Item Stacking

''This page is incomplete - many items have not been yet documented. This page will be updated with the most accurate information currently known, but do not take it as gospel.''

Item Stacking is a mechanic that allows for items to have increased effects based on how many of a specific item a player is holding. Most items stack, however not all stacking is equal, and certain items may stack additive or multiplicative, based on the effect. In most cases, the stack value can be found in the log book entry for a particular item, though whether it is additive or multiplicative is not stated.

This page discusses how item stacking functions when one item is stacked, and does not discuss how it interacts with other items.Note that for some items, the listed value in-game is not reflected in the item code. This page strives to give the true values, rather than stated ones. This is why there may be discrepancies with certain items, because the code says different than the item description.

In addition, the only numbers listed here are ones that stack, as full item descriptions are not listed to prevent confusion.

Additive Stacking
Additive Stacking is when an item linearly increases based on number of items. An example would be if the player is holding a Lens-Maker's glasses, they would have 10% critical strike chance, 2 pairs of Lens-Maker's glasses 20% critical strike chance, up until 10 Lens-Maker's glasses with 100% critical strike chance.

Effective Maximum Count is not a hard limit, but any more than the listed value would have no effect on gameplay whatsoever (typically due to surpassing a maximum value in-game).

If a numerical value present in the item does not show up in the table, it does not stack with number of items.

Multiplicative Stacking
Multiplicative stacking is when an item does not increase linearly based on the stack value, it scales based on the current percentage instead of the base one. Another word for multiplicative stacking is "Diminishing Returns". An example would be that if an item grants 10% damage resistance multiplicative, you won't get 100% damage resistance after 10 items, you would get 0.90^10 damage taken, or ~65% damage resistance, where 0.90 is 1 minus the reduction value, and 10 is the exponent representing the number of said item the player has.

Multiplicative stacking is limited to items that reduce values (lower cooldown, health), because if the value was additive, it would allow players to go to zero with these items.

Effective Maximum Count is not a hard limit, but any more than the listed value would have no effect on gameplay whatsoever (typically due to surpassing a minimum value in-game). In positive cases (cooldown reduction), the value is as close to 0.12 as possible, as 0.12 is the fastest ever recorded human reaction speed. In negative effect cases, as with lunar items, the maximum effective count shows simply at what point it becomes obsolete add new ones - these values should never be sought after in-game due to potentially game ruining effects through stacking. Thus, it is recommended not to stack many lunar items.

If a numerical value present in the item does not show up in the table, it does not stack with number of items.

Tougher Times functions differently, and will thus be present in the next section. There are currently no other common items which have multiplicative stack.

Tougher Times
Tougher Times does not stack like any other item, likely due to the extremely powerful potential of stacking the effect. At first glance, a player may see the item and believe that obtaining 7 of them would grant 100% block chance, but this is not true. Even then, if a player believes that it stacks multiplicative, and that obtaining 30 would grant 99% block chance, this too is not true.

The actual formula for the tough times stacking calculation goes as follows

100% - 100% / (15% * item count + 100%), where the final value received is your chance to block.

For example, with one Tougher Times, the player would have a 13.04% chance to block, and with two Tougher Times, the player would have a 23% chance to block. Knowing this, in order to obtain 99% block chance with the Tougher Times, the player would need to acquire about 700 of the item to get a value this high.

Here is a graph which demonstrates how the chance to block increases as number of tough times increases (and never actually hits 100):

http://m.wolframalpha.com/input/?i=100*%281-%281%2F%281%2B%280.15*x%29%29%29%29+from+0+to+1000

In order to increase efficiency, below listed are values showing how the tougher times scales with number.

Tougher Times suffers from extreme diminishing returns due to the code that actually calculated block chance not reflecting the description of the item. While the block chance initially increases fairly rapidly, it falls off quickly, resulting in requiring a substantially greater amount of tougher times in order to have an effect on block chance. As can be seen in the table, increasing the player’s tough times from 500 to 1000, an astonishing increases of 500 items, only increases the block chance by 0.56%. As such, unless the player has access to an incredibly large amount of items, values this high should not be expected in a regular game due to how little the Tougher Times affects block chance the more the player has. Due to this, it is recommended to take into account how much a Tougher Times will increase the player’s block chance before taking extra, later in the game, as other items which stack linearly may provide far more use in the long run.

Sources:
 * 1) Game Code