How SS is calculated and works

[Krindor]

Posted this on reddit but as some people don't read it there I'll post it here as well.
Introduction

This is something that me and /u/iDervyi been working on the past month. It started with Dervy noticing how weirdly the tooltip showed the GCD/Cast at 4 seconds and higher. Instead of how it works at the regular GCD of 2.5 which is 26,41 per GCD decrease, at 4 seconds it started to become an irregular amount for every decrease in GCD. For example at 8 seconds it was a pattern of 7,7,6,7,13 points per decrease. This made us wonder how the game actually handles SS as it would be impossible for it to follow the regular formula. The only possible way the game could accomplish this was if SS was tiered.



Tiers

To understand how the tiers in this game works. Let’s start with how the game find out what GCD you’re supposed to have. This is done using the formula, the latest formula by Dervy is this: 2.50256 * (1 - (Skillspeed-354)/6600). The game puts in the SS and then divides/multiplies it depending on the GCD/Cast time after that it rounds it down towards nearest 100th of a second. So for example 2.499 would mean a GCD of 2.49.

Now to find the tiers the formula is changed so that we can find out the SS required for each GCD decrease. For simplicities sake a 1 second GCD base will be used. At a GCD of 1 the SS required for a decrease in GCD is 66. As a drop of 0.01 at 1 second is also a 1% decrease we can then conclude that 66 points equals a 1% drop in GCD no matter what GCD/Cast time. This is correct even with the irregular patterns shown by GCD/Cast time over 4 seconds.

So what does these tiers actually mean in practice? It means that the GCD/Cast time will only be affected if the SS actually reaches a tier. Any points other than these are vastly reduced in value or stat weight (In MNKs case this would be a stat weight of about 0.035 str). What this means is that it’s possible to have up to 26 points of SS that is close to worthless, but what it also means is that one point of SS can be worth more than 2 points of a main stat.

So when gear planning it’s good to not only focus on the stat weight but also to try end up with as little extra SS as possible, just like with accuracy.



Delay

While testing this we also noticed that all abilities have a delay of 0.01s meaning that the calculated tier is always 0.01s behind what the tooltip shows. This is important to know if trying to get additional hits in during a buff.



GL/Huton

Another test performed was how the tiers were affected by GCD enhancing moves like GL and Huton, would also expect Ley Lines to be included here. What the tests showed was that these had individual tiers. But the issue with these were that while they were following the 66 = 1% it wasn’t complete accurate as for some odd reason it didn’t have any repeating pattern. While the longer GCD/Cast time while irregular still showed a pattern. This makes it impossible to adjust a formula to get the exact values and the only way is to find the tiers by looking at the tooltips. What this also means it that for BLM there’s multiple tiers to keep an eye on as both longer cast times and ley lines have their own tiers and need to be adjusted accordingly.

TL DR

Skillspeed is in tiers and any point not at the exact tier is worth a lot less.

GCD delayed by 0.01s.

GCD enhancing abilities have their own tiers.



Data

Credits to /u/iDervyi for the massive amount of data in this spreadsheet:

https://docs.google.com/spreadsheets...#gid=898722325

https://docs.google.com/spreadsheets...it?usp=sharing

[Canadane]

I thought that it was already known it was tiered. Or at least, I have had that assumption for a while.
Good work either way!

[Krindor]

I thought that it was already known it was tiered. Or at least, I have had that assumption for a while.
Good work either way!

From the people I spoke with before this was done the common thoery was that while tooltip didn't show it, each point of SS still increased the GCD. There wasn't any data either. It is also quite illogical for it to only be useful only every 26.4 points.

[CookieMonsta]

From the people I spoke with before this was done the common thoery was that while tooltip didn't show it, each point of SS still increased the GCD. There wasn't any data either. It is also quite illogical for it to only be useful only every 26.4 points.

I actually thought it made a lot of sense to be tiered even before Dervy's work. You can save a lot of number space and processing power server side if you implement numbers and math with less precision. FP32 and FP64 hardware isn't cheap so I'm sure YoshiP made this decision to help optimize the maximum possible players per server in combat. The tier-ing gives the illusion of continuous granularity so most players won't notice.

