Disgaea: Hour of Darkness/Items

Unlike in most RPGs, items in Disgaea are complex entities in their own right. They have a level, a rarity, may be inhabitted by Specialists which increase their power, and might be more or less powerful at a particular level because of actions taken while leveling them. All of these factors contribute to their potency. In addition, characters get different levels of benefit from the same item based on a number of factors.

Every character can hold four items. One must be a weapon ('Wpn'), and three must be from the 'Etc' category. Monsters can only use Wpn-Monster weapons, and humanoids can use any Wpn except Wpn-Monster. Every item that a character holds can increase ten statistics of that character, and may have other effects:

Above are the statistics for a very good pair of shoes and a very good sword, when the items are normal rarity, with no specialists, at level 0. In practice you will never find items that have no specialists to start.

The only other type of item has the designation 'Item' and is never equipped on a character: it is used by a character from inventory. These items are generally curative (restoring HP and/or SP), although they do have other uses.

Aside from characters, you have two places to keep items: the Item Bag and the Warehouse. The Item Bag can hold 16 items; the Warehouse can hold 256. The only times you can access items in the Warehouse are when using 'Equip' or 'Item' from the castle menu, or while buying/selling items at the shops in the castle. You can use or equip items from the Item Bag while in the Dark Assembly, in battles, at the Item World, and everywhere that you can use the Warehouse. To switch between the Warehouse and Item Bag, use left and right.

Formulas for Item Leveling
All numbers are related to individual statistics; in particular, the current number of specialists and the specialist counter are different for each stat that the item has.

n=level (as shown in battle screen) x=item generals counter (global to the item) b=base stat of the item (stat of a Normal item) c=specialist counter p=number of specialists currently on the item i=initial stat of the item (stat of the actual item) s=1 if i>0, -1 if i<0, or 0 if i=0

All numbers are computed/stored with high precision; however, the floor of the number is displayed. The death of an Item General or Item King is always calculated after the increase for the level that the General/King was on.

Note: no item can have more than 16 specialist slots.

For those who are interested, Appendix A contains my notes (mostly tables of item stats) from determining these formulae.

What all of this math really means is that:
 * You should always kill Item Generals/Kings/Gods.
 * If you want an extra boost to an item's stats, leave a specialist on the item while leveling it. Each specialist is worth 270 extra points to whichever stat it boosts on a Legendary item, if left for all 100 floors and all Generals/Kings/Gods are killed.
 * If you want to maximize any particular stat on an item, you have to subdue and remove all of the native specialists before you defeat the first Item General; this will require using Mr. Gency's Exit before finishing floor B10. Once you have removed all of the native specialists, but before you kill the first Item General, fill every slot on the item with specialists that boost whatever stat you are trying to maximize (e.g., to maximize ATK, fill the item with Gladiators).  Then, go back into the item and proceed to level it, killing all Item Generals, Kings, and God.  After killing each Item King, the item gains a specialist slot, so exit the Item World at that point and put another specialist on the item.
 * There is no difference between clearing and skipping floors, as long as you kill Item Generals/Kings/Gods.
 * If you level any item with a negative stat to level 100, that negative stat ends up being exactly -100.

Rarity
There are three levels of rarity: normal, rare, and legendary. Below, the properties of each are listed.

Item Benefit
You may notice when equipping an item that you gain more or less benefit from that item than its listed stats. There are four reasons for this: Weapon Mastery, character level, stat aptitude, and identical rarity bonus.

Aptitude
Every class has aptitudes for each of the eight basic stats; these vary from 50% to 150% and show up on the character creation screen and on the character status screen. Aptitudes act as a multiplier to stat gains from items; for example, a level 1 character equipping a normal Muscle World (1000HP) will get 500HP with a 50% HP Aptitude, 1000HP with a 100% HP Aptitude, or 1500HP with a 150% HP Aptitude. The adjustment for Aptitude is applied after all other modifiers.

Weapon Mastery
When equipping a non-monster weapon, you get a bonus to all of weapon's stats equal to the equipping character's Weapon Mastery for that weapon type times 5%. The formula is (weapon stat)*(1 + mastery*.05). The maximum Weapon Mastery is 255, so the maximum Mastery bonus is 1275%.

