Editing Item drops

Items that drop from [[monsters]] or [[item boxes]] follow certain drop rate calculations that determine which item or any item at all drops. Certain items, outside those obtained from monster or item boxes, equally follow calculations that determine the chance to obtain them. Examples include gambling items from [[Coren]] or redeeming [[Lucky Coins]] at the Lucky Roulette minigame. If chance is involved in obtaining items, the mechanism by which it will determine whether the item drops or not is commonly referred to as a "roll".

==Item rolls==
A roll can be synonymously viewed as rolling a dice, where you aim for a specific dice face to obtain an item. For example, if a monster drops an item with a <code>1/200</code> drop rate, it is synonymous to rolling a 200-sided dice where you will obtain the item only when 1 specific face out of 200 faces is rolled.

===Monsters===

Each time an enemy is defeated, the game rolls to determine whether an item will drop, and if so, what that item will be in the following order:

#The game rolls for event drops, such as {{Tool|rare|Event Egg}}, {{Tool|rare|Halloween Cookie}}, or {{Tool|Present (Christmas)}}
#The game rolls for {{Tool|Music disks}} (<code>1/600</code> across all enemies)
#The game rolls based on the enemy's [[Drop anything rate]] (DAR) to determine if the enemy has the possibility of dropping anything else
#The game rolls to decide if the enemy will drop its specified rare item (depending on area, Section ID, and difficulty)
#The game rolls to determine whether the drop is {{Meseta}}, a {{Tool|Tools|Tool}}, or the enemy's set drop (<code>1/3</code> chance for any of these)

The chance to obtain items from enemies can be increased with drop rate boosts. DAR boosts increase the chance to obtain any item at all from monsters, which can also help with its designated rare drop. [[Rare drop rate]] (RDR) boosts only increase the chance for the designated rare drop. However, a monster can't have more than a 100% DAR. Certain monsters already have 100% (Bosses, rare enemies) or high DAR, where DAR boosts can't be utilized fully or only partially. A similar rule applies to RDR, in which the maximum RDR can only be boosted to <code>7/8 (87.50%)</code>. This however only applies to very few monsters (e.g. rare Rappies from VR Temple).

===Item box===

Some Item boxes may be set to drop specific items (e.g. some boxes in {{Quest link|1-1:Planet Ragol}} will only ever drop {{Tool|Monomate|Monomates}}), or specific ''categories'' of items (e.g. some boxes in {{Quest link|1-3:Subterranean Den}} will only ever drop Tools).

For non-drop specific item boxes, each time an [[Item box#Item box drop tables|item box]] is opened, the game rolls to determine whether an item will drop, and if so, what that item will be in the following order:

#The game rolls to decide if the box will drop its specified rare items (depending on area, Section ID, and difficulty). In many areas, item boxes have multiple rare drops assigned to them. The roll order is from top to bottom in the [[Drop charts]]
#The game rolls to determine whether the drop is a [[Weapon]], [[Frames|Frame]], [[Barriers|Barrier]], [[Units|Unit]], [[Tool]], [[Meseta]] or nothing (depending on area and difficulty; [[Yellowboze]] has a higher chance to obtain Meseta from item boxes).

Item box drops '''are not affected''' by '''any''' drop rate bonuses, including (but not limited to): 
* [[Drop anything rate]] (DAR); 
* [[Rare drop rate]] (RDR); 
* [[Anguish]] common weapon rates; 
* {{Tool|rare|Photon Drop}} drop bonuses; 
* Event drop rate bonuses;
* Altered weapon percentage [[pattern|patterns]] from [[Anguish]]

===Calculation===
The overall chance to obtain an item is best explained in an example. Assuming the [[Easter event]] takes place, [[Event Egg|Event Eggs]] can be obtained by killing monsters. [[Claw|Claws]] have weapons as a set drop. The calculation of receiving a Weapon box from killing a Claw in Ultimate is executed by following the roll order from above:

* Roll for Event Egg fails: <code>1 - 1/500 = '''499/500'''</code>
* Music disk roll fails: <code>1 - 1/600 = '''599/600'''</code>
* DAR roll successful: <code>'''3/10''' (30%)</code>
* RDR roll fails: <code>1 - 1/64 = '''59/64'''</code>
* Set drop roll successful: <code>'''1/3'''</code>

The overall chance can now be calculated by multiplying the above rates: 

<code>499/500 * 599/600 * 3/10 * 59/64 * 1/3 = '''1/10.89 (9.18%)'''</code>

From this point further calculations can be executed in a similar fashion to determine more specific drop rates, e.g. what weapon will drop and with what attributes ([[Weapon attribute drop tables]] for further information). 

