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Zanshin proc rate and accuracy bonusFollow

#1 Nov 07 2009 at 7:45 PM Rating: Excellent
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So, I've been helping test crit rates over on BG. In doing so, a crafty trick was discovered (or rediscovered) to test by using a 0 damage weapon (d1, fStr -1) against Hpemdes in sea. I decided to use this to test Zanshin, since I've been curious about exact values, and it's come up a few times in recent discussions.

The below test was completed in roughly 20 hours against a level 72 Ul'hpemde. I set up as Sam/Blm, no Brutal, no accuracy/dex gear and -acc rings, in order to minimize hit rate and ensure no other source of double attack. The results are from the Extra Attacks plugin of KParser (including an extra bit of collated info that I wrote up and will be included in the next release). I removed the DA/TA/Kicks sections as they aren't relevant to this test.

Basic Data 
 
Player               # Melee Attacks    # Melee Rounds    Attacks/Round    # Extra Attacks 
Motenten                       31100             25410                1               5690 
 
Player               # +1 Rounds   # +2 Rounds   # +3 Rounds   # +4 Rounds    # >+4 Rounds 
Motenten                    5685             1             1             0               0 
 
Player               # MultiAttack Rounds    MultiAttack %     Kills w/Min Attacks    Kills w/<Min Attacks 
Motenten                             5687          22.38 %                       0                       0 
 
 
Treat As: 
 
Multi-attacks per attack (Zanshin): 
 
Player               # Missed First Attacks    # DA w/Missed First   Possible Zanshin % 
Motenten                              12636                   5680              44.95 % 
 
Player               Acc. Rate of First Attacks    Acc. Rate of Second Attacks 
Motenten                                50.27 %                        66.67 %



25,410 melee rounds. 12,636 of those missed the first attack, so 12,774 hit, giving a 50.27% hit rate on the first round with a 0.61% confidence interval. Predicted hit rate based on acc vs evasion should be 50.0%.

There were 5680 rounds that had a DA after the first attack in the round missed (12,636) -- that is, Zanshin procs. Zanshin rate is thus 44.95% with a 0.87% confidence interval.

Of the 5680 Zanshin procs, 3787 connected (not shown, but extrapolated from the acc rate on second attacks). This gives a 66.67% hit rate with a 1.23% confidence interval.

Accuracy bonus from Zanshin is thus between 15.44% and 17.90% hit rate, or between 31 and 35 acc. 35 seems the most probable 'round' number in that range.


You'll note that there are reported to be 5690 extra attacks, whereas there were only 5680 Zanshin proc rounds. In the second row you'll see that there was one +2 round and one +3 round (ie: rounds with 3 and 4 attacks). This is obviously a parser error. The Zanshin numbers are restricted to only rounds with 2 attacks, so those mistaken multi-attack rounds won't affect the Zanshin outcome.

There are also five +1 rounds (two attacks) where the first attack was not missed. Again, parser error. The second attacks of those rounds will also have no impact on the Zanshin results because the first hit of those rounds wasn't missed.


Summary: Zanshin proc rate at level 75 is 45%, and provides a +35 acc bonus to the Zanshin hit (subject to correction based on additional sampling).

I also plotted out the effect of the extra attacks and accuracy bonus in Excel across all base hit rates. Excluding the impact of Double Attack traits and gear, Zanshin is effectively the same as a War's Double Attack trait (+10%) when base hit rate is 81%. It's the same as a +20% DA rate when base hit rate is 65%. At 90% base hit rate, Zanshin is the equivalent of +4.75% DA, and at capped accuracy it's +2.25% DA.

It is better to treat the effect of Zanshin as if it were +DA rather than +Acc, in terms of impact on damage. Zanshin does not allow your hit rate to go above the 95% hard cap, for example, although it does raise your average hit rate in any instance when you are not capped. Instead, it gives you more chances to swing, and a better chance to hit on those swings.


Extra trivia: The maximum number of extra hits (not just swings) due to Zanshin occurs at 41% base hit rate, where it reaches 155.3 out of 1000 rounds. The percentage of extra damage due to extra Zanshin hits, though, declines all the way from 20% hit rate (where Zanshin increases melee damage/TP by 67.5%) up to capped accuracy (where Zanshin gives the above mentioned +2.25%).


Edit: Bah, messed up some of the numbers. Fixing.

