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# Computer simulation analysis of resilience vs hit points

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### #1 Tantelus

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Posted 06 March 2007 - 03:05 PM

I wrote a basic simulation to determine the benefit of resilience vs hit points. Basically the program simulates damage, variable between 50%-100% of a controllable base damage, and does iterations till the "character" dies. A crit is calculated as double damage. Resilience effect is calculated as a -1% crit rating reduction and a 2% reduction to damage done when crit for 39.4 rating points.

Limitations: This program does not take into account non linear scaling of damage with crits due to effects like flurry. Nor does it calculate the benefit of a crit based on your opponent, for instance a frost mage specced 40/0/21 will crit harder than 2x. If anyone has any recommendations I'm willing to modify my program.

Longevity is measured in the mean lifetime (MLT), units are number of iterations.

Data:

Basic stats:

10000 HP
0 RES
MLT: 166 seconds

```[B]Hit point difference @20% crit:[/B]

[U]HP[/U]         [U]MLT[/U]
10000      166
10500      175
11000      183
12000      200

[B]Resilience difference @20% crit:[/B]

[U]Res[/U]        [U]MLT[/U]
000        166
050        169
100        172.5
150        175
200        178
300        183

[B]Hit point difference @30% crit:[/B]

[U]HP[/U]         [U]MLT[/U]
10000      153
10500      161
11000      169
12000      184

[B]Resilience difference @30% crit:[/B]

[U]Res[/U]        [U]MLT[/U]
000        153
050        157
100        160
200        166
250        169
300        171

```
So the quick and dirty is this:

At 20% crit, 150 resilience is equal to about 500 hit points or 1 resilience is equal to about 0.33 stam

At 30% crit, 125 resilience is equal to about 500 hit points or 1 resilience is equal to about 0.4 stam.

Overall it seems more beneficial to find socketed gear and toss in gems rather than get pvp gear with resilience.

### #2 Malan

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Posted 06 March 2007 - 03:20 PM

So where is the crossover point at which the resilience becomes better? (if ever?)

### #3 frmorrison

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Posted 06 March 2007 - 03:30 PM

The note about resilience, the PvP gear has decent resilence and good stamina, while most PvE gear doesn't have good stamina. Sockets can make up for the lower base stamina though.

However, your simulation likely doesn't take into account that PvP fights are sometimes about luck, and when resilence stops that big crit that can help you win.

What is resilience's cost vs stamina in the item budget?

### #4 Tiiki

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Posted 06 March 2007 - 03:39 PM

And am I right in thinking that 1 resilience costs the same as 1.5 stam in terms of itemisation (stacking one stat excepted).

In fact, essentially, isn't it the fact that you can have 'lots' of Stam and 'lots' of Resilience on a particular item for less budget that 2 x 'lots' of Stam that makes Resilience useful? I.e. giving two survivability stats to pump instead of just one.

Other than that, it seems to me it's clearly overpriced.

Of course it also dampens spike damage pretty well at high levels, which makes you much easier to heal. Who knows if the 184 seconds at 12,000 HP wasn't 100 seconds of not very much followed by an instagib crit chain?

The best thing to add to your simulation would be throwing out a CSV of current HP over time that could be graphed in Excel, perhaps?

### #5 Tantelus

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Posted 06 March 2007 - 03:43 PM

I'm not entirely sure what the cost of resilience vs stam is but stam is definitely cheaper. If you compare on gems, 10 resilience is an epic gem whereas 12 stam is a blue gem. It is conceivable that 1 resilience = 1.5 stam for item cost. There's no cross over point where 1 stam equals 1 resilience for survivability.

One thing to consider however is damage taken. Say a person is taking 30000 damage in an arena, that clearly exceeds their hit point. In this case, resilience has granted the extra survivability for free, whereas hp just creates a larger pool to heal.

### #6 Tantelus

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Posted 06 March 2007 - 03:45 PM

The results you see are an average of 1000 simulations. I actually have the graph of damage done over time displaying as the program runs, I could try calculating the standard deviation from the mean for high resilience and high stam. That should give a sense of the spiky-ness of the damage being done.

### #7 Avair

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Posted 06 March 2007 - 03:58 PM

One thing to consider however is damage taken.

This is not an insignificant consideration. Serious Arena teams are going to be healing damage, so any calculations on healing should take that into account. If resilience increases the value of the heals (much like Quick Recovery does) than it should be accounted for.

### #8 Tiiki

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Posted 06 March 2007 - 04:02 PM

One thing to consider however is damage taken. Say a person is taking 30000 damage in an arena, that clearly exceeds their hit point. In this case, resilience has granted the extra survivability for free, whereas hp just creates a larger pool to heal.

What exactly do you mean by this?

And I believe, correct me if I'm being really stupid, that the TBC itemisation formula was basically:

1 non-stam stats = 1 of ANY rating/resilience/etc = 2 AP = 1.5 stam?

I.e. it was balanced so 1 hit rating = 1 crit rating because you need more crit rating (22.1 vs 15.8) for 1% at 70.

### #9 levk

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Posted 06 March 2007 - 04:05 PM

This is not an insignificant consideration. Serious Arena teams are going to be healing damage, so any calculations on healing should take that into account. If resilience increases the value of the heals (much like Quick Recovery does) than it should be accounted for.

