Wednesday, August 4, 2010

Great Katana options

Some people in the FFXI community have put a lot of work in trying to figure out all the math behind damage calculations. Some of it is over my head, so I keep to my own simplified logic which I then try to rhyme with what others are saying. Looking for the most ideal Great Katana to replace Hagun for my SAM, I tried to rely on my own formula.

DoT =
(WS_Rate * Average_Melee_Damage + ACC_Adjusted_Average_WS_Damage) /
(Actual_Delay * WS_Rate/Melee_ACC) + 2

Where WS_Rate is how many melee attacks are performed for each WS. This, is basically the make or break factor in my calculations. Although I'm confident that my estimation fits my personal situation (frequency of meditate usage and efficiency of TP usage), it may require some adjusting as I'll discuss later.

The idea behind the above formula is adding the melee damage and WS damage together in proportion to the WS_Rate and divide it by the time it takes per WS in seconds. You may notice the constant number 2 in there. From recording multiple WS and counting melee swings and the time it took, I've concluded that WS and ability delays are both approximately 120 delay or 2 seconds long.

The ACC_Adjusted_Average_WS_Damage may also require some explanation. Basically, in my formula I calculate the expected average WS damage for when all hits connect. Multiplying this value by your WS accuracy rate accounts for missed hits, or in case of single hit weaponskills, a complete miss. This way the formula also applies to other weapon types and weaponskills. The WS accuracy rate is also modified by an accuracy bonus which applies to Kasha, Gekko and other weaponskills. In this case I added 50% acc rate and capped the total value at 95%. This is based on info from this BG thread.

Using the WS_Rate and dividing it by the melee accuracy rate I come up with the average number of attack rounds needed per WS (not rounded). The Actual_Delay is the weapon's delay adjusted with the Haste stat.

To come up with Average_Melee_Damage I used the following.

(Base_damage + fSTR) * (Average_PDIF + MIN(1, 3 - Average_PDIF) * Crit_rate)

The contribution of critical hits to your average damage is dependant on your average PDIF. Normally you'd add 1 to your PDIF for a critical hit, but when your PDIF is 2 or higher the actual contribution is reduced since PDIF is capped at about 3. That explains the MIN function. The question of the origin of my fSTR and PDIF numbers can be answered by: I used estimates from parsed fights on Seaboard Vultures. So, it's not precise like some other people would prefer, but it's good enough for my own ends.

For average WS damage.

(WS_Base_Damage * fTP + WS_Base_Damage * (Additional_WS_hits + Multi_Attack_Rate)) * (Actual_WS_PDIF + MIN(1, 3-Actual_WS_PDIF) * WS_Crit_Rate) * WS_Damage_Bonus


WS_Base_Damage = Base_damage + WS_fSTR + WSC


Actual_WS_PDIF = MIN(2.7, PDIF_During_WS * WS_PDIF_Bonus)

Since Gekko can't crit naturally (i.e. without Sneak Attack) the WS_Crit_Rate is going to be 0 in all my comparissons. I added it for sake of completeness. I split up the formula to make it more readable, but I fear it may still be a bit confusing. I multiply the base WS damage by fTP for the first hit and add it again for all expected additional hits, which also includes Double and Triple Attack procs. The WS_PDIF_Bonus is the 2x multiplier for Tachi Gekko and 1.5 for Kasha. Other weaponskills also have this property.

WS_Damage_Bonus represents the boost from Overwhelm and other gear like the AMK hat. One has to take into consideration whether or not the bonus from the Kasha weapon, Overwhelm and other gear is in fact the same stat. If they are not, then the effects would be compounded. However, I assumed for this example that they are in fact all the same stat and so can be added up respectively.

Even though I got PDIF, accuracy and fSTR estimates from parses, I still needed to estimate the different values for the same variables for when I change gear in between the different setups I want to compare. For accuracy this is not much of an issue, but for PDIF and fSTR I used some creative estimates.

Haste is based on 50% Hasso usage and Haste spell. The more Haste present, the heavier any haste sacrifice from gear will weigh.

Last, but certainly not least. Calculating WS_Rate for different setups and weapons. I had a baseline of 4.4 WS_Rate from my parses. This obviously includes Meditate usage. I needed a way to calculate new values for WS_Rate for the different weapons and gearsets. This is probably the most questionable part of my DoT formula.

WS_Rate = Hits_to_WS / Avg_Attacks_per_round - 0.4

This approximates my measured WS_Rate given my 6-hit Hagun setup. Hits_to_WS for a 6-hit is 5, because you get TP from your WS. Subtracting 0.4 to account for Meditate is going to be skewed if your WS frequency goes very high or very low. The higher it is the less Meditate contributes and vice versa.

Avg_Attacks_per_round is what the name implies. However, care needs to be taken when dealing with both double, triple and "Occasionally attacks" weapon properties. I didn't automate this in the spreadsheet I used and did it by hand for the OAT Magian weapon.

And now for what you've all been waiting for!

The percentage score at the bottom of each column is the DoT relative to the DoT of teh Hagun 6-hit build I'm currently using. All the variable names on the left should be easy to pair up with the names I used in this post.

Notice how both the Keitonotachi weapon options perform worse than Hagun with my gear selection. The Kasha damage obviously loses quite badly given the low PDIF I had on birds. Level correction plays a big role here. On low level mobs where my PDIF could easily be above the 1.35 needed to cap it during WS, the Kasha damage weapon would outperform the Hagun build.

The 5-hit build's sacrifice in Haste and accuracy weakens it considerably. Since this is just for myself I didn't bother doing the numbers for a build including Usukane. It's worth noting here that this setup too will beat Hagun when accuracy is capped. When considering zergs, then the Haste sacrifice become more costly and would make this an unattractive option.

Keeping Hauby and Dusk Gloves on, the 5 Store TP on the Keito can make for a 6-hit build with the same gear as my current Hagun build, but with a Sword Strap. This plus the Strength+Attack Magian G.Katana seem very close. This is the reason why I'm trying to do both of them.

If you have Usukane body and feet pieces and managed to get your hands on 5 more Store TP from Goading belt or something else, then you could 5-hit the OAT weapon and it would become much stronger than all the other options.

I realise this formula isn't mechanical enough to be completely accurate. I honestly don't know how to factor in Zanshin or if I should at all. I chose not to, because that's what makes the most sense to me right now. Another unknown is how Double Attack acts during weaponskills (some claim it can only proc on the first two hits). Having narrowed down my choice to two weapons and generally knowing which is better in which situation, I'm not bothered with being more precise than this. Still, if you see any mistakes or errors in logic, please let me know.

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