Edited, Nov 7th 2009 7:58pm by Kinematics

Edited, Nov 7th 2009 8:05pm by Kinematics
#2 Nov 07 2009 at 11:46 PM Rating: Excellent
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Very awesome work Kinematics as always. Thank you for putting sometime and research into this.

From what I gather from this data. Nothing really changes the view that we have all had on zanshin. Yes it can be good however there shouldnt be a reason to gear/merit around it. Its not to hard for most Sams to get 85~90%acc so that would give us basically a brutal earring on us as far as zanshin affect goes? Anything higher and its basically having a pole grip? I hope Im reading the data right and not misinterpreting it. Good data though.
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#3 Nov 08 2009 at 1:40 AM Rating: Excellent
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It doesn't change anything in terms of how you gear, no, but it does indicate that the trait itself provides a pretty respectable benefit. Also, with numbers available you can show exactly what effect Zanshin has on gear changes instead of just hand-waving it all away.

For example, how much is +5 Zanshin (such as what you'd get with maxed merits) actually worth in terms of final damage? +5 Zanshin would take it from a 45% activation rate to a 50% activation rate. I'll just plug that into my Excel spreadsheet cause I don't feel like doing the math by hand (number of additional hits can be directly correlated to total damage because they provide TP for weaponskills as well):

Hit rate    % Improvement 
60%         2.10% 
61%         2.05% 
62%         2.00% 
63%         1.95% 
64%         1.90% 
65%         1.85% 
66%         1.80% 
67%         1.75% 
68%         1.70% 
69%         1.65% 
70%         1.60% 
71%         1.55% 
72%         1.50% 
73%         1.45% 
74%         1.40% 
75%         1.35% 
76%         1.30% 
77%         1.25% 
78%         1.20% 
79%         1.13% 
80%         1.07% 
81%         1.01% 
82%         0.95% 
83%         0.89% 
84%         0.84% 
85%         0.78% 
86%         0.72% 
87%         0.67% 
88%         0.61% 
89%         0.56% 
90%         0.50% 
91%         0.45% 
92%         0.40% 
93%         0.35% 
94%         0.30% 
95%         0.24%


Hit rate is the base hit rate, not the parsed hit rate, since the parsed hit rate will be inflated by Zanshin itself.

This could also be used to calculate the benefit of Ikishoten. Ikishoten can be considered 1 extra hit's worth of TP for every Zanshin hit, so total TP percent increase is (Zanshin hits + (Zanshin + Base hits)) / (Zanshin + Base hits).

Hit rate    % Add'l TP 
80%              9.66% 
81%              9.11% 
82%              8.58% 
83%              8.05% 
84%              7.53% 
85%              7.01% 
86%              6.51% 
87%              6.00% 
88%              5.51% 
89%              5.02% 
90%              4.53% 
91%              4.06% 
92%              3.58% 
93%              3.12% 
94%              2.66% 
95%              2.20%



And then scaled relative to total weaponskill damage percentage.


Of course the regular Double Attack trait (Brutal or /war) complicates all of this, but we can at least be sure of the basic benefit.




Edited, Nov 8th 2009 1:45am by Kinematics
#4 Nov 08 2009 at 7:00 AM Rating: Excellent
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Additional considerations: The impact of Zanshin on the value of Accuracy to a sam.


Thinking over the numbers, I realized that the value of the accuracy stat itself is significantly affected by these findings. I put together a chart in Excel and determined that the value of accuracy is, point for point, about 50%-60% of the value of accuracy as a stat for any other job.

Here's the chart, using 75% hit rate as the baseline. The total hits with Zanshin are pulled from my other calculations, and are a count of hits out of 1000 rounds at a given hit rate.

