Wednesday, May 20, 2009

DAMN IT SE! I'M A DRAGOON, NOT A MATHEMATICIAN!

This serves as your warning. The details that follow this opening paragraph hurt my head. I can only imagine it will hurt yours as well, but I'm going to go through the pain in order to demonstrate what gear is best overall for TP gain and WS damage. I'm posting this information as a precursor to the equipment details I plan on posting in the next few days. This information also relates to mainly to any job that uses a 2H weapon. I wiil not be getting into the detail of ranged attack or one-handed weapons.

Before we get started, here is my TP gear:

Weapon: Gungnir
Sub: Pole Grip
Ammo: Olibanum Sachet
Head: Askar Zucchetto
Neck: Love Torque
Ear1: Brutal Earring
Ear2: Ethereal Earring
Body: Ares Cuirass
Hands: Homam Manopolas
Ring1: Ulthalam's Ring
Ring2: Rajas Ring
Ring3: Old man
Back: Amemet Mantle+1
Waist: Swift Belt
Legs: Homam Cosciales
Feet: Homam Gambieras
Food: Spaghetti Carbonara


First, the main equation.

(D+fSTR)*pDIF

This equation is what's widely accepted as the formula for calculating your attack damage. This equation also has several mini-equations built into it and you cannot expect a constant number for any piece of it except D.

D = Your current weapon's base damage rating. In my case, Gungnir has a base damage rating of 100.

(100+fSTR)*pDIF.

fSTR = Your STR against a target's VIT. Information about your target's VIT isn't something you're going to usually know off the top of your head, but through extensive testing, you can usually pick up a range. For this blog's purpose, we're going to play with Greater Colibri, who have been found to have a VIT range of 67-69.

The formula for figuring this piece out is (STR-mob'sVIT+4)/4. My understanding is that 4 is the accepted number for increasing your fSTR rating. In my normal TP/Food set up, my STR rating is 80+26. If I'm fighting Greater Colibri, we'll figure this up on the high side of their VIT range and the equation comes out to be (106-69+4)/4. Which = 10.25.

fSTR = 10.25

So now we're at:

(100+10.25)*pDIF

pDIF = Your attack rating against a monster's defense rating. It's all about a ratio. There are different formulas for melee and ranged attack ratios. We'll stick with the melee ratio since Dragoons do not have any hope of ranged attacks.

For starters, we need to figure out the level correction portion of this. Greater Colibri are level 81-82. We obviously are not higher than 75. The correction that comes into play is as follows:

cRatio = Ratio - .05 * level difference

If your base attack is 500 and your target's defense is 500, then your Ratio = 1. In situations where your Ratio = 1, your cRation for fighting a level 82 monster is calculated like this

cRatio = 1 -(.05*7.)

Or...cRatio= .65.

It's not always this simple though. Assuming nothing like Angon or Dia have been dumped onto the Greater Colibri, it's reported their base defense is between 320-330. For our purpose, we'll just say 330. Now your Ratio looks like 500/330. This calculates out to a 1.52 ratio and our formula now looks like this:

cRatio = 1.52-(.05*7)

cRatio = 1.17

The cRatio dumps itself into two formulas to calculate the max and min borders for your damage range. These formulas are not entirely accurate for two-handed weapons since the update, but they serve as a good general framework. These formulas are:

Max pDIF

fMax(cRatio) = .04+ (1.2 x cRatio) (Use this one if your cRatio is between 0 and .5.)
fMax(cRatio) = 1 (Use this if your cRatio is between .501 and .833.)
fMax(cRatio) = 1.2 x cRatio (Use this if your cRatio is between .833 and 2.)

Since my cRatio is 1.17, we'll use the last equation and determine my Max pDIF is 1.64 in TP gear.

fMax(1.17) = 1.2 * 1.17.
fMax(1.17)= 1.40
1.40(1.17) = 1.638 (1.64 rounded up)
fMax = 1.64.