====Drop Rate of multiple rolls====
The overall chance of obtaining items is not conditional by only killing 1 monster or destroying 1 box. For multiple kills or box openings, the overall chance to receive a drop must naturally increase. However, this increase is not linear. The increase is determined by following the binomial distribution formula:

<code>''chance of at least 1 drop'' = 1 - (1-''droprate'')^(''number of events'')</code>

Using the above example, the overall chance of receiving at least 1 weapon box from a Claw by killing it '''10''' times is:

<code>''chance of at least 1 drop'' = 1 - (1-''1/10.89'')^(''10'') = '''1/1.62 (61.83%)'''</code>

Killing more enemies naturally increases the likelihood of receiving an item, but it will never be 100% guaranteed. This is contrary to popular belief, where killing a monster <code>X</code> times for its <code>1/X</code> item drop will give you a guaranteed drop. In reality, the overall chance in this case always comes out to roughly <code>'''63%'''</code> (approaching <code>1-1/e</code>, where e=Euler's number). However, this is statistically defined as the average chance where at least 1 drop will occur.

=====Combined drop rates=====
Some monsters drop the same item but with different drop rates. For a drop rate <code>A</code> and a drop rate <code>B</code> the combined drop rate <code>C</code> is:

<code>C = A + B - A * B</code>

For instance, if one enemy drops an item with a drop rate of <code>1/2</code> and another with a drop rate of <code>1/4</code>, the overall chance of receiving at least 1 drop from killing both monsters is:

