Crystal Shield (perk)

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This article is about the perk. For the item, see Crystal shield.
For other uses, see Crystal shield (disambiguation).
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Crystal Shield is a defensive Invention perk that, upon activation, will add 5% of all damage taken per rank for ten seconds into a pool of life points. This also includes typeless damage. For the following 30 seconds, damage taken will reduce this storage of life points rather than the player's actual life points until the separate pool is depleted or the 30 seconds have passed. It can be created in armour gizmos.

The perk has a 10% chance of activating (11% on a level 20 item). The hit that activates the Crystal Shield will also be added to the life point pool. This perk has a 1 minute cooldown after it has activated.

When the perk triggers, it prompts the message: Your Crystal Shield perk has activated and will begin storing damage to use as ablative hitpoints. When the stored life points deplete, it prompts the message: Your crystal shield lifepoints have been depleted! When the timer ends before the stored life points deplete, it prompts the message: Your crystal shield perk has run out! When the player doesn’t receive significant damage during the perk’s activation period, it prompts the message: You did not absorb enough damage to generate a crystal shield.

Damage from poison can also trigger the perk. Any self-inflicted damage is also added to the life point pool. These include:

Analysis[edit | edit source]

Table of damage reduction provided by Crystal Shield. The damage reduction varies with the rank of the perk, the attack rate of the enemy[note 1], and if the perk is on level 20 gear.

Average damage reduction for the different ranks of the Crystal Shield perk. The attack rate, , of the enemy (given in game ticks) has an effect on the damage reduction. The damage reduction in parentheses correspond to placing this perk on level 20 gear.
Rank Average Damage Reduction
1 0.73% (0.74%) 0.68% (0.69%) 0.70% (0.71%) 0.59% (0.60%) 0.67% (0.69%) 0.58% (0.60%) 0.63% (0.65%) 0.45% (0.47%)
2 1.47% (1.48%) 1.36% (1.38%) 1.40% (1.43%) 1.18% (1.21%) 1.33% (1.38%) 1.15% (1.20%) 1.25% (1.30%) 0.91% (0.95%)
3 2.20% (2.22%) 2.03% (2.07%) 2.09% (2.14%) 1.76% (1.81%) 2.00% (2.06%) 1.73% (1.79%) 1.88% (1.95%) 1.36% (1.42%)
4 2.94% (2.96%) 2.71% (2.75%) 2.79% (2.85%) 2.35% (2.42%) 2.67% (2.75%) 2.31% (2.39%) 2.50% (2.60%) 1.82% (1.90%)
Calculations
Notes
  • A calculator for this is at the top of this page.
  • Assumptions :
    • The pool of life points is always depleted.
    • The player's life points during the reduction phase are not a factor.
    • The enemy is always attacking at the same attack rate.
  • is the proc chance of Crystal Shield to activate (.10 normally, .11 if the Crystal Shield perk is on level 20 gear).
  • when or . This represents summing over all possibilities where integer represents the amount of hits prior to the proc of Crystal Shield. The probability of Crystal Shield proccing on hit is therefore .
  • is the rank of the Crystal Shield perk.
  • is the time of the absorption phase of Crystal Shield. This is taken to be 16 game ticks.
  • is the cooldown time of Crystal Shield. This is taken to be 100 game ticks.
  • is the attack rate of the enemy in game ticks.
  • is the random value uniformly sampled between the enemy's minimum hit and maximum hit. The describes different sets of hits. The sets are regenerated for every new value of .
    • has elements with integer . This is the damage taken before the perk procs.
      • Clarification : This does mean that for that there are no elements in this set.
    • has elements with integer . This is the damage taken during the absorption phase.
    • has elements with integer . This is the damage taken from the end of the absorption phase until the chance for Crystal Shield to proc is no longer on cooldown.
    • The set of values in for integer is the same in both the numerator and denominator of the ratios for any given .
  • The flooring function is used in the term because the game truncates the amount to be added into the pool. This is important because the amount added to the pool is directly related to the amount of damage taken per hit during the absorption phase. This means that for , any damage taken under 20 during the absorption phase will not contribute to the shield. Similarly, for , , and , any damage taken that is under 10, 7, and 5, respectively, during the absorption phase will not contribute to the shield. If each individual hit during the absorption phase is under these respective lower limit values per Crystal Shield rank, then a shield will not form.