Min pDIF

fMin(cRatio) = -0.5 + 1.2 x cRatio (Use this if your cRatio is between 0 and 1.25.)
fMin(cRatio) = 1 (Use this if your cRatio is between 1.26 and 1.5.)
fMin(cRatio) = -0.8 + 1.2 x cRatio (Use this if your cRatio is between 1.51 and 2.)

My cRatio of 1.17 puts me in the first range and gives me the following equation with my numbers plugged in.

fMin(1.17) = -0.5 + (1.2 * 1.17)
fMin(1.17) = -0.5 + (1.40)
fMin(1.17) = 0.9
0.9(1.17) = 1.05
fMin = 1.05.

Understanding how pDIF works takes understanding that with each swing you take, the pDIF value is randomly generated between your fMin and fMax values.

Ok, got all that? Time to put it together after a short review.


Base weapon damage = 100
fSTR = 10.25
pDIF range = 1.05 to 1.64.

Using those numbers and throwing out the 25% damage bonus a Greater Colibri takes from piercing weapons, we see that my base normal swing damage will be 115 (min = (100+10.25)*1.05)) and my max will be 181 (max = (100+10.25)*1.64. Putting the damage bonus in, we get:

min = (115*.25)+115
max = (181*.25)+181

min = 144 damage
max = 226 damage

That's a lot of math. Now knowing the equations themselves, here are the max and minimum ranges for each of the stats.


  • fSTR has a cap of 18. Allegedly this cap is 19 with a relic weapon.
  • cRatio has a minimum of 0.
  • cRatio has a max of 2.
  • When Critical hits occur, your pDIF is raised by a value of 1, but that's another issue for another section.

Second part is understanding the effects of bonuses such as Haste, Double Attack, Attack and Accuracy and Store TP (in order of importance).

Accuracy

Put simply, this is your chance to hit and it caps at 95%. Your accuracy is determined by the following equation (rounded down):

Acc = (Combat Skill + DEX + Equipment + Traits + Abilities)

This is easily the most important thing to cap in a TP set. Gear can be traded off if you're in the neighborhood of this 95% cap, but understand that you will not always be capped or close to capped in most situations with just gear and food alone. At that point, a trade off between Accuracy and some other bonuses comes into play depending on the availability of bards or corsairs.

My TP set gives the following as it relates to determing your Accuracy rating:

Accuracy + 40
DEX + 14
Combat Skill + 7

My natural job traits and merits add the following to this equation:

Combat Skill: 292 (capped polearm skill + 8 merits)
Base DEX: 62
Job Trait: Accuracy Bonus II (+22 Accuracy)

Before calculating, we need to do two other things. The first is determine what our accuracy score is from our DEX. Accuracy value from DEX is determined by (DEX*0.75). Second is to adjust the accuracy value from our combat skill. Anything over 200 is adjusted by a value of 0.9. In my case, it's (200+(99*0.9))

DEX Acc value = +57
Combat Skill adjusted value = +289

Plugging these into the equation above, we get:

Accuracy = (289 + 57 + 40 + 0 + 22 + 0).
Accuracy = 408

Food is added on top of your Accuracy value after all other modifiers from abilities, songs, etc have been added.

Now how do you determine if you've hit the 95% mark? Well that's where you take your accuracy value and put it up against your target's evasion. If (your accuracy) = (target's evasion) then your hit rate has a base of 75%. For every 1 point of accuracy you add over your target's evasion, you increase your chance of landing the hit by 0.5%. In other words, it would take +10 accuracy to increase your chance of hitting by 5%.

There is also a penalty or bonus to take into consideration for level gaps as well. You lose 4 accuracy points for every level you're below your target and you gain 4 accuracy points for every level a target is below you. Knowing your target's level range will help you tremendously in determining what food to take.