[Krindor]

I actually thought it made a lot of sense to be tiered even before Dervy's work. You can save a lot of number space and processing power server side if you implement numbers and math with less precision. FP32 and FP64 hardware isn't cheap so I'm sure YoshiP made this decision to help optimize the maximum possible players per server in combat. The tier-ing gives the illusion of continuous granularity so most players won't notice.

This was my thought as well, from a producers perspective it's quite resonable, but from a player perspective it's going to be quite the severe effect on gear planning, not so much now compared to ARR(Due to being worth completely 0) and early HW due to low amount of secondary stats. Of course the amount of player that will probably even think about this is low, probably even lower than the clear rate of savage content.

But from what we've gathered, it isn't only due to servers, but from sloppy programming which causes performance issues. While I'm not in any way experienced in servers, I do have a self programmed simulator which is able to perform 1,500,000 of 1ms precision checks per second, so if it checks every 1ms that would be enough for 1500 players and I'm still a basic programmer so it would be a lot more efficient with some tricks. The reason I think it's caused by sloppy programming is that the formula used to calculate the GCD is inconsistant across different cast times/GCDs. If it's inconsistent in a way it means that something is not being done right or affecting the formula for some odd reason. An example of this can be seen in the 2nd google docs link comparing the formula and tooltip while under Huton.

[Judge_Xero]

I'm not sure if anything has changed since you did your testing but taking averages from 60+ skill usages with varying amounts of SS is showing per point gains.

The only anomaly being Spells where the Cast is the same as Recast, there seems to be some sort of extra delay.

Bard: @ +462 SS (7%)(93)
Heavy Shot (2.32 in game)
Averaged 2.323

Calculated - 2.325

Bard: @ + 435 SS (6.59%)(93.401)
Heavy Shot (2.33 in game)
Averaged 2.333

Calcualted - 2.335025

Bard: @ + 423 SS (6.409)(93.59)
Heavy Shot (2.34 in game)
Averaged 2.3372

Calcualted - 2.33975

BRD @ + 426 SS (6.4545%)(93.5454)
Heavy Shot (2.34 in game)
Averaged 2.3369

Calcualted 2.338635

Bard: @ +0 SS
Heavy Shot (2.5 in game)
Averaged 2.506

Calculated 2.5

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Also wanted to mention as from above while the issue of a delay where cast/recast times match up is not an issue for most Jobs.
i.e. BLM,BRD,MCH - where Cast times are either longer or shorter than the Recast.

This issue is terrible for Summoner where all of their spells outside of Shadow Flare share a time with the recast. To highlight this I will show some of that data.

SMN - @+452 (6.85%)(93.152)
Ruin (in game 2.33)
Averaged - 2.4439
Calculated - 2.3288

Ruin II (in game 2.33)
Averaged - 2.335
Calcualted - 2.3288

Difference - 0.1089

SMN - @+0 SS
Ruin (in game 2.5)
Averaged - 2.616
Calculated - 2.5

Ruin II (in game 2.5)
Averaged - 2.5046
Calculated - 2.5

Difference - 0.01114

--------------------------------------------------

SMN Comparison
Over 600s @ 2.5 GCD - shoud be 240 attacks
Actually 229.3577

4.5% less casts. Probably close to 2% DPS loss

[Krindor]

snip

Most of the tests we did were done in the last 2 months, with the Huton/GL being tested a week ago.
Tbh except for the tooltip, we have not tested how the delay affects casted spells as neither I nor Dervy have access to a 60 spellcaster and all our tests were performed on NIN/DRG/MNK. But do you by any chance have the raw data available? It would be interesting to take a look at is as we haven't been able to test it ourselves. Also what formula did you use to calculate the GCD?

And those SMN tests seems really horryfying, if a 100ms delay is actually a thing, that is longer on the level of how the game works but a really serious bug.

[Judge_Xero]

But do you by any chance have the raw data available? It would be interesting to take a look at is as we haven't been able to test it ourselves. Also what formula did you use to calculate the GCD?

