Crit PDIF Distribution and other interesting data

**Lovex** · 2011-02-14 14:48

thanks kirchsy

**Byrthnoth** · 2011-02-14 15:27

Originally Posted by Masamune

Nice data Kirschy !

Can you post your data in the "standard format" like used by Kparser please ? (ie 1st column with each individual observed damage value, and 2nd column next to 1st one with corresponding parsed frequencies). Up to you to remove "false crits"

Also i'm wondering if your tests werenot screwed by level of mobs fought: were they ALL really even match ?

Lastly, just to try to explain why seeing way more frequency values near cap:
imagine your data had no cap and has "approximately" a uniform distro shape. Now, "cut" the highest values to 0% frequency, but add all those cut frequencies to the last uncut frequency, thus making visually a frequency spike.
And finally, add a secondary randomizer like raellia explained: the aforementioned spike will become "sparsed" between 3.0 pDIF (max uncut value) and 3,15 pDIF(max *5% 2ndary randomizer). The result is what you showed in the graph of your 1st post.
Hoping to be clear^^

In my experience, Scars Abyssea areas cap out at EM (level 90) monsters, meaning any test done in those zones can be safely assumed to have EM monsters or lower. Insurgency kills on Birds has me thinking fat bats in Tahrongi? If it actually needs to be birds subfamily, maybe Piasa's birds in La Theine?

I'm guessing that if you chop off the distribution from 3.0 to 3.15 above the 3.15 crit frequency (59) and add the removed frequency onto the 2.5 to 2.65 crit area, you should see two flat levels before and after 3.0 pDIF. The spike is an artifact of the 1.05 multiplier elevating sub-3.0 crits above 3.0.
2.5 + (3.0 frequency - 59) = 2.65 to 2.99 frequency average
2.51+(3.01 frequency - 59) = 2.65 to 2.99 frequency average
2.6+(3.1 frequency - 59) = 2.65 to 2.99 frequency average
etc.

It would roughly remove the effect of the 1.05 randomizer, as 3.15 is the one value above 3.0 that can only be obtained through hit with capped pDIF.

**Kirschy** · 2011-02-14 17:25

Spoiler: show

Copied directly from the spreadsheet.

@Thorny: Wow, thank you for pointing that out. That makes it ~1.0%/piece, and an extra 1% for the whole set. Makes a LOT more sense.

EDIT: The mobs were Piasa's birds @ holla. I did re-enter a few times, so they reset to Easy Prey, but went back to capped @ Level 90/Even Match. I'm pretti sure I was capped fSTR/Attack.

**Byrthnoth** · 2011-02-14 17:46

Depending what you use as the true 3.15 value, you get about 2.85-2.89 pDIF average before the 1.05 correction. It comes out to exactly 2.94 with the 1.05 multiplier.

**Raelia** · 2011-02-14 18:40

Originally Posted by Kirschy

What do you mean? The 1.00 - 1.05 random term on crits has been in the game since before abyssea existed. And what scaling difference are you talking about between synthetic and dropped atma?

Just reminiscing about the shitstorm that happened with a few people when I rewrote the otherwiki page on pDIF with much illustration of order of operations and the secondary 5% randomizer. People can be so funny and stupid when something seems too simple to them.

Your data is awesome. Just to throw some clarification: 2.2 Ratio thrown up or down 20% gives 1.76 to 2.64, or 2.76-3.64 after 1.0 from crit. >3.00 is capped to 3.0, so that's .64/.88=72.7% of your crits that will be 3.0 and so within the 3.0-3.15 range. Only 11% of your crits will always fall below 3.00 ( [3.0/1.05-2.76]/.88 ), and the remaining ~16.2% will be evenly spread between, so roughly 80.8% above and 19.2% below. Can you give your counts above and below 3.0 to match this prediction? Give me a minute, I'll dig it out myself, thought that page 2 data was incomplete.

122*3.0*1.35 = 494.1

<494: 1419 46.9%
>=494: 1610 53.1%

This is interesting because you even have the spike at 494 to show your base damage is correct. I can only conclude your ratio was not capped. This isn't surprising since level 82 mobs easily had 340+ defense, needing ~750 attack to cap. Level 90s can only be expected to be higher. Your melee attack value would be useful here, as well as food or buff details (use of Last Resort, Berserk, etc).

