Shield Skill's effect on block rate

[Martel]

Reposting my post from over at FFXIAH over here.

Looking at showmo's test and speculation again, I decided to look through some of the test data I had lying around. I did these test back at lvl 90 but never analyzed the data closely enough to figure block rate vs skill.

I'm only posting results atm, not raw parse data. If there are doubts about any of this, I can dig the parses out. But I pulled this from the spreadsheet I recorded the results to. Besides, that'd be a hell of a lot of parse data. 16k~ hits worth. It'd make things messy.

LVL 90 shield tests
Even Match Monitors, Abyssea Grauberg

Koenig(size 3)
Skill	369(+00)	379(+10)	389(+20)	399(+30)	417(+48)	420(+51)	
Block%	45.0%		46.5%		50.5%		52.4%		57.1%		57.6%
gain	00.0%		01.5%		05.1%		07.4%		12.0		12.6
hits	2860		2126		3086		3034		2049		3295

Tower Shield
Skill	369(+00)	420(+51)	
Block%	29.4%		43.9%
gain	00.0%		14.5%
hits	3093		3137

The size 3 data fits pretty nicely with the 4 skill=1% idea. 'Cept the +10 sample, but we could explain that as variance or lower sample size.

But the rest of the data points match pretty well. Skill+ / 4 = Block rate gain.

Now we need to know how mob lvl fits into that so we can predict block rate.

I still want more data. And more testing on various mob lvls to see if things change at different skill/mob levels. But this looks fairly good.

Now the Size 4 test doesn't quite match. It doesn't really have enough data points. And while 2% isn't a big difference, it's enough to make me wonder if skill works differently for different shield sizes. Although, since Showmo's test was with Aegis(size 5) and mine are size 3 there may be some evidence against that idea. Unless Aegis has the same skill mechanic a size 3, but with a higher base block rate.. ugh.. Too many possibilities.

Still, this is getting pretty interesting. Might do some more tests later. Getting more data on the lvl 95 skill range could be useful.

Links
My Test
Showmo's test

Maybe someone mathy over here can figure out how to apply lvl 90 mobs to this and get those block rates. Or I might need to get some lower and higher lvl mob data.

Anyway, it's not a complete model, but it seems like a good start.

[Martel]

I'm linking some more of my Shield testing from over at FFXIAH.com. I'm not gonna quote it in here, cause it's huge. I had to split it into 3 posts. One for conclusions and thoughts, and 2 for all the parse data. <,<

http://www.ffxiah.com/forum/topic/21...ies/8/#1608266

[Byrthnoth]

Wow, those experiments are heroic.

It might be worth verifying that there's no monster-type-specific component of block rate. Like, try finding another level 105 monster and blocking it at a known shield skill maybe?

[Martel]

Hmmm. That is a good point. The biggest issue though, is finding, and confirming a mobs lvl. At the moment, I'm not certain there Are any other non-NM lvl 105 mobs.

For this purpose, it'd probly simplest to just get a EM mandy, then I can compare that to my earlier tests on EM detectors. Although the old tests were at 90(369 skill) so I'd need to sync. ugh. Or find another lvl 95 mob to compare.

It'd be a fairly simple test... Assuming.. that the mob type block mod wasn't the same for those two types. lol. If there is such a thing, it could be like dmg resistances, where most mobs sit at the default value, but a few are strong/weak to it.

[Byrthnoth]

I can't think of any either. And yeah, there's always a chance that you'll be fighting the same type of mob if you only do two. It's better than one, though.

I'll probably keep updating this post as I think of things, but here's what I see so far:
* Level 95 Martel w/ Gleaming Shield and +0 Skill vs. Level 105 Crawler = 30.5% block rate +/- 1.5%
* Level 95 Martel w/ Gleaming Shield and +52 Skill vs. Level 105 Crawler = 41.6% block rate +/- 1.7% (I added this up twice)

So, there are two ways to look at this:
1) You've added the ~50 skill that you'd expect to get between level 95 and 105, so you should have restored your EM block rate (45.06%), but you didn't.
2) You've added 52 skill and predict +1%/+5 Skill, so you should have added 10% block rate, but you also probably didn't.

[Martel]

Regarding Option 1. A+ combat skills are going up by 7 per lvl right now, correct? This being the case a lvl 105 PLD would have 70 more skill than a 95(assuming no further skill gain changes).

So from that 20 additional skill we do 20/5 =4% so 41.6%+4%=45.6% which basically brings us back to the EM block rate. Thoughts?

