Some number crunching...

Warning: Theorycraft inside.

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Some number crunching...

Postby Joanadark » Wed May 16, 2007 10:19 pm

This is a comparison to represent gearing philosophies that are on either end of the stat-stacking option scale yet still accomplish spike-elimination.

To compare iPoint expenditure, we need to break down what composes these stats.

Assume uncritability due to Defense
Assume uncrushability due to mitigation.
I ignored the Libram for this comparison

On one hand, we’ll have 66.8% Avoidance and 35.6% Block on the first Paladin’s gear.
On the other, we’ll compare 23.21% Avoidance and 79.19% Block on the second Paladin’s gear

Paladin 1 will discount 23.21% from his avoidance stat because it was granted by base agility and defense, which are possessed by the second paladin.
Paladin 2 will discount 30% from his block stat as it came from Holy Shield, and 5.6% from his block stat as it came from Defense, both of which are possessed by the first paladin.

So we are comparing the iPoint usage of:

Paladin 1: 43.59% Avoidance
Paladin 2: 43.59% Block

This is the spectrum of interchangeable stats.

PALADIN ONE:

Assuming that all 43.59% avoidance is acquired through Dodge Rating, the most efficient way to do so, the iPoint cost of this itemization is 823.851 iPoints.

PALADIN TWO:

43.59% Block Chance requires 344.361 iPoints in Block Rating to achieve, discounting the Libram, which doesn’t have an avoidance equivalent.

The difference in budget is 479.49 iPoints. All of that poured into Stam would equal 319.82 stam, 332.61 stam after talents. We will represent this by Paladin 2A.
Let’s pour it instead into Block Value, granting 312 Block Value.
This will be represented by Paladin 2B



Results:
Paladin 1 avoids 43.59% more often than Paladin 2, granting an average of a 43.59% decrease in effective attack frequency.
Paladin 2 takes a hit 43.59% more often than Paladin 1.
Paladin 2A has 3326 HP more than Paladins 1 and 2B.
Paladin 2B reduces all hits taken by 312 more than Paladins 1 or 2A


Now a comparison.

Using the same numbers Lore threw out, let’s say Maulgar hits for approximately 5-6k every 2.5 seconds.
The tankadins are all given 65% armor damage reduction, a baseline 150 Block Value from their shield, and 14k HP.

Paladin 1 has 66.8% avoidance, so we can effectively “spread” damage-causing hits by multiplying the attack speed of 2.5 by 66.8 for an “Average Hit Frequency”.
Therefore, Paladin 1 will take a hit every 4.17 seconds on average.

Paladin 1’s Combat Log:
0:00:00- Maulgar hits you for 3425 (blocked)
0:04:17- Maulgar hits you for 3425 (blocked)
0:08:35- Maulgar hits you for 3425 (blocked)
0:12:52- Maulgar hits you for 3425 (blocked) (ONLY 300 HP left)
0:16:69- Maulgar hits you for 3425 (blocked) (Death)

Time until death- 16.69 seconds
Number of damaging hits survivable- 4




Paladin 2 has 23.21% avoidance, so their AHF is spread to about every 3.08 seconds.

Paladin 2A, with an HP of 17.326k, has this effective combat log:

Paladin 2A’s Combat Log:
00:00:00- Maulgar hits you for 3425 (blocked)
0:03:08- Maulgar hits you for 3425 (blocked)
0:06:16- Maulgar hits you for 3425 (blocked)
0:09:24- Maulgar hits you for 3425 (blocked)
0:12:32- Maulgar hits you for 3425 (blocked) (ONLY 201 HP left)
0:15:40- Maulgar hits you for 3425 (blocked) (Death)

Time until death- 15.4 seconds
Number of damaging hits survivable- 5



Paladin 2B, with an additional 312 Block Value, has this effective combat log:

Paladin 2B’s Combat Log:
00:00:00- Maulgar hits you for 3113 (blocked)
0:03:08- Maulgar hits you for 3113 (blocked)
0:06:16- Maulgar hits you for 3113 (blocked)
0:09:24- Maulgar hits you for 3113 (blocked) (ONLY 1548 HP left)
0:12:32- Maulgar hits you for 3113 (blocked) (Death)

Time until death- 12.32 seconds
Number of damaging hits survivable- 4





While Paladin 1 had the ability to solo Maulgar for the longest duration, each individual hit represented a larger proportional amount of their HP total. Additionally, while hits were more spaced out, the actual hits themselves were larger than P2B, the only one of the other models who he lasted longer than.