As for weird atma values and synthetic atma values being lower for a given tier, GH vs RL was the main candidate of the theory. It probably is just an error after all. I looked back at some of the +Stat figures I had written down and instead found that the actual value can vary for 'Minor' even amongst non-synthetic atma. God help us expecting consistency out of SE ;D Synthetic atma still seem to have more conservative values though, except perhaps the Quest+Dominion obtained ones.

**Kirschy** · 2011-02-14 20:15

Ah I see. I was realli confused -_-

**Byrthnoth** · 2011-02-14 21:02

What do you mean? 494 (the average I posted in the previous post) is what I would predict for capped cRatio if pDIF could be 2.5 to 3.5 (with 3.0 being the cap pre-randomizer). Half are capped to 3, half are below (2.5 being the minimum).

Err... I've had a few glasses of wine, but I'll try to make this coherent.

If you assume an even (flat) distribution of values for the 1.00 to 1.05 multiplier, then values at and above 3 that result from 3.0*(1 to 1.05 multiplier) should occur with even probability. Similarly, low values of pDIF*multiplier (2.5 to 2.625) have been skewed upwards by this same even distribution. So if you take the residual occurrences after you remove the effects of the multiplier (by subtracting a constant number of occurrences that would be the number of legit capped 3.0s from the values above 3), then you have non-legit values that were pushed up from lower numbers. You can move those to the lower end of the distribution to effectively eliminate the 1 to 1.05 multiplier.

If you assume a 3.15 frequency of 63 (59 shown in the parse) then it becomes an average frequency of 31 occurrences per data point pDIF (pre-randomizer) value. Observe below:
http://i318.photobucket.com/albums/m...garu/graph.jpg

Anyway, that's a way to remove the effect of the 1.05 multiplier, depending on your faith in your own ability to eyeball shit.

**Raelia** · 2011-02-14 23:14

Not sure if I stepped on your toes or whatever, my post was just to establish Kirschy's base damage and Ratio value. FStr was certainly capped due to massive +STR, but the scaling of mob defense certainly has not slacked. This is not an argument, it is communal speculation and discussion.

We're not really interested in removing the 5% secondary randomizer anyway

What I can tell you, however, is that the upper range of uncapped crits is going to throw a loose bellcurve under that flat distribution you show, centered on average pDIF, and you can actually see it in Kirschy's graph. It's just interesting. The extremeness of the peak is probably related to how close her average crit pDIF was to 3.0, where if you really exceed it you have far fewer of those just-under-cap values pushing it up.

If you want to work with average pDIF (that is, pDIF=cRatio, as is oft used on parse analysis) you have to remove the 5% randomization using instead a 1.025 factor, the average of the secondary.

If Kirschy's lowest pre-crit pDIF recorded was 1.50, that points to a ratio of 1.5/0.8 = 1.875. Plug this in to find the percentage of capped crits for this value:
1.875 * 1.2 + 1.0 = 3.25
1.875 * 0.8 + 1.0 = 2.5
Spread: 0.75
Do remember that secondary randomization comes after capping, and so is not incorporated here.
[ 2.857 - 2.5 ] / 0.75 = 47.6% always uncapped
[ 3.25 - 3.00 ] / 0.75 = 33.3% always capped
19.1% split between each.
= 57.15%
= 42.85%

So the split is a little flipped, but using this as a model I could decide how to back-calculate what we want if it were useful anyway beyond calculating the mob's defense with a known attack.

It's just fun to practice again. Good data is like a new sex toy - you wanna find all the ways you can use it ;D

**Raelia** · 2011-02-14 23:16

Might as well use this space.

I suppose you were asking why and whatfor I used 494.

93+10, 103 DMG weapon, WRank 11 capped fSTR = 11+8

122 base damage * 3.0 * 1.35 = 494.1

Small perturbations will still cause many 494 damage hits to appear. Because Kirshy's numbers show a very apparent and distinct break at 494 damage we can presume that the 3.0+ crits begin there, correlating with her calculated base damage and confirming her capped fSTR.