Is this true? This is the first time I hear this.

### #10 Shiftir

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Posted 06 March 2007 - 04:09 PM

What he means is resilience would slow the incoming flow of damage thus making the outgoing flow of heals more valuable. Not increasing the size of heals in any way, just increasing the effective "time to live" granted by each heal of X amount.

### #11 Tantelus

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Posted 06 March 2007 - 04:12 PM

Ok so here are the results of the standard deviation calculations at 30% crit rate:
```[U]HP[/U]        [U]RES[/U]         [U]MLT[/U]         [U]SD[/U]
10K         0           102         4%
11K         0           112         4%
10K       100           106         3.7%
10K       200           110         3.4%
```

SD here is the percent standard deviation among the 1000 simulations and represents the variation in how fast you die. As you can see (and probably expected) increased resilience makes death time more predictable while increased HP does nothing. So yes, you're less likely to get omgcrit near the end of your hit points and therefore more likely to get a heal.

As for the healing efficacy, I would calculate the healing bonus factor as follows:

Effective healing = (Raw heal) * ((HP value of your resilience rating)/(Total HP)+1)

This way the % of your effective health coming from resilience would be like +healing on your healer.

### #12 Tantelus

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Posted 06 March 2007 - 04:17 PM

Tiiki, what I mean is that when you're looking at taken damage you have to consider what effect resilience had to that damage. Say your listed taken damage is 30000. With 250 resilience (using my conversion factor at 30% crit rate), it will seem as if you had 11K HP for every 10k HP you had. Therefore the true damage done to you will have been 33000, though only 30k of it had to be healed, since resilience mitigated about 3k damage. Had you gone the higher HP route, you would have had to heal the extra 3k damage as well.

### #13 Viktus

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Posted 06 March 2007 - 04:18 PM

What numbers did you use for the base damage?

### #14 levk

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Posted 06 March 2007 - 04:18 PM

What he means is resilience would slow the incoming flow of damage thus making the outgoing flow of heals more valuable. Not increasing the size of heals in any way, just increasing the effective "time to live" granted by each heal of X amount.

The only time this would be an issue is if the heal you land on a target isn't enough to make them live to see the next heal. At the very best this is single target HPS throughput problem at worst it's lack of avoidance (broken CC or whatnot). I can't imagine resilience on your whole team is a good way to solve it.

### #15 Tantelus

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Posted 06 March 2007 - 04:24 PM

What numbers did you use for the base damage?

I tried a variety of different base damage and it didn't make a difference as far as the numbers go. The decimal point shifted obviously but the outcome was the same. Base damage doesn't seem to make a difference in terms of mean lifetime, in that respect every class benefits from resilience equally. I can't remember what the base damage was for the OP, the 2nd post with the standard deviations used a base damage of 100.

### #16 Ghostz

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Posted 06 March 2007 - 04:29 PM

There's a few benefits to resilience over stamina.

The first one is limiting the luck factor. Crits are what kills people in arenas. If you get crit by two or three people at once, chances are you're dead. Reducing the chances of that is well.. a pretty big deal.

Without any resilience, if all 3 people hitting you have a 30% chance to crit, there's a 2.7% chance that you get crit by all 3 at once.

With 200 resilience, that goes down to a 1.56% chance, and it reduces the overall damage you take from those crits by 10%. So if you get burst for 7000 in crit damage in that time, that's equivalent to an extra 700 life that doesn't have to be healed (mentioned more in the second factor).

Now, the other benefit of resilience over stam is that it reduces damage taken. Stamina is just a buffer and you will need to get healed eventually. In arenas, especially with MS on whoever's being attacked, the healers on your team are capable of pretty limited hps heals. The less damage you take, the longer a healer can keep you up, and taking less crits while having the ones you take do less damage do exactly that.

In 5v5s, we've ran in and literally killed someone in under 3s of attacking them. Its not the most common occurance, but it does happen. I can almost guarantee 80% of the damage done there is crits. Negating one of those crits and having the rest do significantly less will usually mean surviving long enough to get some heals. We've also had occurances where our assisted target is getting tons of heals (usually when something's gone wrong) and we just can't beat him to the ground without a lucky string of crits.

Basically, the whole point of this is that crits are an *extremely* important part of being able to kill someone in arenas, and being able to avoid then will increase ur survivability by a lot. Stamina can only go so far, especially if you're taking more damage than your healers can heal, its only a matter of time.

A third thing that just came to mind is that crits also proc a lot of debuffs. Deep wounds and ignite come to mind right away, but I'm sure there are others as
well.

Edit: Levk, I agree that you probably don't need resilience on your whole team, but it's not a bad stat on the people that are most likely to get focused. That and it comes as a standard stat on most of the best stamina gear in the game anyawy (GM / Gladiator).

### #17 Erongg

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Posted 06 March 2007 - 04:30 PM

note: can't get my spacing working right, sorry for the wierd table.

Try [code=auto:0] for a table created in Courier.

### #18 levk

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Posted 06 March 2007 - 04:38 PM

[Resilience] comes as a standard stat on most of the best stamina gear in the game anyawy (GM / Gladiator).

Which is exactly how I feel about it. I'll take whatever comes with gladiator gear since it's good regardless, but things like the halaa gem are rather pointless.

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