In the case of our level 82 Greater Colibri, it has a base evasion of 340ish (using 340 just cause it's even and probably pretty close to reality). First figure up your accuracy penalty.

Acc penalty = 4 * 7.
Acc penalty = -28

Now my number looks like this:

380 against 340.

In order to reach the 95% cap, remember every +10 accuracy means a 5% boost to your hit percentage. In order for me to hit this cap, I need to be at +40 over the Greater Colibri's evasion, which I am and that means I don't have to eat sushi, I can eat meat w/o having to worry about a loss. Remember a normal melee hit will ALWAYS outdamage any bonus food can give you. Cap this and build from there.

Haste

Haste is not something to be overlooked in any way, shape or form. Put simply, haste is a reduction in your weapon delay. If you reach the Haste cap of 80% for example (which you won't as DRG...), it means your weapon delay has an 80% reduction. A delay of 492 turns into an effective delay of 99.

As Dragoon, I have a TP set that gives me 17% haste. Dragoon can reach the gear haste cap of 25% through a lot of money and a lot of luck. The pieces I wear with haste on them are:

Askar Zucchetto +4%
Swift Belt +4%
Homam Gambieras +3%
Homam Cosciales +3%
Homam Manopolas +3%

In order to reach the haste cap for gear, you need the following:

Speed/Velocious Belt +6%
Walahra Turban +5%
Wyrm Mail +1 +2%
Sword Strap +3% (remember it's not a literal 3% haste, but is the same basic effect and will reduce your TP/swing)
Homam Cosciales +3%
Homam Manopolas +3%
Homam Gambieras +3%

Understanding that SE actually did us a favor by making it easy to calculate weapon delay, we can easily figure out just how much Haste will effect the overall output. Weapon Delay is best explained by saying that for every 60 delay, there is 1 second between attack rounds. With most polearms a Dragoon uses at level 75, there is a delay of 492 on them.

Weapon Delay/60 = time (in seconds) between attack rounds.

So in my case, having no haste on at all result in having 8.2 seconds between rounds or 7.5 attack rounds per minute. Follow the second hand on a clock for 8 seconds and see what happens. Feels like an eternity doesn't it? Using this information with my fMin and fMax numbers, we can see that I'll end up doing 1080 points of damage per minute minimum and 1695 points of damage per minute maximum. Keep these numbers in mind and watch what happens as we stack on haste. Remember the spell Haste adds 15%.

These numbers represent DPM with my current TP gear (cDPM), current TP gear with haste cast on me (cDPMh), and finally current TP gear with max magical haste effects from spells (43%, cDPMhm).


DPM: 1080-1695. 8.2 seconds between attacks, 7.5 attacks/minute, 492 delay, 0% haste
cDPM: - 1267-1989. 6.8 seconds between attacks, 8.8 attacks/minute, 409 delay, 17% haste(17% gear haste).
cDPMh: - 1542-2420. 5.6 seconds between attacks, 10.71 attacks/minute, 335 delay, 32% haste (17% gear, 15% magic).
cDPMhm: - 2617-4108. 3.3 seconds between attacks, 18.18 attacks/minute, 197 delay, 60% haste (17% gear, 43% magic).

Obviously, the faster you swing, the more damage you do, but most people underestimate the importance of this and often times will sacrifice a haste piece in favor of a Double Attack or +attack piece. It needs to be something pretty drastic to change out a haste piece in my opinion.

Store TP

Another primary goal for Dragoon is to put together a 5-6 hit TP build. What this means is, through your gear, food and subjob choices, you need to have 100 TP in 5-6 hits not including your jumps. This assumes your weapon skills land as well. Learning how Store TP works requires learning a couple other things first.

Base TP/swing is calculated based on your weapon delay. Since my weapon delay is 492, my formula looks like this:

13.0 + [(Delay - 480) * 1.5 / 50]

Or

13.0 + [(12) * 1.5/50]

My TP per swing with no bonuses ends up being 13.36/swing. There is no rounding down or up with SE's calculations of this, it's just flat truncated after the first decimal place, so it's 13.3/swing.