The effective threat an individual hit represents for each tank is as follows:

P1- 24.4%
P2A- 19.7%
P2B- 22.2%

Boss DPS on the tanks is as follows:

P1- 1094
P2A- 1482
P2B- 1347




Now, we must recall that the Paladins here represent sitting on the bare minimum requirements for uncrushability and uncritability.

So let us model scaling. By giving each an additional 650 iPoints to play with, Paladin 1 throws them all into Stamina, Paladin 2A throws them all into Stamina, and Paladin 2B throws it all into Block Value.

P1 and P2A now have 478.1 additional stamina, for 4942 more HP.
P2B gains 390 Block Value.



Paladin 1 with an HP of 18,942 and 43.95% more avoidance has this effective combat log:

Paladin 1’s Combat Log:
0:00:00- Maulgar hits you for 3425 (blocked)
0:04:17- Maulgar hits you for 3425 (blocked)
0:08:35- Maulgar hits you for 3425 (blocked)
0:12:52- Maulgar hits you for 3425 (blocked)
0:16:69- Maulgar hits you for 3425 (blocked) (ONLY 1817 HP left)
0:20:86- Maulgar hits you for 3425 (blocked) (Death)


Time until death- 20.89 seconds
Number of damaging hits survivable- 5





Paladin 2A with an HP of 22,268 has this effective combat log:

Paladin 2A’s Combat Log:
00:00:00- Maulgar hits you for 3425 (blocked)
0:03:08- Maulgar hits you for 3425 (blocked)
0:06:16- Maulgar hits you for 3425 (blocked)
0:09:24- Maulgar hits you for 3425 (blocked)
0:12:32- Maulgar hits you for 3425 (blocked)
0:15:40- Maulgar hits you for 3425 (blocked) (ONLY 1718 HP left)
0:18:48- Maulgar hits you for 3425 (blocked) (Death)

Time until death- 18.48 seconds
Number of damaging hits survivable- 6




Paladin 2B, with an HP of 14,000 additional 679 Block Value has this effective combat log:

Paladin 2B’s Combat Log:
00:00:00- Maulgar hits you for 2746 (blocked)
0:03:08- Maulgar hits you for 2746 (blocked)
0:06:16- Maulgar hits you for 2746 (blocked)
0:09:24- Maulgar hits you for 2746 (blocked)
0:12:32- Maulgar hits you for 2746 (blocked) (ONLY 270 HP left)
0:15:40- Maulgar hits you for 2746 (blocked) (Death)


Time until death- 15.4 seconds
Number of damaging hits survivable- 5





The effective threat an individual hit represents for each tank is as follows:

P1- 18.1% (26% improvement)
P2A- 15.4% (22% improvement)
P2B- 19.6% (12% improvement)

Boss DPS on the tanks:

P1- 1026 (6% improvement)
P2A- 1334 (10% improvement)
P2B- 1114 (17% improvement)

Advantage gained due to scaling:

P1- 32%
P2A- 32%
P2B- 29%


It was interesting to note that if I made a model which SPLIT their itemization between Block Value and Stamina, or between Avoidance and Block Rating, either way resulted in significantly less effectiveness than power-housing one stat provided.
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Postby Joanadark » Wed May 16, 2007 10:25 pm

A note about avoidance:

You'll probably have noticed how I dealt with avoidance stats above. I like to treat them as "damage spreaders" as oppose to "damage reducers", since it provides a more accurate representation of what is actually happening.
The way I do this is multiply the attack rate of the boss being tanked by the avoidance percentage of the tank.
This basically creates a picture where an avoidance tank is tanking a hit less often on average, i.e. at a much lower frequency, due to Dodging, Parrying, being missed, etc, as oppose to making the DPS lower multiplicatively, which I think is misleading.