Character Level
For monster weapons and accessories, you get a bonus based on the level of the character. These bonuses do not normally apply until the postgame, since they do not start until level 100, but they become quite substantial at later levels. They are calculated by the following formulas (thanks to Zepy for these):

The maximum level is 9999, so the maximum level bonus is 1299%, or just a little higher than the maximum Mastery bonus.

Identical Rarity
If a character has more than one item with the same rarity equipped, then all such items receive a boost in power. This works as a multiplier after weapon mastery and character level bonuses are applied. The multiplier ranges from 1.1 to 1.3, depending on how many items with identical rarity are equipped:

For example, if a level 1 character equips a normal Nightvision and a normal Muscle Ace, that character will normally get +50 INT, +200 HIT, and +200 HP. However, if the Muscle Ace and Nightvision happen to have the same rarity number--for example, if they both have rarity 46 on the item status screen--then the character will get +55 INT, +220 HIT, and +220 HP, due to the identical rarity bonus.

Item Ranks
Each item is assigned a 'rank', which roughly determines how 'good' the item is. Ranks go from 1 to 42, and they determine what level of enemies will be found in the item world for that item. Below are the 'LV+' ranks for level 1 from the 'Go to Item World' screen (thanks to JungleJim for producing this table):

The levels listed are *minimum* levels; in general, the enemies on any given floor will be higher level than the LV+ number. Also, these numbers are for floor 1; later floors have more powerful enemies.

Hospital Items
The Hospital gives you prizes whenever reach certain numbers for each of HP, SP, and Dec (Deceased) healed. Thanks to JungleJim for these tables:

Ultimate Items
The 'ultimate' items of the game are very difficult to acquire, but worth it (and necessary to beat the most powerful enemy in the game).

For weapons, they are acquired by entering a Legendary item one level of power below of the same type, fighting to level 100, and stealing it from the Item God there.

Once you have any item of rank 40 or above, you can level it to 100, then steal another Legendary item of the same type from the Item God 2 at floor B100.

For reference, the Item God 2 I'm currently fighting has these stats:

(No 'More Difficult Enemies' bills passed)

Except for the level, you can expect these numbers to vary somewhat (+/-10%), but you need to be prepared before you attempt to kill (or steal from) Item God 2.

The ultimate items are:
 * Wpn-Axe: Apocalypse (VERIFY)
 * Wpn-Fist: Ultimus
 * Wpn-Sword: Yoshitsuna
 * Wpn-Spear: Glorius
 * Wpn-Gun: Etoile
 * Wpn-Bow: Galaxy (VERIFY)
 * Wpn-Monster: Nyanko Soul
 * Etc-Robot: Super Robo Suit
 * Etc-Engine: Hyperdrive

The Super Robo Suit can be stolen from Baal.

The Hyperdrive you get automatically from defeating an Item God 2.

Monster weapons are a little different. The rank 40 monster weapon is Nyanko Soul, which can be acquired at the end of a Lucifer Force, or can be raken from Majorly. There are also a rank 41 and rank 42 monster weapon. The rank 41 is the Nemesis, which is a better weapon than Nyanko Soul; it can be stolen from Baal. The rank 42, Nemesis Mk II, is stolen from Prinny Baal, and has better base stats than the Nemesis--but it comes at level 100, and Baal apparently doesn't kill any Item Generals/Kings/Gods, nor does he subdue any specialists when leveling his items.

There is no simple way to get a Legendary second-best item. The easiest way is to play around in high-level item worlds until you see one appear either on the Bonus screen or in some enemy's inventory. For reference, they are:
 * Wpn-Axe: Durandal (VERIFY)
 * Wpn-Fist: God's Fist
 * Wpn-Sword: Cosmic Blade
 * Wpn-Spear: Longinus
 * Wpn-Gun: Infernal Gun
 * Wpn-Bow: Artemis Bow (VERIFY)
 * Wpn-Monster: Lucifer Force (VERIFY)

See the Item World Strategies section for advice on how to deal with the Item World.

Maximum ATK
Since the question arises on a regular basis, this section outlines the maximum ATK a character can have, prior to using Extra Gain and stat stealing.

