Final damage from crit

Critical damage refers to the final damage bonus applied when applied to a critical attack, which we'll denote by CritDMG. Critical rate refers to the likelihood of critical damage being applied to an attack, which we'll denote by CritRate. This is only applicable to Hayatos. Shimada Heart applies final damage additively to the crit component of the damage formula. We'll denote the value of this by ShimadaHeart (this is 49.5% for every end-game Hayato).

$$1 + (\text{CritRate}) * (\text{CritDMG}) + \text{ShimadaHeart}.$$CritDmg as displayed on the stat screen is 35% lower than the value should be for final damage calculations. This is due to a variation mechanic which allows an additive base critical damage modifier to vary from a minimum of 20% to a maximum of 50%, which is where the 35% comes from: it is the average of the range.Let’s say a player has 80% crit damage in his stat window. This means that on critical hits, they will deal 115% more final damage than a non-crit. Let’s also say that he has 100% crit rate, and he now cubes 8% crit damage on his gloves, bringing his crit damage up to 123%. How much final damage did he gain?This is given by $$\frac{1 + 1.23}{1 + 1.15} = 1.037,$$ or 3.7% final damage.Let's continue with the above example, but instead assume that his critical rate is 90% rather than 100%. Not all of his lines will be crits. So, how can we know what his final damage increase is, from critical damage, if he gains the same 8% crit damage from his glove?Now, it’s expressed as: $$\frac{1 + 0.9 * 1.23}{1 + 0.9 * 1.15} \sim 1.035,$$ or 3.5% final damage.Notice that the final damage gain in this setting is less than the final damage gain in the previous example, which is expected.There is another side to gaining final damage through criticals, though. What if instead of gaining critical damage, you gained crit rate? Let’s say that you currently have 125% crit damage in your stat window, with 95% crit rate. You currently have a level 2 Phantom Link Skill, and you’re wondering how much benefit you’ll gain if you level it to 210 for the final 5% critical rate. Final damage in this case is given by $$ \frac{1 + (0.95 + 0.05) * 1.6}{1 + 0.95 * 1.6} \sim 1.032. $$Lastly, let's return to the player from our previous two examples and assess his gains from Decent Sharp Eyes, which gives 10% crit rate and 8% crit damage. Recall that the player's relevant base stats were 90% crit rate and 115% critical damage.Then his final damage is given by $$ \frac{1 + 1 * 1.23}{1 + 0.9 * 1.15} \sim 1.096. $$