The distribution of her crits, however, indicated her to be quite a bit below capped Ratio. That's also why she has a few crits down around 2.5 pDIF, wherein if she was actually capped they would be no lower than 2.76 pDIF or ~454 damage.

**Byrthnoth** · 2011-02-14 23:31

Sorry, I wasn't trying to come off as toe-stepped-on, I just wanted to explain what you did. I'll interpret what you wrote some other night!

Okay, I guess it comes down to how much faith you have in the upper tier of min pDIF equations on the wiki at the moment. The last I remember, Masa was having trouble verifying high-pDIF values on higher level targets because it was hard to keep capped pDIF and stay alive on WAR/DNC against more formidable enemies.

If you predicted that Kirschy's pDIF ranged from 2.5 to 3.5 (with values above 3 floored to 3) then you'd get exactly the distribution she got after applying the 1~1.05 evenly distributed multiplier. It could also be some artifact of a variable pDIF, which we would could guess by looking at her average crit damage with Last Resort on the kparser buffs tab (if she used it).

**Raelia** · 2011-02-15 13:59

Originally Posted by Byrthnoth

If you predicted that Kirschy's pDIF ranged from 2.5 to 3.5 (with values above 3 floored to 3) then you'd get exactly the distribution she got after applying the 1~1.05 evenly distributed multiplier. It could also be some artifact of a variable pDIF, which we would could guess by looking at her average crit damage with Last Resort on the kparser buffs tab (if she used it).

Let's be very careful defining her pDIF range, however. Because she was uncapped it is indeterminate. I believe she was using Last Resort and other buffs and fighting mobs of various EM and below levels, and her high/low spread is out of the range you'd see with a fixed Ratio. Her low end is 1.5-2.36 pre-crit pDIF and her high-end is indeterminate or approaching cap (1.76-2.77). You can not properly call the entire set her 'pDIF range'.

Masa's problems were order-of-operations and a closed mind. Where we all now look at 2.772 and the method I showed (2.2*1.2*1.05) and go 'Oh, now I see where that number comes from!', he harped on testing and cooking up horrendous three-digit-decimals.

**mdkuser** · 2011-02-15 14:17

Her pdif is clearly far from being capped and that would be easily checked by posting the non critical data. One common mistake I tend to read on this forum is people assuming their pdif is capped because they reach the 3.15 magic number.

**Kirschy** · 2011-02-19 15:19

Ran a test using Lv85 apoc to find relic proc rate and got some data to post. It was slightly more controlled this time, I used more attack, and used Red Curry Buns. I took out the Piasa fights, and the relic proc crits. In total, 1451 crits.

http://img510.imageshack.us/img510/6434/pdif2.png

PDIF data: (comma delimited)

Spoiler: show

Other than PDIF stuffs and relic proc data, I decided to get a bit more info on lights. I recognize the data sample size is low, but I still think the data is somewhat interested.

-Piasa's Birds.
-No WS were used at all, meaning almost every fight ended with a melee hit.
-I key'd every blue chest
-I left every red chest
-I marked down on paper every gold chest
-I re-entered once.
-I have all 3x of each chest abyssite.

Total fights: 175
Total melee kills: 173 (The other 2 were counter kills I believe.)

Pearl Lights: 57 (57/173 = ~32.9% chance for pearl off a melee hit... or 1/3)

Total number of chests: 119
Total number of blue chests: 67 (67/119 = 56.3%)
Total number of gold chests: 13 (13/119 = 10.9%)
Total number of red chests: 39 (39/119 = 32.8%)

Since I blind key'd the blue chests, and wasn't paying a ton of attention, I couldn't get a decent tally on the blue chest distribution for Temps/Restore. But it was very easy to go back into my logs to get Limit/Curor bonus. Keep in my mind I had no azure light at any time.

-XP Chest: 13 (13/67 = 19.4%)
--250 limit: 4
--500 limit: 7
--750 limit: 1
--1000 limit: 1
--1250 limit: 0
-Curor Chest: 14 (14/67 = 20.9%)
--200 curor: 4
--400 curor: 6
--600 curor: 1
--800 curor: 1
--1000 curor: 2

I don't have a base to compare it to, but it seems the abyssite raise the chance of getting at least 1 higher tier on the chest by around 75%, and the breakdown from there seems to be a high chance for only 1 tier, and a much smaller chance to get anything higher. The data size is just too small for anything specific.

