage you would have otherwise taken, not 5%.

This is not plus five percent. This is 5% absolute defense score.

It's your approach to defense values as absolute rather than proportional mitigation that's at the root of why you're in such disagreement with so many other posters.

Except that's not usefully portable. I can't do anything with that in the game based on ordinary play experience. I can use the ratio approach.

If I know that I can survive forever standing in the middle of X mobs, I know that if I increase my defense enough to halve the average damage I am admitting then I know I can survive in the middle of 2*X mobs. I don't have to know what DPS they are dealing. I only need to know proportions.

If I can't survive forever standing in those X mobs but I can win, I don't know for sure that I can defeat 2*X mobs if I increase my defense enough to halve my average incoming damage. However, the closer I am to full health at the end of a fight with X mobs, the more likely it is that I can win against 2*X mobs, or something close to it. This gets back to the heart of the assumptions about playing for the immortality line.

It's significantly more useful, because it's trivial to say more defence is better. There's nothing enlightening about that.

It's useful because you can make comparisons between choices, instead of getting lost in a sea of % increases that do not translate across.

Look, just stay with your survivability measure, which is proven to give wrong results already, several pages ago

We're clearly at an impasse so stick with what doesn't work

It seems they have chosen the latter.

Oh?

And can you tell me how often it matters in practice whether that is 15 seconds of 17 seconds? If you needed 16 seconds to win and you were going to die in 15, did you just stand there and die?

Do not translate across to what? I'm sorry, but does your CoH client somewhere list for you the DPS that AVs deal? Do you sit around and calculate the DPS that a Council spawn will deal, and compare it at various team sizes and level offsets? How do you come up with the numbers you will plug into these absolute expressions of survival you put forth as the better way forward? And I'm lost in a sea of numbers?

You've said it yourself - the answers to what's better is completely situational. But that's a non-answer to the question of how to improve a build in broad terms. To actually decide on something, you have to make assumptions. The immortality line model is based a set of assumptions. It happens to be a set of assumptions that work based on observations about how a lot of people play.

I'm going to reiterate that you did not show that. You made a statement about what you think it shows, and then you shot that down. Except that's not what it shows, so it's not very compelling that you shot it down. You didn't prove anything wrong except for, well, invalid conclusions to be drawing from the immortality line.

Yep, it sure hasn't been working for me all these years.

Actually, I am determining incoming damage from the start, as in, the start of where you begin comparing the performance of defense to regeneration.

You cannot say that unmitigated regeneration is worth the same as mitigated regeneration. It's simply untrue.

Regeneration and other damage recovery mechanisms only act on damage that actually arrives. If you have 90% mitigation of incoming default damage thanks to 45% defense, your regeneration is going to be worth 10 times as much in terms of real survivability as it would if you had no defense whatsoever (because only 10% of the original damage is getting through to be recovered by the regeneration). Because the value of regeneration in terms of real survivability contribution (i.e. how much damage you're actually recovering from) is based upon your existing mitigation capabilities, it is impossible to claim that there is a static, constant defense-to-regeneration exchange equivalent for all values of combinations of defense and resistance for any specific value of incoming damage.

Let's assume that there is a world wherein an enemy has a 100% default chance to hit, and players recover 100 hp/sec but only have 1 hp (the damage is applied as a penalty to regeneration before it is applied to hit points). In this state, you would rate defense and regeneration improvements to be completely equivalent on a 1-for-1 basis because 5% defense is reducing incoming damage by 5% and 5 hp/sec is 5% of your regeneration, in other words, they're completely equivalent.

The improvement of 0%->5% defense (100%->95% chance to be hit) is not the same as the improvement of 100->105 hp/sec: incoming damage is being reduced from 100% to 95%, the survival equivalence (i.e. how much DPS you could actually take before getting killed) of the defense improvement would leave you with an equivalence of 105.263 hp/sec (100 hp/sec / .95 incoming damage).

Now, let's do the same thing, but exchange the 100% hit rate for a 15% hit rate (i.e. 85% +def). The amount that this individual would be able to survive is now 666.667 hp/sec (100 hp/sec / .15 incoming damage). According to your math, 5% +def would provide the exact same thing as 5% +regen. Let's test this. Adding 5 hp/sec would provide an increase of 33.333 (((100 + 5) / (.15)) -(100 / .15)). Reducing chance to be hit by 5% would provide an increase of 333.333 (((100) / (0.15 - 0.05)) - (100 / 0.15)).

It's pretty evident that what you're saying is just not true. Thanks to the variable value of regeneration (insofar as it functions more powerfully in the presence of mitigation), it's impossible to say that there is a single exchange rate between the two for anything more than a single point on the plot. Any time you want to find an exchange rate, you have to calculate the equivalence completely anew based upon any changing values of defense or regeneration that the target might have. This is why there was a difference of regeneration contribution between the first example (5 hp/sec more survivable) and the second (33.333 hp/sec more survivable) when the same quantity of regeneration was added.

The other interesting thing you'll notice is also that the values of the individual quantities of defense changed, exactly as predicted by everyone but you. The initial example showed just over a 5% increase in survivability (5.263 more hp/sec survivability) while the second showed a 50% increase in survivability (333.333 more hp/sec survivability). The value of defense as it pertains to how you will survive depends entirely upon how much defense you've got set as your default state. If you have very little defense, further defense will have low comparative values whereas, with very high defense, further defense will have exceptionally high comparative values.

I forgot the exact formula that I got by reverse engineering Arcanaville's survivability spreadsheet, so I rebuilt that one off the top of my head. I don't believe I was ever actually given that formula, but you could probably give credit to Arcanaville or one of the other old school number crunchers.