The optimum character, somewhat surprisingly, is Thursday. This is surprising since Thursday cannot Transmigrate, and therefore misses out on Transmigration bonuses, and cannot equip the Yoshitsuna, which is, by far, the most powerful weapon in the game.

However, both of these flaws are vastly overcompensated by Thursday's 150% aptitude in almost all stats.

The most powerful weapon Thursday can equip is the Nemesis. (The Nemesis Mk II is better in theory, but since you steal it already leveled to 100, and Baal does not kill Item Generals/Kings/Gods, the Nemesis is actually better.)

To truly maximize the Nemesis, you have to get one with 13 specialist slots at level 0, subdue and remove all specialists before completing floor 10, and fill it with Gladiators. Then, after killing each Item King (and thereby adding another slot to the item), fill the new slot with another Gladiator. If you do this, it adds 3,888 ATK to the item.

The Nemesis at level 100 has 45,100 ATK, if you kill all Item Generals/Kings/Gods.

The Nemesis with 13 slots at level 0 will have 16 slots at level 100. These must all be filled by power 19998 Gladiators. If you do all of this, then your Nemesis will have:

3888 (spec. bonus) + 45100 (level 100) + 319968 (specs) = 368956 ATK

You must then do the same thing with 3 Legendary Champion Belts, making sure that each has 13 specialist slots at level 0 and that each has the exact same rarity number as the Nemesis.

3888 (spec. bonus) + 27100 (level 100) + 319968 (specs) = 350956 ATK

Equip the Nemesis and all three Champion Belts on Thursday, at level 9999:

(368956 + 3*350956) * 13.99 (level 9999) * 1.3 (rarity bonus) * 1.5 (aptitude) = 38,788,069 ATK

Add Thursday's intrinsic ATK:

10 (base stat) + 9998 (level gains) * .45 (level gain multiplier) * 10 (base stat) = 45,001 ATK

For a grand total of 38,833,060 ATK.

The second-best character for ATK is Priere, and the third-best character for ATK is a Divine Majin. However, there is no known cap on the number of points that can be gained through Extra Gain and stat stealing, which makes these kinds of evaluations somewhat irrelevant. (Though it should be noted that, once it is set up, getting points through Extra Gain should be much faster than getting points through stat theft.)

Item Leveling Formulae Notes
These are just my notes, unsupported, for those who want to have some idea of how I went about figuring out the item formulae. There are some things that are missing, but it's a mostly-complete set of data.

Legendary Infernal Gun (not counting specialists) Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Infernal Gun (E-0)     300               300              1500   300 Infernal Gun (E-1)     316               316              1576   316 Infernal Gun (E-2)     332               332              1652   332 Infernal Gun (E-3)     348               348              1728   348 Infernal Gun (E-4)     364               364              1804   364 Infernal Gun (E-5)     380               380              1880   380 Infernal Gun (E-8)     428               428              2108   428

Infernal Gun (ENG-9)   444               444              2184   444 Infernal Gun (ENG-10)  460               460              2260   460

Infernal Gun (SNG-9)   444               444              2184   444 Infernal Gun (SNG-10)  460               460              2260   460

Infernal Gun (EKG-9)   444               444              2184   444 Infernal Gun (EKG-10)  490               490              2410   490 Infernal Gun (EKG-11)  507               507              2491   507 Infernal Gun (EKG-12)  524               524              2572   524 Infernal Gun (EKG-14)  558               558              2734   558 Infernal Gun (EKG-18)  626               626              3058   626 Infernal Gun (EKG-19)  643               643              3139   643 Infernal Gun (EKG-20)  700               700              3420   700 Infernal Gun (EKG-21)  718               718              3506   718

Infernal Gun (EKNG-20) 660               660              3220   660 Infernal Gun (EKNG-21) 677               677              3301   677

Infernal Gun (SKG-10)  490               490           4  2410   490

Infernal Gun (SC1-10)  490               490           4  2410   490 Infernal Gun (SC1-19)  643               643           5  3139   643 Infernal Gun (SC1-20)  700               700          12  3420   700

