Physical Damage Limit +%

I wanted to explain in simple way how Physical Damage Limit +% (PDL) works, because someone asked me this on PM and I thought it will be better to answer it like this, so more people can find a way back to this info if needed.

1. How it works?

First I need to simply explain whats pDIF. For details check this https://www.bg-wiki.com/ffxi/PDIF Simply put it, it's variable that multiply our damage and is based on ratio of our attack to monster's defense. Depends on that ratio, there might be randomization going on to receive the final pDIF value. We don't really care about this randomization for this discussion tho, because it's not really relevant for PDL (there is another small randomization of +0~5% for melee weapons, but it's also not really relevant for this topic, because it's separate factor that happens anyway). What we care for PDL is pDIF cap. pDIF caps for individual weapon types and jobs can be found in the same bg wiki link I posted.

To make it simple I will exclude most other factors and write it like this:

PDL+% is simply a direct multiplier to pDIF cap, which means it lets you reach higher pdif values, but doesn't help you to reach them. You must have enough ratio of your attack to monster defense I mentioned earlier, to take advantage of that higher pDIF cap provided with PDL+%.

So if you don't have enough ratio to reach pDIF cap, PDL+% won't affect your damage at all.

PDL+% effect can be then wrote like this:

2. Crit factor and examples

Melee crit pDIF cap is basically non-crit pDIF cap +1. This means PDL+% is less effective for melee crits, than for melee non-crits.
It will be easier to understand looking at examples:

BLU pdif caps for Sword without any PDL+% would be:
With PDL+20% it would be:
Like you see with PDL+20%, pDIF cap for non-crit hits raised by 20%, while for crits it only raised by ~15.3% ( 4.9/4.25 ), which is a consequence of PDL+% being applied before that static +1.

For ranged critical hits PDL+% is as effective as for ranged non-critical hits, because critical pDIF cap is calculated with non-crit pDIF cap x 1.25

So for example PDL+20% on RNG with Gun would increase both non-crit pDIF cap and crit pDIF cap by 20%:

If something is still not clear enough, please post your questions below.

An implication here is that WSs with large attack boosts (Howling Fist, Ascetic's Fury, Mandalic Stab, Ground Strike, Blade: Kamu, etc.) are more likely to benefit from PDL gear.

However, it is worthwhile to note the conflict of using PDL gear. If you are already doing good damage, you are probably capped cRario and PDL will help you do better damage. If you are doing shitty damage, you are probably uncapped attack and PDL will not help you at all and tradeoffs you make to get it will probably not be worth it. This is true even for WSs with moderate attack boosts (basically everything except Ascetic's Fury and Blade: Kamu). So PDL gear helps you boost your DPS when your DPS is already high, which makes it very useful for extreme zergs (but extreme zergs are uncommon.)

So PDL gear is good when doing old content or some new content when using SP buffs and strong debuffs. In those cases, it can be a substantial boost to your damage. However, I personally do not care about doing an extra 15% damage in old content and am rarely doing Sheol - Gaol with SPs. Most of the time, PDL gear is not worth using for PDL for me. This is something you should have special builds for if you do that content, not full-time.

This is a little exaggeration.

You don't need SP buffs and strong debuffs to overcap attack in all new content. Also SP buffs arent that uncommon. Half of the Shaol C runs are with SP buffs and lower floors don't require sp buffs to cap attack on many jobs.

What is other new content anyway?


Why? Most people use SPs in Shaol-Gaol. What's the point of not using them there?

Seems like exemplar point parties would be a pretty common use case for PDL gear.

I definitely appreciate the more detailed and analytical explanation, goes far beyond my typical answer when asked about +PDL and I just compare it to switching from a 20oz cup to a 32oz cup. Its just a larger cup, and without extra liquid in it, there's no difference seen.

Thank you for doing this Simon

If I did Sheol - Gaol, I certainly would. I just don't have a group and cannot invest the regular time I would need to make one. Without meaningful Sheol - C farming (been doing MM) and a mule GEO, the number of times I am attack capped in a week can be counted on one hand.

Omen, Dynamis D, Ambuscade, etc. all still exist.

You often attack cap in those without SPs as well.

Does the amount of atk you need on crits go up with the change to pdif (think mighty strikes or like crit based builds on something like AM3 builds). Or does it not matter and if you're capped on non-crit you should be good on crit. Also do you have any data or math on when diminishing returns in WS sets start to appear between stacking WSD/WSC/PDL.

Pdif Caps at same amount of attack for crits and non crits.