**Raelia** · 2011-02-19 19:04

Same analysis as before:

130+8+14 = 152 DMG

(( 2.2 * 0.8 ) + 1.0 ) * 1.35 * 152
pCritmin = 566

3.0 * 1.35 * 152
3.0 = 615

3.0 * 1.05 * 1.35 * 152
pCritmax = 646

There's only a 0.38 margin above 646 to reach it as a maximum, so 645 is acceptable.
Your 3.0+ jump is at 615, as predicted with capped fSTR
Your minimum, however, bugs me.

544 / 152 / 1.35 / 1.025 = pDif of 1.65, meaning your ratio dipped as low as 1.65/0.8 = ~2.0 at some point. This is the maximum ratio to still crit that low, it could have been lower.

Or you may have caught a Tough which could have been 4 levels above you, dumping your 2.2 ratio to a 2.0 cRatio. Abyssea mobs make pretty large jumps in level when 'evolving' as you kill them, but you had more than a few crits below capped ratio minimum. Were you /checking often?

I know it's hard to keep ratio capped, it's just a major pitfall to parsing like this. It's just too easy for someone to come along and point this out after other speculations and make everything suspect.

Proposition: Eliminate the fights where you had crits below 566 and show what and how much data you have left.

Other suggestions: Bring a Corsair along for Chaos Roll and with even regular +% food you should be almost undeniably capped. If you were Mithra I could suggest Blackened Frogs for their uncapped awesomeness (I keep a stack stashed).

**Kirschy** · 2011-02-19 21:04

Originally Posted by Raelia

Same analysis as before:

130+8+14 = 152 DMG

(( 2.2 * 0.8 ) + 1.0 ) * 1.35 * 152
pCritmin = 566

3.0 * 1.35 * 152
3.0 = 615

3.0 * 1.05 * 1.35 * 152
pCritmax = 646

There's only a 0.38 margin above 646 to reach it as a maximum, so 645 is acceptable.
Your 3.0+ jump is at 615, as predicted with capped fSTR
Your minimum, however, bugs me.

544 / 152 / 1.35 / 1.025 = pDif of 1.65, meaning your ratio dipped as low as 1.65/0.8 = ~2.0 at some point. This is the maximum ratio to still crit that low, it could have been lower.

Or you may have caught a Tough which could have been 4 levels above you, dumping your 2.2 ratio to a 2.0 cRatio. Abyssea mobs make pretty large jumps in level when 'evolving' as you kill them, but you had more than a few crits below capped ratio minimum. Were you /checking often?

I know it's hard to keep ratio capped, it's just a major pitfall to parsing like this. It's just too easy for someone to come along and point this out after other speculations and make everything suspect.

Proposition: Eliminate the fights where you had crits below 566 and show what and how much data you have left.

Other suggestions: Bring a Corsair along for Chaos Roll and with even regular +% food you should be almost undeniably capped. If you were Mithra I could suggest Blackened Frogs for their uncapped awesomeness (I keep a stack stashed).

I can play with the data later for ya later, but I was using Red Curry buns... and the birds definitely cap at lv90, they never go above Even Match, so there's no level correction.

**Xilk** · 2011-02-21 05:55

for what its worth, I've checked mobs in Visions zones while exp'ing trying to get max level. Everything I've seen so far caps at 90.

**Raelia** · 2011-02-21 07:26

Originally Posted by Xilk

for what its worth, I've checked mobs in Visions zones while exp'ing trying to get max level. Everything I've seen so far caps at 90.

I wasn't too much in doubt of that, was just a convenient possibility after noting a probable 2.0 cRatio.

I noticed there's no easy way to trace a given damage instance back to the fight in which it took place in KParser to eliminate the fights with sub-566 crits. You don't have to go through that much trouble to sate my curiosity, Kirschy.

**Kirschy** · 2011-02-21 10:29

Originally Posted by Raelia

I wasn't too much in doubt of that, was just a convenient possibility after noting a probable 2.0 cRatio.

I noticed there's no easy way to trace a given damage instance back to the fight in which it took place in KParser to eliminate the fights with sub-566 crits. You don't have to go through that much trouble to sate my curiosity, Kirschy.