Infernal Gun (SC5-10)  490               490          22  2410   490 Infernal Gun (SC6-10)  490               490          27  2410   490 Infernal Gun (SC7-10)  490               490          31  2410   490

Infernal Gun (SC8-10)  490               490          36  2410   490 Infernal Gun (SC8-19)  643               643          46  3139   643 Infernal Gun (SC8-20)  700               700          96  3420   700 Infernal Gun (SC8-23)  754               754         103  3678   754 Infernal Gun (SC8-25)  790               790         108  3850   790 Infernal Gun (SC8-29)  862               862         117  4194   862 Infernal Gun (SC8-30)  980               980         240  4780   980 Infernal Gun (SC8-31) 1000              1000         244  4876  1000 Infernal Gun (SC8-32) 1020              1020         249  4972  1020

Infernal Gun (SC8N-20) 660               660          48  3220   660 Infernal Gun (SC8N-30) 880               880         120  4280   880 Infernal Gun (SC8N-31) 898               898         122  4366   898

Infernal Gun (SC8.0-20) 700              700          48  3420   700

Infernal Gun (SC1.0-20) 700              700           6  3420   700

Infernal Gun (SC1.2-20) 700              700          18  3420   700

Normal Cosmic Blade Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Cosmic Blade (0)       300   300  2000   300   300   300   300   300 Cosmic Blade (9)       444   444  2909   444   444   444   444   444 Cosmic Blade (EKG-10)  505   505  3310   505   505   505   505   505 Cosmic Blade (EKG-19)  662   662  4309   662   662   662   662   662 Cosmic Blade (EKG-20)  740   740  4820   740   740   740   740   740 Cosmic Blade (EKG-21)  759   759  4941   759   759   759   759   759 Cosmic Blade (EKG-29)  911   911  5909   911   911   911   911   911 Cosmic Blade (EKG-30) 1080  1080  7030  1080  1080  1080  1080  1080

Cosmic Blade (EKKNG-30) 930  930  6030   930   930   930   930   930

Cosmic Blade (ENG-10)  460   460  3010   460   460   460   460   460 Cosmic Blade (ENG-19)  604   604  3919   604   604   604   604   604 Cosmic Blade (ENG-20)  620   620  4020   620   620   620   620   620 Cosmic Blade (ENKG-20) 680   680  4420   680   680   680   680   680

Normal Cross-Trainers Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Cross-Trainers (0)                         5          20 Cross-Trainers (ENG-10)                   17          40

Normal Falcon Shoes Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Falcon Shoes                              25         100 Falcon Shoes (ENG-10)                     47         160

Normal Protein Shake Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Protein Shake (0)            480 Protein Shake (ENG-10)       730

Normal Plunder Hand Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Plunder Hand (0)                                            30 Plunder Hand (ENG-10)                                       55

Normal Cha-Ching Hand Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Cha-Ching Hand (0)                                          40 Cha-Ching Hand (ENG-10)                                     70

Normal Bravery Belt Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Bravery Belt (0)                   310  -100 Bravery Belt (ENG-10)              475  -160 Bravery Belt (EKG-10)              521  -145

Normal Shaolin Belt Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Shaolin Belt (0)                   400  -130 Shaolin Belt (EKG-10)              670  -185

Legendary Black Belt Name                    HP    SP   ATK   DEF   INT   SPD   HIT   RES Black Belt (0)                     750  -225 Black Belt (EKG-10)               1210  -325 Black Belt (EKG-20)               1720  -410 Black Belt (EKG-30)               2405  -442

E: Empty EKG: Empty, killed generals (kings, god) EKG-9: Killed general, then used Gency EKNG: Empty, killed 1st general, not second ENG: Empty, did not kill generals SKG: 1 Coach Specialist, placed when item is at level 8, killed item general SNG: 1 Coach Specialist, placed when item is at level 8, did not kill item general SC#: # Coach Specialists, placed when item is at level 0, killed item general SC#.#: # Coach Specialists, placed when item is at level 0, killed item general, # Coach Specialists, place when item is at level 19, killed item general.

Other notes:

Level 0-10, no exit, same as exitting at Level 1, 2, 3, 4, 5, 8, 10.

Accidentally discovered that using Mr. Gency at level 11, without exitting at level 10, erases Item General Kill.

