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Glancing blows are combat events that can occur when fighting a mob of equal or higher level.
These occur only on white damage and result in the attack having its damage reduced in proportion to the difference between the attacker's weapon skill (capped at the attacker's level * 5), and the target's defense skill.
At current Glancing blows occur at about 20% of the time versus mobs that are above your level. These attacks only do 75% of their normal damage versus a mob that is 3 levels above you. Bosses are counted as "your level+3".
Against mobs with defense roughly equal to or higher than your Attack Rating (i.e. your weapon skill), you will have a chance to land a glancing blow instead of a normal hit. A glancing blow only occurs on white melee damage and does less damage than a normal blow. If the attacker's weapon skill is less than his level * 5, the damage reduction will be proportional to the difference between the attacker's weapon skill and the target's defense.
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Effect from Weapon skill
Weapon skill greater than the normal max for your level (i.e. your level * 5) does not reduce the chance for a glancing blow to land.
 Prior to 2.0.1, extra weapon skill did reduce the severity of the damage reduction, but this is no longer the case.
Glancing blows do not occur against players, only against mobs. At present ranged attacks do not result in glancing blows.
Glancing Blow chance
Pre 2.1
Players have a chance to perform a glancing blow against mobs equal to 10% plus 2% per point of difference between attack rating and defense. Nonmelee classes level 30 and higher have a 60% chance to glancing blow. Nonmelee classes from level 11 to level 29 have a (level  10) * 3% chance of a glancing blow. Weapon skill above your level * 5, as from gear or racial bonuses, affects neither the damage reduction nor the chances of landing a glancing blow. A mob's Defense skill is equal to its level * 5.
This formula means that, for a level 60 player with fully trained weapon skill, 30% of all whitedamage melee attacks will be Glancing Blows against level 62 mobs, and 40% of all whitedamage melee attacks will be Glancing Blows against level 63 mobs.
The presence of your weapon skill in this formula, rather than just your level, explains why training up a newlyacquired weapon skill against mobs close to your own level results in many, many Glancing Blows at first.
Post 2.1
The release notes for patch 2.1 say the following:
 Glancing Blows have significantly less of a chance to occur during a player's melee attacks when targets are near the player's level.
The new formula seems to be:
glancing blow chance = 10 + mob defense  player weapon skill
For a level 73 mob, that's a 25% chance of glancing blow.
The pre2.1 automatic base glancing blow chance for nonmelee classes, when attacking targets level 30 and higher, seems to have been removed.
Post 3.0
Experimentally, players using Recount have consistently seen 24% of their melee autoattacks against Raid Boss monsters be glancing blows.
Post 3.3
Caster classes no longer have an increased chance to land a glancing blow.
Glancing Blow damage reduction
The damage of a glancing blow is complicated. It starts by calculating the difference between the target's Defense and the attacker's attack rating, where the attack rating is capped at the attacker's level * 5 (just as it is for determining the chance of a glancing blow occurring). This is then used to calculate a minimum and maximum damage factor. The actual damage factor is then randomized between these two values. The low value starts at 1.3  0.05 * rating difference. If the attacker is a caster then this is reduced by 0.7 more. The smaller value of this and 0.6 is kept as the low end. If the attacker is a melee class then instead the lower value of 0.91 and (1.3  0.05 * rating difference) is used for the low. Regardless, the low end will not go below 0.01.
The high end of the range starts at 1.2  0.03 * rating difference. Casters are reduced a further 0.3. The high value regardless of class is kept between 0.2 and 0.99.
The average reduction from a glancing blow is therefore (high + low) / 2 using the formulae above. This gives a level 60 player, with a weapon skill of 300 or more, a 15% damage reduction with all Glancing Blows against level 62 mobs, and a 35% damage reduction with all Glancing Blows against level 63 mobs.
As of 2.0.1, the player's weapon skill is capped at level * 5 in the damage reduction formula, just like it is in the formula for determining the chance of a glancing blow. (Before 2.0.1, glancing blows landed against a level 63 NPC by a level 60 player with +10 Weapon Skill would do nearly as much damage as the player's ordinary hits did.)
Glancing Blow Implications  Crit Cap
The fact that 24% of all whitedamage melee attacks made against a Boss Mob will be Glancing Blows, no matter what you do, has implications when choosing how much Crit Rating gear to use. Due to the tablebased nature of WoW's attack resolution system, Glancing Blows take precedence over critical hits. If your combined miss, dodge, parry, block, glancing blow, and crit chance against a mob is 100% or higher, you will never see a normal whitedamage hit made against that mob (all your hits will be either glancing blows or critical hits). If it exceeds 100%, it is your critical hit chance that gets "pushed off the end" of the table. Any Crit Rating gear added past this point will not improve your critical hit chance with whitedamage melee attacks at all. This is sometimes called the "Crit cap" (see Critical_Strike#Crit_Cap).
In the worst case  dual wielding with no hit rating (27% miss chance) from the front of a Raid Boss mob (10+% parry, 6.5% dodge) who can block (6.5% chance), the crit cap is 26%. Moving behind such a mob removes the chance to block and parry, increasing the crit cap to 42.5%. Adding hit rating, or +hit chance talents, will raise this cap by reducing the chance to miss. Adding Expertise will raise this cap by reducing the chance to parry and dodge.
In a raid situation, it is easier to approach the crit cap than you might think. Consider a dualwielding enhancement shaman with talents but no hit rating (19% miss), meleeing from behind (6.5% dodge, 24% glance). His crit cap would be 49.5%. With a dual mongoose proc (9.6% crit), Leader of the Pack (5% crit), Grace of Air (3.48% crit), Elixir of Major Agility (2.31% crit) and Seal of the Crusader (+3% crit), the shaman would be crit capped with only 26.11% crit from his gear and talents.
Melee commonly exceeding the 40% crit mark should be cognizant of the cap and adjust their buffs and weapon enchant accordingly.
"Yellow damage" melee attacks, including both Instant attacks such as Sinister Strike and onnextswing attacks such as Heroic Strike, do not produce Glancing Blows. For these attacks, added Crit Rating gear beyond the "Crit cap" described above will improve your critical hit chance.
Ranged weapon attacks (Bows, guns and crossbows) do not have glancing blows at all, thus weapon skill does not affect this for them. It works the same for all classes that can use ranged weapons (hunters, rogues and warriors).
See also
 Combat
 Combat rating system
