How about some graphs?
Let me first start off saying that yes, reaching the soft cap is desirable and more defense is better than less defense.
However, the notion that the 5% from 40-45 provides the same survivabillity as the 40% from 0-40 is certainly inaccurate. Such a derivative concept is a measure of the rate of change in percent of damage taken, this is not the same thing as survivability. Does someone at 40% Def die twice as much as someone at 45%? I don't have any numbers whatsoever to empirically say for sure, but I'm willing to bet not.
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some graphs:
Wait, what about defense?
Quote:
The person with 40% defense will get hit twice as often as the person with 45% defense, and the disparity actually grows as you face higher level opponents.|
Originally Posted by Deacon_NA
Does someone at 40% Def die twice as much as someone at 45%? I don't have any numbers whatsoever to empirically say for sure, but I'm willing to bet not.
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This should translate to twice the number of deaths, but it's quite possible they're both good enough to never die.
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don'T attempt to read tHis mEssaGe, And believe Me, it is not a codE.
Quote:
At 45% defense, you block twice as many hits as you do at 40% defense.|
Originally Posted by Ironblade
Phrasing it that way is flat-out wrong.
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That means if 40% defense blocks 10 attacks, 45% defense will block 20 attacks.
5% more is blocking exactly as many shots as the first 40%.
I have nothing more to add.
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Everything Dark Armor | The Softcap
don'T attempt to read tHis mEssaGe, And believe Me, it is not a codE.
I appreciate the graphs, Lightslinger. They really made it all clear to me. 
Freedom: Blazing Larb, Fiery Fulcrum, Sardan Reborn, Arctic-Frenzy, Wasabi Sam, Mr Smashtastic.
Quote:
I hope these words have never been written before: the argument as phrased by SpittingTrashcan makes sense, something about the mortality line.|
Originally Posted by Dechs Kaison
At 45% defense, you block twice as many hits as you do at 40% defense.
That means if 40% defense blocks 10 attacks, 45% defense will block 20 attacks. 5% more is blocking exactly as many shots as the first 40%. I have nothing more to add. |
However, in the above equation, you're "giving" the inherent accuracy (or inaccuracy, maybe) of critter attacks to the softcap.
The way I math it:
100 incoming attacks
50 "blocked" by the standard miss
40 additional incoming attacks blocked by 40 defense
45 additional incoming attacks blocked by 45 defense
Would that I had the graph skillz as exhibited above.
Quote:
Inaccurate though.|
Originally Posted by Sardan
I appreciate the graphs, Lightslinger. They really made it all clear to me.
|
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Quote:
Sure, because you keep repeating the same WRONG statements.|
Originally Posted by Dechs Kaison
At 45% defense, you block twice as many hits as you do at 40% defense.
That means if 40% defense blocks 10 attacks, 45% defense will block 20 attacks. 5% more is blocking exactly as many shots as the first 40%. I have nothing more to add. |
Based on 100 attacks:
With no defense, 50 fail to hit.
With 40% defense, 90 fail to hit.
With 45% defense, 95 fail to hit.
Quote:
| 5% more is blocking exactly as many shots as the first 40%. |
Let's rephrase: Having 45% defense causes you to be hit half as much as 40% defense. True.
However, this is NOT the same as saying that that final 5% stops as many attacks as the first 40%. That is plain false. The first 40% of defense stops 4/5 of the attacks that would have hit. The extra 5% stops half of the remainder.
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I haven't started a maths fight since I left university.
You're both arguing based on different premises. Some insist that you count inherent inaccuracy as part of your defense. Dechs believes that it should no. This debate has no useful outcome if you're both using different assumptions to form your premises.
The random number generator pulls floating point numbers between 0 and 100 out of a gerbil's intestines.
If you have no defence then only numbers below 50 cause a hit
If you have 40 defence then only numbers below 10 cause a hit.
If you have 45 defence then only numbers below 5 cause a hit.
Numbers are allotted evenly (Unless the gerbil has been eating fast food, when all the numbers are below 5 and your defence means nothing).
40 defence stops 80% of valid attacks (being ones that would otherwise have hit you). (i.e. ignoring numbers above 50 because they wouldn't hit you anyway.)
Since this means you only have 20% of attacks left hitting you, the next 5 defence cannot block the same number of attacks as the first 40. If it did you would be getting hit by -60% of attacks.