<code>1/2 + 1/4 - 1/2 * 1/4 = '''1/1.6''' (62.5%)</code>

{{Guides}}
[[Category:Guides]]
@@ Line 1: / Line 1: @@
-Items that drop from [[monsters]] or [[item boxes]] all follow a common set of drop rate calculations that determine which item drops, if one drops at all. Items obtained via other methods, such as gambling {{Meseta}} with [[Coren]] or redeeming [[Lucky Coins]] in {{Quest link|Gallon's Shop}}, use their own unique sets of calculations. If chance is involved in obtaining items, the mechanism by which the drop is determined is commonly referred to as a '''roll.'''
+Items that drop from [[monsters]] or [[item boxes]] follow certain drop rate calculations that determine which item or any item at all drops. Certain items, outside those obtained from monster or item boxes, equally follow calculations that determine the chance to obtain them. Examples include gambling items from [[Coren]] or redeeming [[Lucky Coins]] at the Lucky Roulette minigame. If chance is involved in obtaining items, the mechanism by which it will determine whether the item drops or not is commonly referred to as a "roll".
 ==Item rolls==
-A roll can be envisioned as rolling a many-sided die, where rolling a 1 means the item will drop. For example, if a monster drops an item with a <code>1/200</code> drop rate, it is equivalent to rolling a 200-sided die.
+A roll can be synonymously viewed as rolling a dice, where you aim for a specific dice face to obtain an item. For example, if a monster drops an item with a <code>1/200</code> drop rate, it is synonymous to rolling a 200-sided dice where you will obtain the item only when 1 specific face out of 200 faces is rolled.
 ===Monsters===
-Each time a monster is defeated, the game rolls to determine whether an item will drop, and if so, what that item will be, in the following order:
+Each time an enemy is defeated, the game rolls to determine whether an item will drop, and if so, what that item will be in the following order:
 #The game rolls for event drops, such as {{Tool|rare|Event Egg}}, {{Tool|rare|Halloween Cookie}}, or {{Tool|Present (Christmas)}}
-#The game rolls for [[music disks]] (<code>1/600</code> from any monster)
+#The game rolls for {{Tool|Music disks}} (<code>1/600</code> across all enemies)
-#The game rolls based on the monster's [[drop anything rate]] (DAR) to determine if the monster has the possibility of dropping anything else
+#The game rolls based on the enemy's [[Drop anything rate]] (DAR) to determine if the enemy has the possibility of dropping anything else
-#The game rolls to decide if the monster will drop its specified rare item (depending on area, section ID, and difficulty)
+#The game rolls to decide if the enemy will drop its specified rare item (depending on area, Section ID, and difficulty)
-#The game rolls to determine whether the drop is {{Meseta}}, a [[tools|tool]], or the monster's set drop. Each of these categories has an equivalent <code>1/3</code> chance of being rolled
+#The game rolls to determine whether the drop is {{Meseta}}, a {{Tool|Tools|Tool}}, or the enemy's set drop (<code>1/3</code> chance for any of these)
-====Drop rate boosts====
+The chance to obtain items from enemies can be increased with drop rate boosts. DAR boosts increase the chance to obtain any item at all from monsters, which can also help with its designated rare drop. [[Rare drop rate]] (RDR) boosts only increase the chance for the designated rare drop. However, a monster can't have more than a 100% DAR. Certain monsters already have 100% (Bosses, rare enemies) or high DAR, where DAR boosts can't be utilized fully or only partially. A similar rule applies to RDR, in which the maximum RDR can only be boosted to <code>7/8 (87.50%)</code>. This however only applies to very few monsters (e.g. rare Rappies from VR Temple).
-The chance to obtain items from monsters can be increased with drop rate boosts. [[drop anything rate|DAR]] boosts increase the chance to obtain any item at all from monsters, which can also help with its designated rare drop. [[Rare drop rate]] (RDR) boosts only increase the chance for the designated rare drop. However, a monster can't have more than 100% DAR. Certain monsters already have 100% (bosses, rare monsters) or otherwise high DAR, meaning strong DAR boosts like the 25% weekly boost won't have their full effect. A similar rule applies to RDR, in which the maximum RDR can only be boosted to <code>7/8 (87.50%)</code>. This, however, applies to very few monsters (e.g. rare Rappies from VR Temple).
-The [[drop charts]] show the combination of a monster's DAR and RDR. Individual DAR and RDR values are visible by hovering with a mouse over the drop rate or by tapping on them on mobile devices.
-====Set drops====
