Ice Shards
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The subject of this article was removed from World of Warcraft after the Mists of Pandaria cleared.

Ice Shards  

 
Usable by  
Class  Mage 
Properties  
Location  Frost, Tier 2 
Affects  Critical Strike Bonus 
Ranks  3 
Requirements  
Points required  5 
Spec specific  Yes 
Ice Shards is a mage talent that increases the mage's critical strike damage bonus for Frost spells by 33% per rank, up to 100% at max rank 3. Ice Shards is present in many frost builds, as it is a key talent for increasing frost damage output. Since this talent only improves damage done by crits, it combines well with talents that increase frost crit chance. Shatter is a popular talent for increasing critical strikes, combined with other talents and abilities that help Shatter by increasing freeze opportunities, such as Frostbite. Also, Empowered Frostbolt, Arcane Instability and Arcane Potency all directly increase critical strike chances for frost spells, without relying on Shatter.
Rank table Edit
Rank  Critical Strike Bonus 

1  + 33% 
2  + 66% 
3  + 100% 
Mathematics Edit
Spell critical strikes normally add a bonus equal to 50% of the base spell hit, meaning a hit for 1000 damage will crit for 1500 damage. The talent percentage is applied to this bonus damage, doubling the bonus at Rank 3. This means that with Rank 3 Ice Shards, a spell that normally hits for 1000 damage will crit for 2000 damage. The following formula will compute a critical strike given base spell hit damage, where X is the number of points in Ice Shards:
Crit damage = Hit damage * (1.0 + 0.5 * (1.0 + 0.333*X))
Ice Shards stacks with the talent Spell Power. With both talents at max rank, a Frost spell that hits for 1000 will crit for 2250, a bonus of 1250 damage. The following formula will compute a Frost critical strike with both talents, where X is the number of points in Spell Power and Y is the number of points in Ice Shards:
Crit damage = Hit damage * (1.0 + 0.5 * (1.0 + 0.25*X + 0.333*Y))
Burst damageEdit
Points  Crit Multiplier  Net gain 

0  1.5   
1  1.66  +11% 
2  1.83  +22% 
3  2.0  +33% 
Ice Shards increases your crit multiplier by +0.166 per point you spend on the talent.
Long term damageEdit
This is a formula that calculates how much of a boost in long term damage (over a large number of spell casts) you can expect to get from this talent when using frost spells that can crit. The formula uses the "three outcomes" model, as well as a concept from probability theory called expected value. This calculation does not take into account resists and partial resists.
Mathematical derivation Edit
The "three outcomes" model states that in WoW, when one casts a spell there are three possible results: a hit, a critical hit, or a miss. If we know the probability of each outcome, we can use probability theory to calculate the expected value of damage. Then, we can calculate the percentage difference in damage we can expect to see from various crit rate/hit rate/talent point combinations.
[(chance to crit) × (crit damage)] + [(chance to hit and not crit) × (average damage)] + [(chance to miss) × 0]
 C = Chance to get a crit.
 H = Chance to hit.
 T = Talent points in Ice Shards.
 A = Average spell damage (including all damage modifiers).
 1.5×A = Normal crit damage
 (1.5 + (T/10))×A = Crit damage due to Ice Shards.
 (1−H) = Chance you will miss (and do 0 damage).
 (H−C) = Chance to hit and not crit.
Without Ice Shards, the expected amount of damage one does with spells is:
C×1.5×A + (H−C)×A + (1−H)*0
With Ice Shards, one expects:
C×(1.5+(T/10))×A + (H−C)×A + (1−H)×0
The percentage difference would be:
( (C×(1.5+(T/10))×A + (H−C)×A) − (C×1.5×A + (H−C)×A) ) / (C×1.5×A + (H−C)×A)
This expression simplifies to:
T×C / (5C+10H)
∀ T={0,1,2,3,4,5}, 0 ≤ C ≤ 1, 0 ≤ H ≤ 1, and (HC) ≥ 0
Results Edit
Essentially, this result states that the increase in long term damage you get from this talent depends on three variables. The first variable is T, the number of talent points you spend on the Ice Shards talent. The second variable is C, your crit rate. And the third and final variable is H, your chance to hit.
This result may seem counterintuitive (i.e. lower hit rates leads to higher bonus). This is a consequence of the the "three outcomes" model. Crits and hits share the same "probability space", and therefore hit rate puts a cap on crit rate. It must be thought of in this way: if you are missing more often, then the critical hit to "normal" hit ratio is higher.
See also Edit
External links Edit
 Expected value at Wikipedia