For the Formula I just used 66 = 1% Reduction (I'm fairly adamant that the Tiers are simply used for the Visual Display of Cast/Recast and are a combination of the 776,776,7676 Pattern found on EA and rounding)

BLM

https://www.fflogs.com/reports/pGQPW...42&view=events

https://www.fflogs.com/reports/pGQPW...ne&view=events

https://www.fflogs.com/reports/pGQPW...ne&view=events

https://www.fflogs.com/reports/pGQPW...ne&view=events

https://www.fflogs.com/reports/pGQPW...ne&view=events

https://www.fflogs.com/reports/pGQPW...ne&view=events

BRD

https://www.fflogs.com/reports/ZNK68...97&view=events

https://www.fflogs.com/reports/ZNK68...97&view=events

https://www.fflogs.com/reports/ZNK68...97&view=events

[Krindor]

For the Formula I just used 66 = 1% Reduction (I'm fairly adamant that the Tiers are simply used for the Visual Display of Cast/Recast and are a combination of the 776,776,7676 Pattern found on EA and rounding)

I'll have a look at them tomorrow as I'm just about to head off to bed so no need to rush it

Compared to the formula I'm using, which is the current one Dervy is using our calculated results differ. Also to be noted is that while the 66 = 1% is something that can be used, changing it to fit the tiers of the desired speed is better. An easy way to do it is, as the 66 = 1% is derived from the amount of SS required for one tier for 1 second GCD, therefore for a 2.5s GCD that's 66/2.5 = 26.4. From that we can gather that we get a recurring pattern of 26,27,26,27,26.

[Judge_Xero]

I'll have a look at them tomorrow as I'm just about to head off to bed so no need to rush it

Compared to the formula I'm using, which is the current one Dervy is using our calculated results differ. Also to be noted is that while the 66 = 1% is something that can be used, changing it to fit the tiers of the desired speed is better. An easy way to do it is, as the 66 = 1% is derived from the amount of SS required for one tier for 1 second GCD, therefore for a 2.5s GCD that's 66/2.5 = 26.4. From that we can gather that we get a recurring pattern of 26,27,26,27,26.

Updated the above post.

That's an interesting way to look at finding the tiers for the visual GCD/Casts. One thing to consider though is that it doesn't work for Empyreal Arrow (66/15 = 4.4).

The minimum recurring pattern being 7,7,6 7,7,6 7,6,7,6 tells us that there are a maximum of 10 rounding points per 66 points of SS. So you would still have that same pattern given a 10 second Cast.

--------------------------------------------

What I propose is that there are only Tiers for showing the visual representation of SS. But the actual effect of SS is valued per point.

-------------------------------------------

Take for example the 2 second cast time column.

SS value 467 (+113 SS)

This data point is special because you have a decrease in Recast Time but not a decrease in Cast time. It lands on the recurring 7 data point for EA @ 14.74 Recast.

Data Point = 1.96/2.45

Calculated value of that Data Point = 1.712% (113/66) (98.2879)

2s = 1.965758
2.5s = 2.4572

-----------------------------------

The previous Data Point @ 460 (+106SS)
1.96/2.46

Calculated value of that Data Point = 1.606% (106/66)(98.394)

2s = 1.96788
2.5s = 2.45985

-----------------------------------

For whatever reason SE seems to have chosen to do their rounding @ the 4th decimal. That is why 1.96788 is rounded to 1.968 but visually in game only shows to the second decimal 1.96. But 2.45985 goes to 2.46.

Same with looking at the very first rounding point @ 361 SS

1 second cast @ +7 SS (calculated 0.106%)(99.893)

In game 0.99s
Calculated 0.99893

Visually in game this gets rounded to 0.99 when really it's 0.999 but you only see to the 2nd decimal place, but also the reason "why" it simply doesn't show it still as a 1s cast.

----------------------------------

So I think there are two things going on here.

Visually in game for how the Cast/Recast/GCD is displayed goes off the 776 pattern at which point it does a rounding check to visually display the effects of the stat.

The actual effects of the stat on skills is given for every point of stat - but is really hard to pinpoint due to:

Attack Speed Swing (i.e. 2.5s GCD could be in the range of 2.45-2.55) so it takes a lot of averages to get accurate results.
Server Latency
System Latency
Perfect Testing - Requires perfect skill queuing for 100's of data points.