-A monster's '''set drop''' is the type of item that it will drop if it fails its rare item roll and doesn't drop either Meseta or a tool. A set drop is a category of item, not a specific one; for example, a [[Bartle]]'s set drop is a weapon, so it can drop any weapon that would be able to be dropped in the area and section ID it appears in. A set drop can be a [[Weapons|Weapon]], a [[Frames|Frame]], a [[Barriers|Barrier]], a [[Units|Unit]], or nothing.
-====Rare monsters====
-Some monsters can spawn as a rare variant. The spawn rate is <code>1/500</code>, with the exception of the Episode 4 boss [[Kondrieu]] spawning at a rate of <code>1/10</code>. Rare monsters have 100% DAR and a very high RDR. The overall chance to obtain an item from a rare monster can be calculated by combining the spawn rate with the RDR. For instance, on Episode 1 Ultimate, [[Hildetorr|Hildetorrs]] spawn with a rate of <code>1/500</code> and drop a [[Heaven Punisher]] on {{Bluefull}} ID with a drop rate of <code>1/204.8</code>. The overall chance to obtain this item from a [[Hildelt]] thus is <code>1/102,400</code>. The weekly Rare Monster boost increases the spawn rate by 50%.
 ===Item box===
-Some item boxes may be set to drop specific items (e.g. some boxes in {{Quest link|1-1:Planet Ragol}} will only ever drop {{Tool|Monomate|Monomates}}), or specific ''categories'' of items (e.g. some boxes in {{Quest link|1-3:Subterranean Den}} will only ever drop tools).
+Some Item boxes may be set to drop specific items (e.g. some boxes in {{Quest link|1-1:Planet Ragol}} will only ever drop {{Tool|Monomate|Monomates}}), or specific ''categories'' of items (e.g. some boxes in {{Quest link|1-3:Subterranean Den}} will only ever drop Tools).
-For non-drop-specific item boxes, each time an [[Item box#Item box drop tables|item box]] is opened, the game rolls to determine whether an item will drop, and if so, what that item will be in the following order:
+For non-drop specific item boxes, each time an [[Item box#Item box drop tables|item box]] is opened, the game rolls to determine whether an item will drop, and if so, what that item will be in the following order:
-#The game rolls to decide if the box will drop its specified rare items (depending on area, section ID, and difficulty). In many areas, item boxes have multiple rare drops assigned to them. The roll order is from top to bottom in the [[drop charts]]
+#The game rolls to decide if the box will drop its specified rare items (depending on area, Section ID, and difficulty). In many areas, item boxes have multiple rare drops assigned to them. The roll order is from top to bottom in the [[Drop charts]]
-#The game rolls to determine whether the drop is a [[weapon]], [[frames|frame]], [[barriers|barrier]], [[units|unit]], [[tools|tool]], {{Meseta}}, or nothing (depending on area and difficulty; {{Yellowboze}} has a higher chance to obtain Meseta from item boxes).
+#The game rolls to determine whether the drop is a [[Weapon]], [[Frames|Frame]], [[Barriers|Barrier]], [[Units|Unit]], [[Tool]], [[Meseta]] or nothing (depending on area and difficulty; [[Yellowboze]] has a higher chance to obtain Meseta from item boxes).
 Item box drops '''are not affected''' by '''any''' drop rate bonuses, including (but not limited to):
-* [[drop anything rate]] (DAR);
+* [[Drop anything rate]] (DAR);
-* [[rare drop rate]] (RDR);
+* [[Rare drop rate]] (RDR);
 * [[Anguish]] common weapon rates;
 * {{Tool|rare|Photon Drop}} drop bonuses;
-* event drop rate bonuses;
+* Event drop rate bonuses;
-* altered weapon percentage [[pattern|patterns]] from [[Anguish]]
+* Altered weapon percentage [[pattern|patterns]] from [[Anguish]]
 ===Calculation===
-The overall chance to obtain an item is best explained in an example. Assuming the [[Easter event]] is currently active, {{Tool|rare|Event Egg|Event Eggs}} can be obtained by killing monsters. [[Claw]]s have weapons as a set drop. The calculation of receiving a weapon box from killing a Claw on Ultimate is executed by following the roll order from above:
+The overall chance to obtain an item is best explained in an example. Assuming the [[Easter event]] takes place, [[Event Egg|Event Eggs]] can be obtained by killing monsters. [[Claw|Claws]] have weapons as a set drop. The calculation of receiving a Weapon box from killing a Claw in Ultimate is executed by following the roll order from above:
 * Roll for Event Egg fails: <code>1 - 1/500 = '''499/500'''</code>
-* Roll for music disk fails: <code>1 - 1/600 = '''599/600'''</code>
+* Music disk roll fails: <code>1 - 1/600 = '''599/600'''</code>
 * DAR roll successful: <code>'''3/10''' (30%)</code>
-* RDR roll fails: <code>1 - 1/64 = '''63/64'''</code>
+* RDR roll fails: <code>1 - 1/64 = '''59/64'''</code>
-* Roll for set drop successful: <code>'''1/3'''</code>
+* Set drop roll successful: <code>'''1/3'''</code>
 The overall chance can now be calculated by multiplying the above rates:
-<code>499/500 * 599/600 * 3/10 * 63/64 * 1/3 = '''1/10.89 (9.18%)'''</code>
+<code>499/500 * 599/600 * 3/10 * 59/64 * 1/3 = '''1/10.89 (9.18%)'''</code>