Baseline:   75%                                                                                
            Based only on Acc:                                                      Based on Total hits: 
Hit rate    % Total Improvement   % Marginal Improvement    Total Hits w/Zanshin    % Marginal Improvement 
75%         0%                    0                         854.0625                0 
76%         1%                    1.33%                     860.98                  0.81% 
77%         3%                    1.32%                     867.8075                0.79% 
78%         4%                    1.30%                     874.05                  0.72% 
79%         5%                    1.28%                     879.775                 0.65% 
80%         7%                    1.27%                     885.5                   0.65% 
81%         8%                    1.25%                     891.225                 0.65% 
82%         9%                    1.23%                     896.95                  0.64% 
83%         11%                   1.22%                     902.675                 0.64% 
84%         12%                   1.20%                     908.4                   0.63% 
85%         13%                   1.19%                     914.125                 0.63% 
86%         15%                   1.18%                     919.85                  0.63% 
87%         16%                   1.16%                     925.575                 0.62% 
88%         17%                   1.15%                     931.3                   0.62% 
89%         19%                   1.14%                     937.025                 0.61% 
90%         20%                   1.12%                     942.75                  0.61% 
91%         21%                   1.11%                     948.475                 0.61% 
92%         23%                   1.10%                     954.2                   0.60% 
93%         24%                   1.09%                     959.925                 0.60% 
94%         25%                   1.08%                     965.65                  0.60% 
95%         27%                   1.06%                     971.375                 0.59%




As you can see, once you reach 79% hit rate (the point at which Zanshin's acc bonus pushes Zanshin hits' acc past the acc cap), the value of each 2 points of acc (1% hit rate) is at most +0.65%.

To put it in comparison, consider the typical choice between OHat and Turban, assuming you have a base accuracy of 80% without any headgear. For most jobs the OHat would be worth 85%/80% = +6.25% damage, which is matched by haste when you have 20% haste after adding the Turban.

For sam, however, the OHat is worth 914.125/885.5 = +3.23% total damage. You'd actually have to be heavily slowed (~50% slow, total) before the OHat would win over the Turban.

Which of course leads to the piece of equipment that is central to all sams' lives, the Haubergeon. 13.75 accuracy, will round up to 14 accuracy. That's +7% hit rate. Will assume base hit rate without a body piece is 80%. That's worth +4.5% total damage (+5.2% for the HQ), not the traditionally attributed 8.75% (10% for HQ) (values go down, of course, as you approach the acc cap).

For the lol comparison with Askar, for someone without a Rajas with the choice between hauby + rose grip vs askar + pole grip, the difference is the value of 4% DA and 2 att vs that aforementioned 4.75% bonus from the hauby's accuracy. The hauby setup is still ahead, but the difference is barely 1%, not the huge margin it's usually treated as.

On the other hand, Askar hands fall further behind Dusk Gloves (aside from the movement speed issue), since the acc from the dex is worth barely 1.25% total damage in the mid-80's rather than ~2.4%.

And for the Askar head vs Turban, the 1% extra haste on the turban begins to outperform the str+dex at about 50% total haste instead of needing to be near 70% haste or so.

I'm sure other gear will come up that needs to be reconsidered. These are just the first things that come to mind. Plus someone needs to be more motivated than me and look at the impact DA has on these numbers. I might get to that later today, after some sleep.

Edited, Nov 8th 2009 2:57pm by Kinematics
#5 Nov 08 2009 at 9:43 AM Rating: Good
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This needs to be added to a sticky. Was a great read, thx Kinematics.
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#6 Nov 08 2009 at 10:52 PM Rating: Excellent
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Wrote up and posted a bunch more tabular data on the BG thread on this (http://www.bluegartrls.com/forum/84153-zanshin-proc-rate-accuracy-bonus.html), but it's big and wouldn't fit well here. So just adding a quick summary here based on the additional impact of DA, and the results when subbing sam.

The more DA you have, the less improvement in average accuracy Zanshin causes. The difference between DA proc'ing first and Zanshin proc'ing first is minimal for most hit rates of interest (70%+).

Currently it looks like Zanshin rate while subbing sam is 25%, while still getting the same +35 acc bonus applied.

So, Value of Accuracy (stat):

As sam with no DA: about 55% of face value
As sam with Brutal/Pole Grip: about 60% of face value
As sam/war with Brutal/Pole Grip: about 65% of face value
As any job subbing sam: about 75% of face value


Illustration:

Adding 12 acc to a sam/war gives about the same improvement in total damage as adding 8 acc to mnk.
Adding 10 acc to a sam/not-war gives about the same improvement in total damage as adding 6 acc to mnk.
Adding 12 acc to anyjob/sam (war, drg, drk mainly) gives about the same improvement in total damage as adding 9 acc to mnk.
#7 Nov 09 2009 at 1:22 AM Rating: Good
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Excellent stuff, thanks a lot for this information, Kinematics.
#8 Nov 10 2009 at 7:44 PM Rating: Decent
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So...does this mean Zanshin is no longer lolzanshin, or a 'holy crap, it might actually have a benefit' zanshin?