Although, I still can't explain why I'm getting 12.6% outta that 52 skill rather than the expected 10%. can't say I'm all that unhappy with getting more block rate than expected. But it is confusing.

The size 3 test are rather lacking compared to the thoroughness of the Ochain tests. Not many points to compare.

[Martel]

Oh shit. Thanks for drawing my attention to this again. I found a mistake in my excel sheet where over 100~ hits had been excluded from the non block section. Updating materials.

[Byrthnoth]

I don't see very strong evidence for a change of slope at 400 skill.


Edit: I mean, I can see what you were going on, but I'd argue that your higher predicted slope is mostly due to your value at 399. It is probably a little high. I mean, you gain about 0.5% Shield skill between 399 and 404 skill, and 404 skill was tested twice. If we accept that 399 is high, then you get about the same slope even if you just fit the <400 skill range.

[Martel]

Huh, that is a niiice straight line. <,<;

So, I think what you're saying is that the 399 test just happened to come out a bit high, and it's just a bump, rather than a change in slope?

Honestly, I border on mathematically illiterate. It's surprising that I even thought I found something. This being why I usually just post data and let other ppl figure stuffs.

So, any idea how this might work then?

[Byrthnoth]

Yeah, each of your data points has a certain amount of variability in them (1~2% 95% confidence interval width), but they're more likely to fall at the middle of the distribution than the outside.

Look here. The higher your sample size (left graph), the more spread out the distribution is initially, but then eventually becomes a stable distribution of probabilities. When you count up the number of heads you get in 64 coin flips, in the left graph example, you're going to get one of the values on the x-axis. It's more likely it'll be towards the center than the outsides, but it still can be towards the outside.

Imagine that you toss your coins and get 23 Heads out of 64 tosses. That's on the low end of the blue n=64 distribution (the probability of it happening is low), but it's the result you got. That's why we use confidence intervals. If you take the 95% confidence interval around your low result, you are going to get something that includes 32 heads, the true mean. That's what it means to say "I'm 95% confident that the true mean is contained within 23/64 +/- 9 tosses."

So what I'm saying is, your 399 skill sample is likely "high" in that distribution. You tossed your coin 3000 times and came up with a 51.5% chance of heads instead of a 50% chance.

I'd propose that Shield Skill is linear with some modifier. I forgot about the 7/level thing, so how about this as the equation?:
Monster Level = ML
Paladin's current Shield Skill = Skill
Paladin's Shield Skill at a certain Level = PLD( Level )
Shield Type Base block rate = Base

( Skill - PLD(ML) )/4.6 + Base = Block Rate

If I'm not mistaken, there is a maximum block rate (below 100%) for shield types other than Ochain? So we would need to cap the "( Skill - PLD(ML) )*Slope" at some positive value?

Edit: Two more things
1) I'm betting O.chain's "Base" is either 95% or 100%.
2) It would be useful to know what the minimum block rate for shields in general is. Legion Scutum on a job without Shield Skill would be the best way to find out.

[Martel]

Hmmm. I think I understand basically what a confidence interval is, now. Just not how you get one. Any way, setting math aside briefly(I think i need to take some classes or something.)

I'm not quite certain how this formula is supposed to work. "Paladin's Shield Skill at a certain Level = PLD( Level )". Is that supposed to be the base skill for the PLD's current lvl, or?

There is supposed to be a block cap for non-Ochain shields. Generally believed to be about 65% for size 3 shields. But personally, I've never done a block cap test for them. And I don't recall seeing any good one's either.

That may be another thing for me to do. Test the cap, and determine at what point additional skill+ stops adding block rate.

A block rate floor test was part of my plans already. But I don't have a legion scutum. And BLU is my only high lvl, shield equipping job, that has no skill. And blu can't wear many shields. Hmmm.

[Byrthnoth]

I figure Legion might be good because it's a tower shield (easiest to see) and is already the lowest possible proc rate. I have two flayer pops, so I can try to get one if I can get some people to help me. The odds aren't very good though.

You can read it like:
Block Rate = (Current Shield Skill - The skill a capped Paladin would have at the Monster's level)/4.6 + Base

So, for instance:
Block Rate = 100% = (433 - 474)/4.6 + Base
100% = -9% + Base
109% = Base

Base is probably actually a minimum block rate + Shield Type Block Rate, which could be 10% + 100%, for instance.

[Martel]

Legion would be pretty ideal. I might have to try to get one myself. I might have a pop/partial lying around.