As to Diminishing returns your best bet is to either use one of the spreadsheets/simulators floating around or test it yourself. Or we could get into a long drawn out conversation about what really is Diminishing returns or what are reasonable situations/buffs. A lot of situations will favor wildly different optimal gear sets especially when it comes to PDL.

I would also note that when Simon Ses says "This means PDL+% is less effective for melee crits, than for melee non-crits." this is true in a percentage sense, but if you think of it as the PDL added say 100 damage on average to your non crit damage, it still adds 100 damage on average to your crit damage as well its just that it's a smaller percentage of the total damage. Also that is before Crit dmg gear/traits which still get to multiply that 100 dmg along with the rest of the dmg so it can still a decent stat for melee crits but it can get silly for ranged crits.

Should you prioritize weapon skill damage or PDL gear in attack capped situations?

If we are living in the bubble of attack is always capped:

For Multi hit WS(non-front loaded or very lightly front loaded) PDL will usually come out well ahead of ws dmg as long as you can support it because it effects all hits and ws dmg only works for the first hit of a ws. The actual value of ws dmg vs PDL will depend on number of average hits (including multi attack chances) and of course other stats matter too. For Multi hit ws Double Attack or Triple attack is usually far more appealing than WS dmg as well.

For single hit or heavily front loaded ws where you can largely discount the extra hits (like savage blade) you can try to roughly maximize (1+PDL)*(1+wsdmg) of course your other stats matter too and this is very much a simplification that ignores any additional hits or multi attacks which is why I very much recommend spreadsheets or simulations but just to give some rough idea.

In real scenarios even when planning for largely attack capped scenarios if theres two sets with nearly identical damage when attack capped but one is significantly better when attack isn't capped I will always go for the one thats more flexible after all buffs and debuffs aren't on 100% of the time.

If you are capped on non-crits, you are capped on crits.

Since recent discussion, I would call it diminishing input, not returns :)

Diminishing input is generally the same for 1% of pdl and WSD, but it still doesn't mean they are even. There is no general rule for what is better, because it depends on:
- number of hits in WS
- amount of fTP on the first hit (EDIT: and is fTP replicated on all hits)
- WSC %

Edit: I wrote that 8h ago but couldn't send. Jakey answered it with more details.

Input sounds wrong to me can we call it Diminishing Effect? :D

Diminishing returns is fine as we've always used it in the context of speaking of percentages. It's equally valid to call it such as long as it's clear what the returns are being judged as.

Deevalue ~ French accent ~

It's actually very confusing because people are confused between percent vs percentage point. The former is multiplication and the later is often an addition.

Supposed that you have 4.0 PDif cap. A 10% increase in PDL is 4.0*0.1 = 0.4. Where as the PDL +10% on the RSE neck is 0.1 and 4.1/4.0 is 1.025 or a 2.5% increase.

Now supposed that you changed job and now your PDif cap is 3.6. A 10% increase in PDif is 3.6*0.1 = 0.36. Where as the 10% PDL neck piece is now giving a 3.7/3.6 = 1.028 or 2.8%

So the same 10% PDL actually gives different percent value. It is because they are percentage points, not percent.

If we throw out the "percent" and directly use the PDL value which is 0.1 (for 10 "percent") then the situation is a whole lot simpler to understand. Assuming everything is perfect (100% acc, capped atk... etc) with only PDL as your variable then you can simply work on the math based on the amount of PDL you already have.

So 1 "percent" PDL would be 0.25% in damage if you have 4.0 PDif and 0.28% if 3.6 Pdif. Of course if you have to move your base PDif for whatever reason (like a ton of other gear) then you have to readjust the % value as they change base on total PDif. It's also called constant returns to scale as each value add the exact same amount as the previous one even if the percent is lower. Like the 2nd cake is 100% increase of 1 cake where as the 5th cake is only 25% of 4 cakes even if each cake is exactly the same.

Of course, it would be a whole lot easier if we simply pick one base PDif as the standard of reference it would save us a whole lot of pain and suffering. Like 1.0 for example.

except you're incorrect about the necks and the rest just sounds HELP I AM TRAPPED IN 2006 PLEASE SEND A TIME MACHINE

Oh yeah sorry. It's still the same it's called percentage point not percent.

So assuming 4.0 PDL. The 1st 10% PDL is 4.0*0.1 = 0.4; 4.0/0.4 = 0.1 the 2nd 10% is still 0.4 (unless PDL stacks upon itself) and 0.4/4.4 = 0.09 or 9%

While PDL still increase by the same amount of 0.4 for every 10 percent point of PDL, the total percent increase for each unit is lower. It's still constant returns to scale, not diminishing returns to scale. It's only because the input is lower as a percentage compare to the previous one.