Second, you need to understand that Store TP is a % increase, not a straight up addition to your TP/swing. In other words, if you have a piece of gear that's Store TP+10, it's adding 10% of your TP (total 14.63 of my base) and not literally 10TP to my base (23.3...).

So if our base TP/swing is 13.3, we can easily do some math to see that we need 7.5 swings to reach 100TP from 0TP. Depending on your TP return from the WS you're using (let's say 15 return TP from a no-buffed, full hit Drakesbane), then we need 6.4 swings to reach our next 100TP. That means we do not have to add much for our 6-hit build. In my TP set, using Carbonara as food and subbing SAM, I have Store TP+25. This works out to the following:

(13.3 * 0.25) + 13.3 = 16.6 TP/swing, which puts me just over a true 6 hit build at 6.02 swings/100TP (if starting at 0TP). Using this information in combination with the Haste cDPMh above, I'll be able to WS approx every 25-30 seconds.


Double Attack

Double Attack is a bit of an enigma for people to understand. Obviously on it's surface, people see "2 attacks/round > 1 attack/round" and obviously, that would be true. However, people need to understand that having something like "Double Attack + 5%" only increases the chance Double Attack will proc on that particular attack round. It is not a constant like Haste.

In my standard TP set up, I have +7% Double Attack. For the sake of this blog post, we'll assume that Double Attack will actually process 7% of the time. This means after 100 attack rounds, I will have picked up 7 additional swings.

Using my fMin and fMax values from above, this means I will have dumped out a minimum of 1008 damage (144*7) and a max of 1582 (226*7) and I will also have gained enough TP to dump a weapon skill.

This trait should be treated as a bonus and only used if it's included with a piece of gear that you would use anyway. Wearing something other than a Pole Grip or Brutal Earring purely for Double Attack will likely result in a far smaller DPM rating.

Putting it all together

Quick review of the important information:

Target: Level 82 Greater Colibri

pDIF range = 1.05 to 1.64.
fMin: 144
fMax: 226
Accuracy %: 95% (380 vs. 340 acc)
cDPMh: - 1542-2420. 5.6 seconds between attacks, 10.71 attacks/minute, 335 delay, 32% haste (17% gear, 15% magic).
TP/hit: 16.6
Double Attack: 7%

Taking everything here at it's literal meaning, over a two hour xp session on these birds will mean the following if there is no down time from being disengaged, no mobs, etc and assuming I'm NOT using weapon skills:

Total number of basic swings (w/o double attack): 1285
Total number of double attacks (7%): 90
Total number of swings: 1375
Total number of hits (95% acc): 1306
Total minimum damage: 188, 064
Total maximum damage: 295,156

And just for comparison...Valkyrie's Fork with rest of set up the same.

Total number of basic swings (w/o double attack): 1285
Total number of double attacks (10%): 128
Total number of swings: 1413
Total number of hits (85% acc): 1201
Total minimum damage: 153,728
Total maximum damage: 241,201

Conclusion

It's important to remember that I figured these numbers at literal percentages and could be off. I may also have screwed up some calculations somewhere, but the important thing to take from this post (aside from it being very long) is the general framework that a Dragoon operates in when it comes to basic weapon attacks and how to get the most from them. Feel free to post if I messed up somewhere and I will correct it.


Coming Soon:

Gungnir vs. Valkyrie's Fork - A Closer Look At How Gungnir Can Be Beaten.

(Or at least kept up with...)



3 comments:

  1. Too much Math make Seney's head assplode.

    ReplyDelete
  2. So where do you wear that Ring3?
    --Nice To Meet You :)

    ReplyDelete
  3. I wear it in the same place Tentacle wears her Ring3. :)

    ReplyDelete

Qtipus' Information

FFXI subscriber since NA release.