Damage reduction
  • The average ratio of damage taken, , from Crystal Shield to that of without Crystal Shield is
  • The average damage reduction is then, after some rearranging,
Simplifications
  • This can be simplified if the assumption is that every value of integer , integer , integer , is taken to be the same . In this scenario, there is no random element and the above is then only dependent on the proc chance and the attack rate of the enemy. This simplification is increasingly accurate in the limit of large . A value of constant damage taken under 80 will have a noticeable effect. All examples provided in the table above are using large enough values of such that the values should not change to 2 decimal places in percent.

Using these simplifications, the damage reduction reduces to

Proof of the simplification
Regarding Crystal Shield

We start from the main equation:

The second summation within the brackets in the numerator can be split up.

Split up the damage reduction component.

The first term of the numerator is equal to the denominator.

If we want to know the damage reduction over a large number of hits, we could use the statistical average of the received damage, this means becomes a constant value . We also drop the floor function in the numerator and add a value to correct for the error.

The second summation in the numerator has no terms that change on increasing , the summation can thus be simplified to a product of the range of the index and the summands.

Place terms not dependent on outside of the summations.

Drop common term in numerator and denominator.

To simplify even further we need to find the infinite sum equivalents of the remaining summations. Since (p = perk proc chance), the following is true[math 1]

Take the derivative of (2):

The second term in (3) is equal to (2):

Combine (2) and (3) with diffent constants:

If we take and in (2) we get:

For , and in (4), we get:

The summations (5) and (6) occur in (1) and can be substituted:

Where . This represents the rounding error introduced by dropping the floor function. , so for we have <4% error for ignoring and can therefor safely be ignored for most practical situations.

Extreme uses of Crystal Shield[edit | edit source]

The Crystal Shield perk has two additional effects. In scenarios similar to this, the damage reduction from Crystal Shield is extremely high (much, much higher than the values in the table above).

  • Life saver: If the player were to normally die due to any hit (type or soft/hard typeless) and the player has life points stored in the shield (reduction phase), the player will not die; instead, the player is left with however many life points were stored in the Crystal Shield.
  • Damage immunity: If the player has very low life points, and a lot of life points stored in the pool of the shield, then the player has a lot of time to take "free" hits. An example: Assume the player has 100 life points remaining and the Crystal Shield has stored 3000 life points. Assume the damage taken per hit is a static value and would normally be 5000 damage. Since the player only has 100 life points, every 5000 hit going forward is only going to hit the player for 100. Since the Crystal Shield reduction phase is active, this 100 life points is taken from the Crystal Shield before the player's life points. This would mean that the player would be able to take up to 30 hits (or if the duration of reduction phase runs out) before the damage taken affects their own life points. In the most extreme case, the player could have up to 30 seconds of damage immunity (the length of the reduction phase), however this is only possible if the player has extremely low life points.
Crystal Shield (life saver)
Crystal Shield (damage immunity)
Life saver: An example of Crystal Shield 3 saving the player's life. In this example, the player takes 3 hits during the absorption phase - an , a , and a . This means that the life points stored in the pool is (as can be seen once hovered over on the buff bar). Next, should the player take a hit larger than the current life points, the player will be alive with as many life points stored in the Crystal Shield ( in this case).

