Critical Hit Chance Edit

Here is a very rough formula for computing your Critical Hit chance. Note that all formulas here are extreme simplifications and aren't more than 90% accurate, especially at levels <20,000:

baseCritChance = 0.06 + (agi * 0.07 + luk * 0.22) / (enemyHp / 50);
baseCritChance += agiWarai * 0.11 + lukWarai * 0.14;
if (baseCritChance > 0.35)
  baseCritChance = 0.35
totalCritChance = baseCritChance + agiWarai * 0.11 + lukWarai * 0.14;

(Note that a Wariai is essentially a ratio of one stat to your others. If you had totals of 500,000 HP, 300,000 Atk/Def, 200,000 Agi and 100,000 Luk, then your AgiWarai and lukWarai would each be 0.2, because each has an effective 100,000 points allocated).

The multipliers from your equipment and character/player levels factor into Warai calculations, so realistically most players will not see their crit chance ever exceed 35%. Even with 100% of your stats pumped into luck, you'd never see a crit chance above 49%

For a case study, assuming your Agi is 10% of your total stats:

Jousting Fox - Need 2500 Agi for 36% crit (or 750 Luk)

Orochi - Need 250,000 Agi for 36% crit (or 75,000 Luk)

Black Mother - Need 500,000 Agi for 36% crit (or 150,000 Luk)

Suzaku - Need 930,000 Agi for 36% crit (or 275,000 Luk)

Genbu - Need 2,500,000 Agi for 36% crit (or 750,000 Luk)

In terms of critical hit chance, Agility is marginally valuable. Luk is about 3x as important, but doesn't provide Combo Rate. Because enemy HP scales so rapidly, and it's hard to keep your Agi/Luk at a reasonable percentage of your total stats, critical hit chance plays a significantly diminshed role as the game progresses.

Critical Hit Damage Edit

Critical hits do 1.75x to 2.75x damage, depending on your critical hit chance. With a minimal critical hit chance (5%) you will do 1.75x to 2.17x. With 15% crit you do 1.75x to 2.53x. With 25% crit and above, you do 1.75x to 2.75x. However, as you continue to increase your crit chance, you slightly increase the chance of hitting for 2.75x. That is then multiplied by (1 + 0.2 per Critical Damage Ring).

With 25% crit and 3 rings, you would do 2.8x to 4.4x damage per hit (average 3.6x).

Critical Rate Ring Edit

The Critical Hit Chance ring gives a +8% chance to crit and does stack with itself. This is added after the Agi computation, and combo rate cannot exceed 70% (or 72% in the bonus area)

Critical Damage Ring Edit

Each Critical Damage Ring stacks and gives 20% more critical damage (additive with itself, multiplicative with damage, so 3 rings multiplies your base crit damage by 1.6)

Combo Rate Edit

The Combo Rate formula is similar to the Critical Hit Rate formula, but only uses Agi. Your combo rate does not diminish as you combo more in one round.

baseComboChance = 0.06 + (agi * 0.52) / (enemyHp / 50);
baseComboChance += 0.24 * agiWarai
if (baseComboChance > 0.5) 
   baseComboChance = 0.5;
baseComboChance += 0.24 * agiWarai

Assuming you run agi as 10% of your total stats:

Jousting Fox - Need 540 Agi for 52% Combo

Orochi - Need 50,280 Agi for 52% Combo

Black Mother - Need 100,000 Agi for 52% Combo

Suzaku - Need 190,000 Agi for 52% Combo

Genbu - Need 522,000 Agi for 52% Combo

Combo Rate Scaling Edit

As your combo rate approaches 70%, its impact on your damage increases exponentially:

The list below shows a mapping from Combo rate to average damage multiplier:

6% -> 1.06x

20% -> 1.25x

35% -> 1.54x

52% -> 2.08x

61% -> 2.56x

70% -> 3.29x

Reaching the max combo rate requires you to have a Combo Rate ring and nearly 40% of your total stats (modifying for 5/3/3/2/1 multipliers) be Agi (but due to weapon multipliers, this means you'd need to put 75% of your points into Agi, which isn't practical). However, if you're aiming for the numbers listed above to reach 52% chance, the 9% chance from the Combo Rate ring will increase your dps by an extra 25%.

Combo Rate Ring Edit

The Combo Rate Ring gives a +9% chance to perform a combo and does not stack with itself.

Combo + Crit Bonus Area Edit

When inside a Combo/Crit bonus area:

critRate = critRate * 1.05 + 0.075;

comboRate = comboRate * 1.1 + 0.075;

And then these bounds are enforced:

20% > critRate > 60%

45% > comboRate > 0.72%

This bonus area is primarily valuable if you have a very low agi/luk to reach those minimums, for characters with very high agi/luk, the benefit may be reduced if it puts you above the limits.

Hard Mode Edit

In hard mode, all the listed calculations remain roughly correct, calculated against the enemy's modified HP. For simplicity sake, just use the numbers listed for each boss and multiply the Agi needed by 11x to get the Hard Mode Agi needed.

A note on hard mode accessories:

Critical Rate (8% more) and combo rate (9% more) rings are not affected by the enemy's current HP. If you're deciding whether to use an AGI+5 or a combo rate ring, the AGI gem provides more combo rate up until enemies reach about 20,000,000 life, and more crit than a crit ring until enemies reach about 2,500,000 life. However, bear in mind that direct scaling of combo from AGI caps at 50% and crit at 35%, so your reasons for using a combo rate ring are only: 1 - you are past the Hard Mode Elemental Gods, or you are at max combo and you want more.

Keep in mind Crit rings stack, so you could theoretically get around 60% combo and 60% crit chance using 1 combo rate ring and 3 critical rate rings along with plenty of AGI and some Luck. With 60% crit chance, you would see 58% of your critical hits landing for 2.75x (at 35% chance, you'd see only 33% of your crits landing for 2.75x) - so thanks to the way crit damage calculations work, there is a reasonable amount of scaling to motivate you to accumulate more crit.