For example, in a situation where the damage dealt by a hit can one-shot an avoidance stacking tank with 12k HP, but the avoidance tank has 50% avoidance, it is misleading to calculate your figures basing things around avoidance reducing incoming damage. The hit, in this case, when it eventually comes, will STILL one-shot that tank, but a calculation saying that 50% avoidance is 50% less damage being taken will predict otherwise.
Instead, avoidance "spreads" incoming damage, by increasing the dead time in between taking damaging attack rolls.
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Postby Joanadark » Wed May 16, 2007 10:27 pm

and yes, I know that the numbers I used are unrealistically high, they are that way deliberately for the sake of trend comparison.
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Postby Daromire » Wed May 16, 2007 10:34 pm

you my dear math friendly fellow tankadin are nuts :? ... and by that I mean. English, do you speak it? (help me out here and break this down for a dummy :P)
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Postby Everlight » Wed May 16, 2007 11:30 pm

Reserved for when I have the time to digest the maths thoroughly.

Good work there. Your maths agrees with the math I've done on avoidance tanking and its scalability. The stuff on block value is particularly of interest.
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Postby Daeren » Thu May 17, 2007 12:42 am

One short note, to be able to avoid arcing smashes is pretty ownage.
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Re: Some number crunching...

Postby Lore » Thu May 17, 2007 7:06 am

Joanadark wrote:Using the same numbers Lore threw out, let’s say Maulgar hits for approximately 5-6k every 2.5 seconds.
The tankadins are all given 65% armor damage reduction, a baseline 150 Block Value from their shield, and 14k HP.


Note that the number I mentioned in the other thread was how about much damage he does to me when he hits me, not his pre-mitigation damage (which is something more like 15000-21000 or something).

So with a block value of 312, he'd be hitting you for an average of 5188.
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Postby Sabindeus » Thu May 17, 2007 8:46 am

So it seems in general, avoidance is king?
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Postby Joanadark » Thu May 17, 2007 9:02 am

So it seems in general, avoidance is king?


well, that depends entirely on what it is you're looking for.

taking the least damage over the length of the encounter? sure.
being able to solo a boss without dying for the longest length of time? absolutely.

being easiest for healers to keep alive? not by my interpritation.
and certainly being the lowest possible threat-generation rate tank.



so it comes down to what you view the first priority of a good tank is. I have my views, and others have theirs.

Theres two sides to every issue, mine and wrong. heh. kidding.
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Postby Alixander » Thu May 17, 2007 9:09 am

Query: Would you be willing to do a more balanced setup. You've shown extremes, and theory should be that a balanced setup would be between the two extremes, but that's just theory, I would like to see some actual numbers. Let's say... around 48% total avoidance, and 52% block (this would be if he had almost nothing but defense, thus the non-holy shield based block bonus would be 65% divided by 4, times 3).
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Postby Lore » Thu May 17, 2007 9:11 am

Stacking tons of either will just get you killed. You need both to survive the encounter. The decision on whether to add more HP/mitigation or avoidance largely depends on what kills you most frequently. Basically, if you're dying to spike damage, you need more mitigation. If you're dying to healers going OOM, you need more avoidance.
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Postby Joanadark » Thu May 17, 2007 10:24 am

Stacking tons of either will just get you killed. You need both to survive the encounter. The decision on whether to add more HP/mitigation or avoidance largely depends on what kills you most frequently. Basically, if you're dying to spike damage, you need more mitigation. If you're dying to healers going OOM, you need more avoidance.


this seems reasonable to me.
Its just tough to fully accept balancing in such a way though, because both mitigation and avoidance are self-reinforcing.
In fact I just did some extensive discussion of this on the "path we follow" thread replies in response to coriel.
take a look at it there.
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Postby Arcand » Thu May 17, 2007 10:47 am

Lore wrote:if you're dying to spike damage, you need more mitigation. If you're dying to healers going OOM, you need more avoidance.