In case it isn't already obvious, that number is absurd.
However, at 40 defence you are being hit by 20% of valid attacks. At 45 defence you are being hit by 10% of valid attacks.
Half the number of hits does not mean double the number of misses. It does mean you are taking half as much damage.
If you die with 40 defence and are not being hit by enough damage to kill you twice over, 45 defence may have prevented your death.
Or you may need to take better care of your gerbil.
Quote:
*wild applause* |
Originally Posted by Edana
The random number generator pulls floating point numbers between 0 and 100 out of a gerbil's intestines.
If you have no defence then only numbers below 50 cause a hit If you have 40 defence then only numbers below 10 cause a hit. If you have 45 defence then only numbers below 5 cause a hit. Numbers are allotted evenly (Unless the gerbil has been eating fast food, when all the numbers are below 5 and your defence means nothing). 40 defence stops 80% of valid attacks (being ones that would otherwise have hit you). (i.e. ignoring numbers above 50 because they wouldn't hit you anyway.) Since this means you only have 20% of attacks left hitting you, the next 5 defence cannot block the same number of attacks as the first 40. If it did you would be getting hit by -60% of attacks. In case it isn't already obvious, that number is absurd. However, at 40 defence you are being hit by 20% of valid attacks. At 45 defence you are being hit by 10% of valid attacks. Half the number of hits does not mean double the number of misses. It does mean you are taking half as much damage. If you die with 40 defence and are not being hit by enough damage to kill you twice over, 45 defence may have prevented your death. Or you may need to take better care of your gerbil. |
P.S. My gerbil liked it too.
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Should I summon Arcanaville to let us all know about the math concerning Defense?
There I was between a rock and a hard place. Then I thought, "What am I doing on this side of the rock?"
This discussion shows how nonintuitive percentages can be. A neophyte might think "It was costly to get the set bonuses to get me to 40% defense. Going to 45% probably isn't worth it because I'm nearly there anyway." I believe Dechs is trying to say is that last 5% of defense is just as important, just as valuable, as the first 40%. How can that be? Isn't each 5% increment exactly as valuable as a previous 5% increment?
Let's first look at an unfortunate turn of phrase Dechs used.
Quote:
But look at this example:| "5% more is blocking exactly as many shots as the first 40%" |
Quote:
|
Based on 100 attacks: With no defense, 50 fail to hit. With 40% defense, 90 fail to hit. With 45% defense, 95 fail to hit. |
Let's say that I can survive 10 incoming hits "per round". With defense at 40% I can handle 100 incoming attacks, with 10 hitting.
But now I manage to move to 45% defense. Does that give me a small incremental edge? No, I can literally double the incoming aggro compared to what I could handle at 40%, because at 45% the damage I took fell by half compared to damage taken at 40%. Since only 5 attacks will hit out of 100 but I know I can survive 10, I can adjust my settings such that there are 200 incoming attacks and get back to 10 landing for damage.
It's nonintuitive to most of us that that final 5% would cut damage in half because no previous 5% increment cut it in half. Because the first 40% allowed me to handle 100 attacks and the last 5% allowed me to handle an additional 100 attacks, this is the reason many people say the last 5% is just as valuable as the entire first 40%.
Thus I think what Dechs meant to say was not that the last 5% blocked as many shots as the first 40% but rather it lets you handle as many incoming attacks as the first 40%.
Bah, I should've just read further in the thread. Dechs wrote:
Quote:
| By doubling what you block with 5%, you double the incoming DPS you can survive. |
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Quote:
Thank you! This is a very clear way of saying it|
Now I get my defense to 40%. I can adjust my difficulty so that there are 100 incoming attacks, with 10 hitting. Pretty impressive: the rooms are now full of spawns 5 times bigger than I could handle with no defense! I am uber! But now I manage to move to 45% defense. Does that give me a small incremental edge? No, I can literally double the incoming aggro compared to what I could handle at 40%, because at 45% the damage I took fell by half compared to damage taken at 40%. Since only 5 attacks will hit out of 100 but I know I can survive 10, I can adjust my settings such that there are 200 incoming attacks and get back to 10 landing for damage. |
That last 5% defense cuts your incoming damage in half, which is what I meant by doubling your survivability when I made my (apparently badly worded) post.
Aw hell, do I have any way to back out of this with any semblance of dignity left?