I do this all the time, so do hundreds of other players.

"Don't take the Carnie mission, they suck. Don't take the Malta mission, they are too tough."

This is yet another place in this discussion where Bunny, you are valuing your model and math over the application of knowledge in the game.

And yes, I have looked at the spreadsheet. One of my gaming buddies is a mathematician, working for 'the man'. We discuss these sorts of things all the time. He can prove mathematically that 2+2 = 5.

Bunny, you are not modelling how the game actually works and having knowledge that can actually be applied is all that's important when I make characters. I want to know how tough I am going to be based upon all my options and your model does nothing to help with that.

Mathematically, of course some level of regeneration can become better than defense. But the amount needed is not any where close to what can be obtained easily in game and again, that is all that matters.

But the specifics of the point makes no sense, given the numbers others have shared and my (and apparently others') years of experienced play.

All you proved was that it provides wrong results when used as a metric for something it isn't made to measure. No matter what I want, using a thermometer to measure volume provides wrong results.

The thing is, while both of the methods presented in this thread work and are correct, the survivability line is more applicable for in-game situations. I want to know how tough I am, i.e. what is the maximum DPS I can take without faceplanting. I'm interested in running missions at as high difficulty settings as possible without dying (it happens, of course, when the RNG hates me), but I'm not really interested in knowing whether I'll live 50 or 60 seconds against an arbitrary DPS figure. This is why the survivability line method helps me when I plan builds while yours does not.

I think it's my fault. Sorry guys!

It's absolutely your fault!

But that doesn't mean you're wrong :-)

Funny thing... in that thread I agreed with the OP because in that case he was correct (because the exact question you asked was mitigation value vs mitigation value). In this thread the OP poses a "surviability vs survivabilty" hypothesis... and is unfortunately very wrong.

Nah, we actually had this same argument in an older thread. So this is at least thread three. I'd contribute to yet another thread, but I think y'all have this one covered, and I've been forbidden from continuing to argue on the intarwebs. Well, this particular argument with this particular person, anyway.

I know I wandered across it in my own musings back during the great I4 Regen wars. It pops out of a fairly basic attempt to calculate how long a given average DPS that's going to kill something eventually takes to do so.

T = HP/DPS

But when there's regen in the picture, "DPS" has to be "net DPS", which is (applied DPS - HP regen rate). Since we are talking about DPS that will win out, we know that regen rate is lower than applied DPS, so the quantity has a reasonable sign.

T = HP/(DPSa-R)

Applied DPS is the part of raw DPS that gets past your mitigation.

T = HP/((1-M)*DPSr-R)

All that's left then is to note that average raw DPS can be expressed as Damage/Time.

T = HP/((1-M)*Damage/T-R)

That can be rearranged into the formula posted before.

They really were trying every angle the could.

i.e. math troll. Stop feeding.

IIRC it was Arcanaville who created the immortality line calculations in her huge post about Defense.

I could be wrong.

Sorry, I've been traveling and missed this thread.

So, to catch up:

1. I think the OP was trying to say that for any value of defense, and for any value of regeneration, there exists a value of incoming damage where, theoretically speaking and on average, the two have identical mitigation. That's true, and obvious, and not generally in dispute. Basically, since X% defense mitigates X% of incoming damage (or 2X, depending on who you talk to: its not important here), for *any* value of regeneration Y there is some value of damage D such that X * D = Y. X just equals Y/D.

The more interesting debate is for what values this is an interesting observation, in the sense of being useful to anyone.

No one has ever made credible claims that there is any direct (as in proportional) relationship between numerical defense and numerical regeneration, like the 2:1 rule for resistance (which itself is situational).

2. The damage mitigation equations do come from me, although I should clarify that to the best of my knowledge, I was the first to post them in their current form and popularize them on the US forums. There was another poster, Dr. Rock, who apparently did likewise and apparently independently on the Euro forums, albeit in a slightly different form. My claim to fame was the Defense and Scrapper comparison threads where I used them in analyses: Dr. Rock's claim to fame was a VB program, if I remember correctly, that implemented them in a comparison app.

Prior to the mitigation equations, there were two predecessors. First, Havok's spreadsheets which became Circeus' spreadsheets for tanker mitigation, which used a spreadsheet calculator approach not too dissimilar from my damage mitigation spreadsheets, but with a completely different focus. Second, posts that started like this: "suppose someone attacks you 1000 times for 100 points of damage each attack" that did the calculations manually and rarely if ever factored in regeneration.

3. The critical error on the part of the OP is that they think there exists some "survivability model" that doesn't factor incoming damage but *does* factor in regeneration, and makes predictions. I know of no such model, although its possible someone out there is spouting one. I think the number crunching community is well aware of the fact that since Regeneration operates linearly, but Defense and Resistance operates proportionately, you can't do that. Defense and Resistance can be compared to each other independently of incoming damage, to a first order approximation, because their average behavior is both proportional to incoming damage and therefore incoming damage can be factored away. But Regeneration is linear, and independent of incoming damage, and can't be so compared.

If the OP wants to see the average survivability model actually used to do real comparisons, factoring in not just regeneration but also starting health, I would point to the dated, but still methodologically valid Scrapper Comparison thread which reposts that stuff from the I7 analyses, which was the last time I did such a holistic comparison with those average formulas.


Edit: ok, I finally stumbled across the related thread. After reading this:

I'm not sure I want a piece of this. That's a sign this doesn't likely go anywhere interesting. Its a weird perspective, and you can't disprove a weird perspective. Its just a perspective that I strongly recommend no one else adopt. It will leave you in a position of no one being able to communicate with you.