Of course, eventually I'll grasp what all that math just said once I look it over twenty times. I haven't been playing lately due to work. >.<

And did we ever determine if Zanshin procs during a WS?

Edited, Nov 10th 2009 7:46pm by Nohytuu
#9 Nov 11 2009 at 12:59 AM Rating: Good
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Nohytuu wrote:
So...does this mean Zanshin is no longer lolzanshin, or a 'holy crap, it might actually have a benefit' zanshin?

Of course, eventually I'll grasp what all that math just said once I look it over twenty times. I haven't been playing lately due to work. >.<

And did we ever determine if Zanshin procs during a WS?

Edited, Nov 10th 2009 7:46pm by Nohytuu


no, regarding meriting zanshin or buying equip for the +zanshin it has, zanshin is as crushingly lol as it's ever been. also, it's likely that zanshin can't proc on WS, but hard to tell since y/g/k are all uniformly 95% ACC anyway.

however, this *does* show that (for example) my comments in a recent thread about zanshin never changing any gear comparisons were misguided. basically, in cases where +ACC vs +something else were a close comparison, the +something else is more likely to win if you consider zanshin. i can't think of concrete examples offhand, but there's bound to be some (askar body vs NQ haub in certain situations, probably).

edit: i say that it's likely that zanshin can't proc on WS b/c i've never got 1% TP return WSs while soloing SAM/DNC. people on ffxi wiki report otherwise, but to be blunt, i don't believe them. in the thread kinematics linked however, someone suggests a (i thought) rather ingenious way of testing for zanshin on WS: WSing mandragora. you can zanshin guarded hits even if you do damage. a 2-hit gekko (maybe with wooden katana? SAM/NIN vs black mandies?) with no DA gear would be definitive proof of zanshin on WS.

Edited, Nov 11th 2009 2:13am by milich
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#10 Nov 11 2009 at 3:04 AM Rating: Good
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Quote:
edit: i say that it's likely that zanshin can't proc on WS b/c i've never got 1% TP return WSs while soloing SAM/DNC. people on ffxi wiki report otherwise, but to be blunt, i don't believe them.


I'm also very dubious on whether Zanny can proc on WS, but when it comes to SAM/DNC solo - don't you equip Brutal?

I was thinking I can't remember seeing a 1% return whilst I went through the campaign medals, but thats prob just my memory playin alcholic tricks on me, but Brutal is the one piece of equipment (like Rajas) that never seems to come off (except for AF)
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#11 Nov 11 2009 at 3:11 AM Rating: Good
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Sandmasterr wrote:
Quote:
edit: i say that it's likely that zanshin can't proc on WS b/c i've never got 1% TP return WSs while soloing SAM/DNC. people on ffxi wiki report otherwise, but to be blunt, i don't believe them.


I'm also very dubious on whether Zanny can proc on WS, but when it comes to SAM/DNC solo - don't you equip Brutal?

I was thinking I can't remember seeing a 1% return whilst I went through the campaign medals, but thats prob just my memory playin alcholic tricks on me, but Brutal is the one piece of equipment (like Rajas) that never seems to come off (except for AF)


i do, but i don't think it's too likely to see my 5% DA kicking in at the same time as my 5% miss chance. possible (inevitable, really), but if i saw it a lot, i'd think it was zanshin.
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#12 Nov 11 2009 at 8:04 AM Rating: Decent
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Yeah, meriting Zanshin is still lol, but I wasn't aware that the Zanshin swings have an accuracy bonus, spiffy

As far as testing on whether or not Zanshin can proc on WS, a good way to do it might be to try to WS targets that have one Utsusemi shadow remaining. From what I've read elsewhere, standard swings that miss due to Utsusemi do allow Zanshin to proc. While the rules might work differently for WS, my guess is that if Zanshin could normally proc on a WS, it should also proc in this fashion. If it can't, then Zanshin probably never procs on a WS period.

Edited, Nov 11th 2009 9:13am by Fynlar
#13 Nov 12 2009 at 9:24 AM Rating: Decent
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A crafty trick method of testing indeed. I wonder what sly genius 'discovered' it and thought to apply it to the crit testing in the first place. Smiley: tongue
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