Created a level 0 Infernal Gun with no specialists by using 4 Mr. Gency's Exits on level B1, and saving/reloading a bunch of times. The odds of a specialist appearing on level 1 seem to better than 1 in 4, as long as there is an unsubdued specialist in the item. Other items I did not do this with, but values come out the same, which supports my theories. The Cosmic Blade I took out for testing, always removed its native residents by exitting at level 9; all other items were me getting Coaches so that I could do an 8-Coach test.

Belts are so that I can determine equations for negative stats.

Item Benefit Formulae Notes
Weapons Lev  Apt   WATK  CATK  WMas 46 100   6087   6087   0  54  100   6087   6087   0  45  100   6087   7608   5 202  100   6087   6087   0 438   60   6087   4565   5 3240  100   6087  37739 104

Lev  Apt   WDEF  CDEF  WMas 3240 100   1500  9300  104 438   50   1500   937    5

For all statistics, (humanoid) weapons give:

(Weapon stat) * (1 + .05*(Weapon Mastery)) * (Aptitude)

Accessories

Lev  Apt   AHP   CHP   Ratio R/Apt 3518  70   7884  41446 5.26  7.51  0.27   278 3240  100   7884  57080 7.24  7.24  0.13   117 3123  120   5028  42959 8.54  7.11 536  110   7884  26626 3.38  3.07  0.01     4 532  110   7884  26537 3.37  3.06  0.03    14 518  110   7884  26277 3.33  3.03  0.03    15 503  110   7884  26017 3.30  3.00  0.32    65 438   50   7884  10603 1.34  2.68  1.17   236 202  100   7884  11904 1.51  1.51  46  100   7884   7884 1.00  1.00

3240 100   5028  36402 7.24  7.24 503  110   5028  16592 3.30  3.00

3518	70	7884	41446 3240	100	7884	57080 3123	120	5028	42959 1014	110	7884	34863 1006	110	7884	34776 1000	110	7884	34689 999	110	7884	34602 995	110	7884	34602 840	110	7884	31914 835	110	7884	31827 830	110	7884	31740 829	110	7884	31654 826	110	7884	31654 825	110	7884	31654 824	110	7884	31567 823	110	7884	31567 822	110	7884	31567 821	110	7884	31567 820	110	7884	31567 819	110	7884	31480 818	110	7884	31480 816	110	7884	31480 639	110	7884	28358 536	110	7884	26626 532	110	7884	26537 518	110	7884	26277 503	110	7884	26017 438	50	7884	10603 202	100	7884	11904 100	100	7884	7884 46	100	7884	7884

And, once again, someone (Zepy) on the message boards posts an almost-perfect formula:

Monster weapons(calculated by character levels): Below lvl 100: 100% lvl 101 ~ 500: ((lvl - 100) / 2 + 100)% lvl 501 ~ 2000: ((lvl - 500) / 5 + 300)% lvl 2001 and above: ((lvl - 2000) / 10 + 600)%

Just add in aptitudes and note that the divisions above are integer division (thus floor'ed):

lev <= 100: floor(stat * apt / 100) 100 <= lev <= 500: floor(stat * apt * floor((lev - 100) / 2 + 100) / 10000) 500 <= lev <= 2000: floor(stat * apt * floor((lev - 500) / 5 + 300) / 10000) 2000 <= lev: floor(stat * apt * floor((lev - 2000) / 10 + 600) / 10000)

Identical Rarity Bonus Notes
86802 2166 Divine Majin/Mastery 164 Item                ATK      Rarity Yoshitsuna       869532           6 Super Robo Suit   16425           6 Prinny Costume        0           6 Bahamut's Scale       0           6 SRS+PC            18067 Y+PC             956485 PC+BS                 0 SRS+PC+BS         19710 Y+PC+BS         1043438 Y+SRS+PC+BS     1151744

Item                 HP      Rarity Mistral Fist          0           0 Super Robo Suit  133795           0 Infernal Shield       0           0 Angel's Sandals       0           0 MF+SRS           147174 MF+SRS+IS        160554 MF+SRS+AS        173933

All of this matches JungleJim's formula, so I assume it is correct.