No?
Didn't think so.
The wording is very important, and the way I phrased things is completely wrong. I apologize for my arrogant stubbornness and relentless accusations of inability to comprehend. The fault is my own inability to communicate my thoughts correctly.
Ouch. I'll be honest. That hurts a little inside to type that.
The point I was trying to make is that the last 5% does as much for your survivability as the first 40%.
Quote:
Yes, this is what I was trying to say. Thanks, Sardan.|
Originally Posted by Sardan
Thus I think what Dechs meant to say was not that the last 5% blocked as many shots as the first 40% but rather it lets you handle as many incoming attacks as the first 40%.
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Let this debacle showcase what happens when an engineer tries to explain something.
Where to now?
Check out all my guides and fiction pieces on my blog.
The MFing Warshade | The Last Rule of Tanking | The Got Dam Mastermind
Everything Dark Armor | The Softcap
don'T attempt to read tHis mEssaGe, And believe Me, it is not a codE.
Quote:
I hear ya. I think I set some kind of record for number of times I edited my own post, trying for clarity. I would submit it, read it, and go "argh, that's not the right way to state that." Wash, rinse, repeat about 15 times. |
Originally Posted by Dechs Kaison
Let this debacle showcase what happens when an engineer tries to explain something.
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Quote:
This is kind of what I was getting-- that the wordings were wrong even if the number agreed. That's why I wanted some visual representations. They're sometimes easier to digest.
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Originally Posted by Dechs Kaison
Let this debacle showcase what happens when an engineer tries to explain something.
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Okay, assuming identical rolls all the time.
- 0% defense = Getting hit 50% of the time.
- 25% defense = Getting hit 25% of the time (half as often, or 1/2 normal)
- 37.5% defense = Getting hit 12.5% of the time (half as often again, or 1/4th normal)
- 43.75% defense = Getting hit 6.25% of the time (half as often yet again, or 1/8th normal).
- 45% defense = Getting hit 5% of the time (1/10th normal).
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Quote:
And if you're fighting Cimerorans and they manage to hit, you are HOSED. |
Originally Posted by Hyperstrike
Note: This doesn't absolve you from lucky-shot syndrome with large numbers of enemies. Given a large enough group, even a statistically small number of hits will be enough to ruin your day.
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When I tank them on a resistance based tank, they quickly get my base defense to -100. Once, I took my shield tank on the ITF to get the Roman shields and see just how effective the debuff resistance was. Unfortunately, (well, unfortunate for testing the debuff resistance) the team had a lot of buffs and my defense was over 100% most of the time. Even when they got a couple of hits in, I'd still be 40+ points above the soft cap. This is why we do not aim for the soft cap. We want as much defense as we can possibly get.
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Just to summarize:
The build I settled on has 45% Ranged Defense, 33% AoE, 19% Melee, 40% Energy/Neg, 28% Fire/Cold, 19% Smash/Lethal, and 23% Psi.
I could lower Psi by 3 to raise AoE by 3, but I probably won't.
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er, wouldn't it be better to focus on either positional defense *OR* typed defense, rather than have a bunch of each?
Paragon City Search And Rescue
The Mentor Project
Quote:
Some of them will overlap on sets that provide multiple defense type bonuses.
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Originally Posted by Ironblade
er, wouldn't it be better to focus on either positional defense *OR* typed defense, rather than have a bunch of each?
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Clicking on the linked image above will take you off the City of Heroes site. However, the guides will be linked back here.
You've got 45% ranged defence, 33% AoE defence and I'm struggling to think of any attacks outside dominator's psi assault that are melee typed. While there is a total of 3 or 4 psi attacks that don't have a positional component; what exactly is the 23% psi defence expecting to work on that's of more benefit than boosting the AoE?
45% defense means that you have a 5% chance to be hit. This reduces your damage taken to 1/10, twice the effectiveness of 40%.
The last five percent prevents as much damage as the first 40%.
Using your numbers, if we start with 100 pts of incoming damage:
Someone with no defense takes 50. 50 pts are avoided.
The 40% defense person takes 10. 90 pts are avoided.
The 45% defense person takes 5. 95 pts are avoided.
The first 40% defense prevents 40 pts of damage. The 45% defense prevents only 5 additional pts.
Paragon City Search And Rescue
The Mentor Project