I wish I had DRK lvl'd now. They can wear lots of shields. Have no skill, and share lots of gear with PLD. And i could go DRK/PLD,RDM, etc to get low skill samples... aaaarrgh.
RDM has really bad skill, but really bad is not none. Although a test with 237 skill may yield some info.
BLU might be worthless without legion.. I can't think of a single size 3 or higher shield they can wear. And size 1 &2 are subject to overlap.

God, I'm kinda screwed on this test.

Ahhh, the new reading for the formula makes perfect sense now.

So now we need to discover the block floor, then test various shield types for their base rates. I'm just so screwed in not being able to test this...... If I end up lvling DRK..

BTW, I should note 474 would be a capped and merited PLD's skill. So - merits it'd be 466.

[Martel]

Oh, BLU can wear Acheron shield. It's not size 4, and it has +10 skill on it, but since it's size 3 I could actually get a test sample with it. Although I'm not certain that would tell us what we need to know.

[Mojo]

I'm a bit behind what's been posted and haven't really had time to read about the new data, but I'd just like to point out something I noticed in earlier tests regarding shield blocks and damage reduction. Any time you're looking at damage reduction, the minimum unblocked damage you take needs to exceed 100 damage per hit in order for any truncation error to be less than 1%. It certainly makes gathering data more difficult, but it's completely necessary if you want an accurate analysis on how shield blocks actually work.

[Foldypaws]

Not really. You can pull the actual value out of the average even if you can't tell from the min/max

Let's say my shield blocks, hypothetically, either 31% or 32%.

If incoming hits are a flat distribution from 40-50, blocked hits would have a range of 27-34 in both cases.

However, if you look at the value on each hit, you have (27,28,28,29,30,31,31,32,33,33,34) for the 31% reduction case, and (27,27,28,29,29,30,31,31,32,33,34) for the 32% reduction case.

The average in the first case is 30.55 damage/hit, the second case is 30.09 damage/hit.

You don't need the unblocked damage to be greater than 100 to figure out a 1% difference in damage reduction.

[Martel]

The primary goal of this round of testing was block rates and how skill/mob lvl affects them. While I could use some of this data for dmg reduction test(fuckers hit like trains even with PDT gear.) Actually, taking a look through the data, very little of it meets the 100 min req.some of the size 3 tests do look usable though.

My old tests on Detectors don't meet those requirements either. And those tests are where I got my current block dmg- numbers. They tended to avg about 100 dmg a hit, but 100 certainly wasn't the minimum..

I always did feel that my numbers for shield def bonus and the creed hands enhancement weren't accurate enough to be relied upon. Sonofa... another test project. Hmm... and trying to test with a sync'd at 75 for SDB.. oooohhh god.

Edit: Saw Foldy's post after I posted. Even if it's not absolutely necessary for the dmg to be that high, it would improve the accuracy if it was, no? If i was testing specifically for dmg- values, I think I'd push my dmg taken as high as I could reasonably survive.

[Foldypaws]

Edit: Saw Foldy's post after I posted. Even if it's not absolutely necessary for the dmg to be that high, it would improve the accuracy if it was, no? If i was testing specifically for dmg- values, I think I'd push my dmg taken as high as I could reasonably survive.

Not necessarily. High damage is necessary if your variance is low. If every hit does the same damage, you need 100 damage hits to reliably pick out 1% differences.

As the variance increases, you need a lower and lower average to pick up the same difference. If raising your damage doesn't also keep your variance the same or higher (which it should if you're using PDT gear to modify it, but not if you're using defense), then it helps, but remember that you're going to be dominated by the highest uncertainty between your sample size count, and your distribution variance.

It's almost certainly not worth tanking fewer mobs to increase damage taken, for example. I'm not sure whether you're doing this vs just one or multiple.

[Martel]

So a wider range of dmg is more accurate? Or just doesn't require as high dmg per hit? I'm not sure how I'd influence the dmg variance of a parse sample.

Would it be best to ignore crits for this sort of thing? As they have a different dmg range/distribution, and a much smaller sample.

I figured out a way to fairly reliable automate the curing aspect of my testing. So using 1~2 mobs lets me start it then afk for a few hours till its done. Whereas faster methods get increasingly more intense. Kinda an effort vs time thing.

[Foldypaws]

crits probably aren't going to be so useful.

You could influence the damage variance with defense. It's probably not worth it though, as I pointed out, a damage variance of 10 at 45 damage average is enough to pick out 1% differences. I'm sure any sample you use will have significantly more than a range of 10, and probably more than an average of 45.

I just brought it up because it was asserted that you need over 100, which you absolutely don't.