Damage immunity: An example of Crystal Shield 3 providing damage immunity. In this example, the player takes 5 hits during the absorption phase - a , a , a , a , and a . This means that the life points stored in the pool is (as can be seen once hovered over on the buff bar). Next, the player's life points are at the start of the reduction phase. If the player takes damage that is greater than , the damage removed from the pool will be reduced to (regardless of how high the hit would have been). In this case, two hits are taken during the reduction phase, both of which are larger than player's life points and as a result are removed from the pool. This can be seen once the life points displayed on the buff bar updates to .

Sources[edit | edit source]

MaterialRarityPerk ranks with X materials
Standard gizmoAncient gizmo
12345123456789
Clear parts.png
Clear partsCommon01111001111111
Subtle components.png
Subtle componentsUncommon111–21–31–31111–21–31–41–41–41–4
Faceted components.png
Faceted componentsRare1112–33000133–4444

Suggested gizmos[edit | edit source]

Gizmo layout Possible perks
Faceted components.pngFaceted components.pngFaceted components.png
Faceted components.pngFaceted components.pngFaceted components.png
Faceted components.pngFaceted components.png
Chance decreases with Extreme invention (3).png and level 120. Chance scales from 40% at level 120 up to nearly 100% at level 50.
  • Other possible perks:
Noxious components.pngNoxious components.pngNoxious components.png
Noxious components.pngNoxious components.pngNoxious components.png
Faceted components.pngNoxious components.pngFaceted components.png
Chance increases with Extreme invention (3).png and level 120.
  • Other possible perks:
Zaros components.pngZamorak components.pngZaros components.png
Zamorak components.pngZamorak components.pngZamorak components.png
Faceted components.pngZaros components.pngFaceted components.png
Chance is highest at level 100. Chance decreases with Extreme invention (3).png.
  • Other possible perks:
Culinary components.pngCulinary components.pngCulinary components.png
Culinary components.pngOceanic components.pngCulinary components.png
Faceted components.pngCulinary components.pngFaceted components.png
Chance is highest at level 120. Chance decreases with Extreme invention (3).png.
  • Other possible perks:
Faceted components.png
Faceted components.pngFaceted components.pngFaceted components.png
Faceted components.png
  • Other possible perks:
Faceted components.png
Faceted components.pngSubtle components.pngFaceted components.png
Faceted components.png
  • Other possible perks:
Explosive components.png
Explosive components.pngFaceted components.pngExplosive components.png
Explosive components.png
  • Other possible perks:
Explosive components.png
Explosive components.pngSubtle components.pngExplosive components.png
Explosive components.png
  • Other possible perks:

Update history[edit | edit source]

The update history project is a work-in-progress – not all updates to this topic may be covered below. See here for how to help out!
  • patch 11 March 2019 (Update):
    • The following message now gets filtered: "Your crystal shield lifepoints have been depleted!"
  • patch 12 June 2017 (Update):
    • A debuff icon has been added to tell you when Crystal Shield comes off Cooldown (similar to Crackling).
    • A tooltip has been to the Crystal Shield defence active buff icon which shows how many temporary life points you have.
    • A 1 minute cooldown text line has been added to the Crystal Shield and Crackling perk descriptions.

Notes[edit | edit source]

  1. ^ To be more precise, it is really the frequency of ticks that the player is taking damage and not really the attack rate that determines the effective attack rate. However, in the simplest case, this is the attack rate of the enemy. As an example, take 4 enemies, each with an attack rate of 4, attacking the player with their hits offset by one tick from each other (enemy A attacks tick 1, enemy B attacks tick 2, ...). In this example, this is effectively the same as an attack rate of 1 to the player. This means that as long as the player is taking at least one hit every tick, regardless of the number of enemies attacking, the effective attack rate is 1. Conversely, if these same enemies, each with an attack rate of 4, are attacking the player on the same tick (enemy A attacks tick 1, enemy B attacks tick 1, ...), then the effective attack rate is 4. In general, more enemies attacking the player leads to a higher frequency of ticks that the player is taking hits, lowering the effective attack rate.

References[edit | edit source]