The thing is, we as FFXI players almost always frame our metrics in terms of percentages. We don't care if WSDMG +30% increases DPS by 1320, we care if WSDMG +30% increases DPS by 20%. As a result, we don't ever judge them on their raw values, so things like WSDMG, and PDL, and MAB all do give diminishing returns by the definitions that we use.

This thread is giving diminishing returns.

3 or 4 of you might, the rest just care about "is number bigger" They want a picture that confirms "big number big, small number small" but that's it.

The guy asking for a uptodate set doesn't care if pdl+10% achually gives X% (doesn't even know how to use it in the first place)

Different subset. I'm talking about the players that participate in contexts thst use terms like diminishing returns.

It has a meaning and is expressed as a percentage because we use it to compare different pieces in a gearset, or buffs in a buff strategy. Should I use stat X or stat Y? Well which one gives the best overall increase? Us humans tend to fall into the trap of "if Z is better, then MOOAR of Z must be best", which is where the concept of diminishing returns kicks in.

I had a feeling this would happen...

Ok so there's two main relations I see being discussed as Diminishing returns which I do not view as Diminishing Returns but I understand the perspectives of why they get lumped under Diminishing Returns. Diminishing Returns as a term is useful for getting people off your back while not triggering math PTSD about why you balance out certain stats but it is not very precise and suggests that you see actual Diminishing Returns as you increase a stat which other than a few skill relationships I can't think of many actual Diminishing Returns in this game off the top of my head its usually linear or exponential until hitting a cap.

1) Some seem to view a linear multiplier as Diminishing Returns in the sense that if you already have say +50% ws dmg and you add 1% ws dmg your first hit ws dmg only increases by .6667% not 1% beacause 151/150 = .6667% so when dealing with a linear multiplier and you increase it incrementally you see incrementally smaller percentage increases but each point of that linear multiplier increased you damage by the same amount.

For example your first hit say did 1000 damage before ws dmg the first point of ws dmg adds 10 damage as does every point of ws dmg 1500 damage at 50% ws dmg to 1510 at 51%. This is a linear relationship.

So to not be Diminishing Returns by that standard you need a 1.01^x relationship if I look at 1.01^(x+1)/(1.01^x) I get 1.01 regardless of x so there I've made a multiplier that increases the relative total by 1% for every point regardless of how many you already have but had to make it exponential to achieve this.

I would rather just call a linear relationship linear and not lump it together everything that's not at least exponential.

2) Some view two or more linear multipliers multiplying each other as Diminishing returns. Personally I see this more as increasing returns of competing stats or just as multiple linear multipliers.

For example MAB and Affinity are both linear multipliers if you hold all other stats equal each point improves damage by some constant amount based on where you held those other stats at and which nuke/ws and mob you are looking at however each point also improves the damage per point of the other stat because they multiply each other. If I go from 100 MAB to 200 MAB my return per point of affinity has doubled. Its not that my MAB has Diminished Returns but my Affinity has increased returns as I increased my MAB and vice versa and because MAB is far more available we value affinity far more.

When you have multiple linear multipliers what you want to optimize for is their product.

"Diminishing returns" in this game mainly has meaning when you're measuring DPS improvements in terms of ratios. It's the same thing as measuring end behavior of numerical functions.

If adding one point of "X" to your set increases your DPS by 10, you can represent the effects of stacking X as:

(Vast simplification for argument's sake)
DPS = 10*x


As Jakey mentions above, this is a linear relationship, which does not converge (until you reach some game-defined cap). "Diminishing returns" only comes into play if you compare the marginal benefit of adding more points of X:

Marginal DPS improvement (percentage) = (10 * (X+1)) / (10 * X) = (X+1)/X

If X is very small to begin with, then the "percent increase" of adding more X is pretty high. But as you keep stacking X, the marginal benefit of adding more X decreases, until it converges to 0.

But always remember that the absolute benefit of adding X does not converge (until you reach the cap): it always increases DPS by 10 with every X you add. When "diminishing returns" is used here, colloquially, it just means that "at some point, each new addition of X is carrying your DPS less than it used to."

After all, if your DPS is ***to begin with, then a fixed increase to DPS helps a lot. But if your DPS is already pretty high, then the same fixed increase to DPS is less noticeable, comparatively. But the absolute DPS increase is constant.