I'm sorry, I completely forgot to look up the info. I went back through my logs and did a search for the 544 value:

[11:25:43]Kirschy scores a critical hit!
[11:25:43]The Geier takes 637 points of damage.
[11:25:44]Kirschy's Food effect wears off.
[11:25:45]Kirschy's Stoneskin effect wears off.
[11:25:45]The Geier scores a critical hit!
[11:25:45]Kirschy takes 0 points of damage.
[11:25:46]Kirschy scores a critical hit!
[11:25:46]The Geier takes 548 points of damage.
[11:25:46]The Geier readies Helldive.
[11:25:46]The Geier hits Kirschy for 82 points of damage.
[11:25:48]Kirschy uses a red curry bun.
[11:25:48]Kirschy gains 135 limit points.
[11:25:48]yKirschy obtained 25 cruor.
[11:25:48]Kirschy's body emits a faint pearlescent light!
[11:25:48]Kirschy scores a critical hit!
[11:25:48]The Geier takes 544 points of damage.
[11:25:49]Hesasa casts Cure V.

Seems the 548 hit was also when my RCB wore off. I guess you can take those two out of the data pool. The 549 values were all with food/hasso on. I can't think of anything else that would affect the values aside from that.

**Appie** · 2011-02-22 17:42

Not to hijack the thread, but since it was already talked about on the first page, thought I might as well place it here.

I did the full counter test. And it looks pretty conclusive to me. Abyssea Vunkerl on bunnies. This is with Relic shoes stance (60%), Roaring Laughter (+10?), Gnarled Horn (+10), Lv90 Spharai (+11), Merits (duh) (+5), Ultion Mantle (+2), Temple Hose +1 (+3), Usukane Gote (+2), fulltimed on TP and WS to be safe. Yes this is way overkill, but I'm unsure what the exact buff is from Roaring Laughter, so I placed some buffer, which wasn't needed, at all:

Code:

Damage Taken

Damage Taken Summary
Player             Total Dmg   Damage %   Melee Dmg   Range Dmg   Abil. Dmg  WSkill Dmg   Spell Dmg  Other Dmg
Appie                  28238   100,00 %       28238           0           0           0           0          0
Total                  28238   100,00 %       28238           0           0           0           0          0


Melee Damage Taken
Player             Melee Dmg   Melee %   Hit/Miss   M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Appie                  28238  100,00 %    158/649     75/221   178,01      1   291/291  291,00    0,63 %


Defenses

Passive Defenses
Player             Evasion  Evasion %   Parry  Parry %   Counter  Counter %   Intimidate  Intimidate %
Appie                  177    21,93 %       0   0,00 %       472    74,92 %            0        0,00 %

Acc:

Code:

Melee Damage
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
Appie                416613   64,34 %   1919/112   94,49 %     0/667   165,21    815   118/948  287,39   42,47 %

So ya, caps at 80% by the looks of it, so no near invincble MNK. The theory of mobs getting at least 20% hitrate looks true. I don't know (yet) wether Perfect Counter would bypass this cap. I'm only doing that test if people want it tested, I personally use it mostly for when I need to counter, the nice spike damage isn't very high on my agenda to spam it and then be without when I would need it.

This does however make GH close to useless for relic monks, so best option is to equip VV? Now the shit Spharai buff at lv90 of 11% suddenly makes sense, since it would make 15% at 99 most likely, making you capped with just 1 equipment piece and merits.

I do wonder however where the +3 counter trait buff falls into place in all this. I don't know if stance simply bypasses that stuff and simply goes to 60% or that it goes to 63% now? Iirc it does bypass the lv10 base trait doesn't it? It's been ages since I read up on this shit that I only use the numbers 60% for stance and 10% for the lv10 trait. I'll give that test a whirl maybe tomorrow with no counter atma's, unless somebody here can already give me an answer.

**Cream Soda** · 2011-02-22 18:02

This does however make GH close to useless for relic monks, so best option is to equip VV?

Best option would be to get vereth.

Second best option, assuming the cap is conclusive, would be to use VV (well actually the one w/ trip attack and hp- is better but it has hp-)

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