-From this point, further calculations can be performed in a similar fashion to determine more specific drop rates, e.g. which weapon will drop and with what attributes (see [[weapon attribute drop tables]] for further information).
+From this point further calculations can be executed in a similar fashion to determine more specific drop rates, e.g. what weapon will drop and with what attributes ([[Weapon attribute drop tables]] for further information).
-====Multiple rolls====
+====Drop Rate of multiple rolls====
-The overall chance of obtaining items by killing several monsters or destroying several boxes can also be calculated. For multiple rolls, the overall chance to receive a drop naturally increases. However, this increase is not linear. The increase is determined by following the binomial distribution formula:
+The overall chance of obtaining items is not conditional by only killing 1 monster or destroying 1 box. For multiple kills or box openings, the overall chance to receive a drop must naturally increase. However, this increase is not linear. The increase is determined by following the binomial distribution formula:
-<code>''chance of at least'' 1 ''drop'' = 1 - (1 - ''drop rate'') ^ (''number of events'')</code>
+<code>''chance of at least 1 drop'' = 1 - (1-''droprate'')^(''number of events'')</code>
 Using the above example, the overall chance of receiving at least 1 weapon box from a Claw by killing it '''10''' times is:
-<code>''chance of at least'' 1 ''drop'' = 1 - (1 - ''1/10.89'') ^ (''10'') = '''1/1.62 (61.83%)'''</code>
+<code>''chance of at least 1 drop'' = 1 - (1-''1/10.89'')^(''10'') = '''1/1.62 (61.83%)'''</code>
-Killing more enemies naturally increases the likelihood of receiving an item, but it will never be 100% guaranteed. This is contrary to the popular belief that killing a monster <code>X</code> times for its <code>1/X</code> item drop will give you a guaranteed drop. In reality, the overall chance in this case always comes out to roughly <code>'''63%'''</code> (approaching <code>1 - 1/e</code>, where e = Euler's number). This is statistically defined as the average chance where at least 1 drop will occur, and is particularly useful when performing calculations such as "how many runs will it take to get this item?"
+Killing more enemies naturally increases the likelihood of receiving an item, but it will never be 100% guaranteed. This is contrary to popular belief, where killing a monster <code>X</code> times for its <code>1/X</code> item drop will give you a guaranteed drop. In reality, the overall chance in this case always comes out to roughly <code>'''63%'''</code> (approaching <code>1-1/e</code>, where e=Euler's number). However, this is statistically defined as the average chance where at least 1 drop will occur.
-====Combined drop rates====
+=====Combined drop rates=====
 Some monsters drop the same item but with different drop rates. For a drop rate <code>A</code> and a drop rate <code>B</code> the combined drop rate <code>C</code> is:
@@ Line 78: / Line 66: @@
 For instance, if one enemy drops an item with a drop rate of <code>1/2</code> and another with a drop rate of <code>1/4</code>, the overall chance of receiving at least 1 drop from killing both monsters is:
-<code>1/2 + 1/4 - 1/2 * 1/4 = '''1/1.6 (62.5%)'''</code>
+<code>1/2 + 1/4 - 1/2 * 1/4 = '''1/1.6''' (62.5%)</code>
-====Multiple drops====
-The numbers above show the process of obtaining at least 1 item, which is sufficient for most players who hunt for a certain drop once. The chance to obtain multiple items can be calculated too. For example, if a monster drops an item with a drop rate of <code>1/200</code> and is killed 100 times, the chance of it dropping <code>3</code> items or more can be calculated:
-<code>''chance of at least'' 3 ''drops'' = 1 - P(0) - P(1) - P(2)</code>, where <code>P(k)</code> is the chance of ''exactly'' <code>k</code> item drops.
-So, in this example, the chance of receiving exactly 0, 1 or 2 drops has to be calculated. The general formula for <code>P(k)</code> is:
-<code>P(k) = n_C_k * p^k * (1-p)^(n-k)</code>, where:
-* n: number of trials, in this example '''100''' monster kills
-* k: number of successes, which for P(0) is '''0''', P(1) '''1''', etc.
-* p: probability of success, which is the drop rate of '''1/200'''
-* n_C_k: the binomial coefficient, which is defined as '''n!/(k!(n-k)!)''' with "!" referring to the factorial
-The process of evaluating each <code>P(k)</code> value is the same, it is shown here for <code>P(2)</code>:
-* n = '''100'''
-* k = '''2'''
-* p = '''1/200'''
-* n_C_k = 100!/(2!(100-2)!) = '''4950'''
-<code>P(2) = 4950 * (1/200)^2 * (1-1/200)^(100-2) = '''1/13.21'''</code>
-Repeating the process for <code>P(0)</code> and <code>P(1)</code> we arrive at:
-<code>''chance of at least'' 3 ''drops'' = 1 - 1/1.65 - 1/3.29 - 1/13.21 = '''1/70.91 (1.41%)'''</code>
 {{Guides}}
+[[Category:Guides]]