Hordie bastage stole my line. ;)
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Postby Lore » Thu May 17, 2007 11:14 am

Self-reinforcing yes, but they both help in different ways.

Avoidance primarily helps by putting gaps in the amount of damage you're taking. HP and Mitigation work together to ensure that you survive the damage when you do take it.

The most important thing to understand the balance that's necessary is the synergy between the tank and the healer. Back in the days of downranked heals, you could stack tons of HP and mitigation and get away with very little avoidance because you'd generally be receiving a pretty steady flow of low-rank heals that cost very little mana from your healers while keeping you topped off. Nowadays, most healers just keep max-rank heals casting, cancelling at the last second if the tank doesn't need it. This means that when the tank takes damage, most of his or her healers let their casts finish - which results in the same amount of healer mana being spent regardless of how much damage is being taken. That's where avoidance comes in; if you dodge the attack, no mana is spent.

However, since not only is it impossible to achieve 100% miss/dodge/parry, but there are also other types of damage being dealt on occasion from spells and whatnot, no matter how much avoidance you have you WILL take damage. That's where the HP and mitigation come in. You have to be able to survive the spike damage.

I brought up Aergis' tank simulator and ran 20 fights each against the Maulgar preset with two extreme examples. Both tests used the same healer setup:

3 healers
12000 mana
1200 +healing
20 spell crit
300 mana/5

For the high-avoidance test, I used the following tank stats:

8000 hp
10000 armor
30% miss
30% dodge
30% parry
30% block
300 block value

These were my results:

Code: Select all
-----------------------------------
Total table for 20 fights.
-----------------------------------
Miss rate : 31.37
Dodge rate : 33.5
Parry rate : 31.13
Block rate : 13.02
Crush rate : 0
-----------------------------------
Avg length of fight : 4.13 minutes.
Avg incoming dps : 380.32
-----------------------------------
Spike death : 100%
OOM death: 0%


100% spike death, average of 4 minutes. It's worth noting that not all of the deaths were just due to his special attack (which 1-shots this particular tank), the one I could see the end of was actually just from taking 2 hits in a row.

For the high-mitigation, low-avoidance test, I started with the following stats:

20000 hp
17000 armor
5 miss
5 dodge
5 parry
90 block (to push crushing blows off)
300 block value

and got these results:
Code: Select all
-----------------------------------
Total table for 20 fights.
-----------------------------------
Miss rate : 5.7
Dodge rate : 6.41
Parry rate : 4.69
Block rate : 92.39
Crush rate : 0
-----------------------------------
Avg length of fight : 1.98 minutes.
Avg incoming dps : 1913.3
-----------------------------------
Spike death : 0%
OOM death: 100%


I noticed that the tank was dying in about half the time this way, so I started bumping up his HP and mitigation to see if adding more helped. By the time I got to a point where I was getting similar time til death (4.29 minute average) my tank had 35k hit points, 22k armor, and 800 block value.

So then I thought I'd take the average values between the two tanks and see what the results were. I ended up with:

19000 hp
16000 armor
17.5 miss
17.5 dodge
17.5 parry (for more realistic numbers you could balance these out to something like 25 dodge, 11 miss, and 16.5 parry and get the same results)
550 block value

That's actually not too crazy for a well-geared endgame main tank, particularly post-2.1. Here's my results:

Code: Select all
-----------------------------------
Total table for 20 fights.
-----------------------------------
Miss rate : 19.3
Dodge rate : 18.05
Parry rate : 17.93
Block rate : 53.45
Crush rate : 0
-----------------------------------
Avg length of fight : 5.49 minutes.
Avg incoming dps : 1104.92
-----------------------------------
Spike death : 0%
OOM death: 100%


As I expected, averaging the two extremes to a more balanced level made the tank live longer by a little over a minute, with 0 spike deaths.
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Postby Lore » Thu May 17, 2007 11:18 am

PS: I didn't really pay much mind to item value in that test, purposefully left that open for continued discussion.
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