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Critical Hit Rate
For melee weapons, critical hit rate is the sum of the base rate (5%), gear/atma (0100%), merit points (05%), Buffs, Weapon Skill modifiers, and player Dexterity relative to target Agility (also known as dDEX, 015%). As there is no cap to critical hit rate, it can be taken all the way to 100%, guaranteeing that every attack is a critical hit. Categoryspecific caps are marked. It also only takes whole number values, so it is impossible to have something like a 12.5% Critical Hit Rate.
Weapon Skills with the description "Chance of Critical Hit varies with TP" modify Critical Hit Rate during Weapon Skill. Generally, the base modification at 100TP varies from 0% to 40%, and extra Critical Hit Rate is awarded for TP over 100.
Example: A Thief has 115 Dexterity, Level 5 Critical Hit Rate Merits, +4% Critical Hit Rate in gear, and is fighting a monster with 96 Agility. They have a 5% + 4% + 5% + 0% + 2% (dDEX=19) = 16% Critical Hit Rate.
For ranged weapons, critical hit rate is the sum of the base rate (5%), gear/atma (0100%), merit points (05%), Buffs, Weapon Skill modifiers, and player Agility relative to target Agility (also known as dAGI, no known cap). Dexterity does not affect critical hit rate for ranged weapons.
Contents
Melee Critical Hit Rate (dDEX)
dDEX (Player DEX  Target AGI) determines the contribution of Dexterity to melee critical hit rate. This is added on to the base rate and merits to determine the total critical hit rate. Because this value depends on the target's Agility, which will be determined by its level and job combination, Critical Hit builds are sensible in some places and not sensible in others.
Based on the chart below, you can see that there is an extremely significant jump in critical hit rate when dDEX is increased from 40 to 50 (from 4% at dDEX=39 to 15% at dDEX=50), but no further boost to critical hit rate once dDEX is greater than 50.
dDEX  Crit Rate 
06  +0% 
713  +1% 
1419  +2% 
2029  +3% 
3039  +4% 
4050  +(dDEX35)% 
Ranged Critical Hit Rate (dAGI)
dAGI (Player AGI  Target AGI) determines the contribution of Agility to ranged critical hit rate. This is added on to the base rate and merits to determine the total critical hit rate. This value does depend on the target's Agility, but there are few times when critical hit rate builds are optimal (vs. times when they're less optimal) because adding the same amount of AGI always grants the same amount of critical hit rate and ranged critical hits are a constant multiplier of the damage you would have done otherwise.
 Crit Rate = +floor( dAGI÷10 )%
This has been tested for the range dAGI = 0~90.
Merit Points
Critical hit rate is also a merit category available to all jobs. It can be merited a total of 5 times. Each merit upgrade grants a 1% increase in critical hit rate. It costs 15 merits to fully upgrade (1>2>3>4>5). This is likely the most popular merit choice in the "other" category.
Testing Critical Hit Rate
If you have something giving you an unknown amount of Critical Hit Rate, then the easiest way to find it is to use Abyssea Atmas and gear with known potency to force a 100% Critical Hit Rate. Lets say you have Y% known critical hit rate and X% from an unknown source. If you swing your weapon (or use your Weapon Skill) and get a noncrit return, you know that:
 100% > Y% + X%
Furthermore, if you manage to Critical Hit 303 times in a row, you can say with 95% certainty that your Critical Hit Rate is 100%. You can think of it like this:
 .99^n = Probability of Critical Hitting "n" times in a row if your critical hit rate is actually 99%.
Now, there's also a chance that you critical hit "n" times in a row with a 98% critical hit rate, so to accurately calculate the odds you have to add up all the .XX^n values over the range of possibilities. If you're using something like Razed Ruins and Gnarled Horn with 5 Critical Hit Rate merits, you know that your minimum Critical Hit rate is 75%. Then the equation would become:
 .99^n + .98^n + .97^n ... .75^n = Probability of Critical Hitting "n" times in a row if your Critical Hit rate is actually between 99% and 75%.
That equation happens to equal 95% when n = 303, hence the above statement.
Example: So say that you have a piece of equipment (like Assassin's Vest) with an unknown boost to Critical Hit Rate. The testing method would recommend you go to Abyssea, put on Atma of the Gnarled Horn, Atma of the Razed Ruins, and Atma of the Dark Depths (95% Critical Hit Rate with 5 merits) and the equipment. Swing away at something, and increase your critical hit rate by 1% per noncrit. The first sign of negative evidence (a noncrit) is enough to increment. At the final level, you should end up Critical Hiting 303 times in a row without seeing any regular hits, which makes you 95% confident that you've found your target value. From that point, you would add up your sources of critical hit rate and subtract them from 100%. The remainder is the critical hit rate on the equipment.
Past Critical Hit Rate tests relied on long parses against Hpmedes (N=10000+, as is seen in the references), Abyssea brought with it the possibility of a new way to test unknown Critical Hit Rate boosts. Overall, this is much faster than a similarly accurate Hpemde parse. On average, you would expect to swing 531 times to determine the critical hit rate of an unknown source with 95% confidence. The test will go much faster if you undershoot Critical Hit rate with your initial guess than if you overshoot it, and you should be able to get within 5% very quickly. This same method can be applied to Weapon Skills, using them as the X% unknown Critical Hit Rate.
Enhanced By
Abilities
 Rogue's Roll: Up to ~+20% critical hit rate depending on result.
 Blood Rage: +20% critical hit rate while in effect.
 Impetus: Up to +50% critical hit rate with consecutively landed attacks.
 Mighty Strikes: 100% critical hit rate while in effect.