Critical Chance and Critical Damage

In order to answer this, we need to look at the damage formula (credits to Erich von Manstein ):

"Damage = attack^2 / (attack + defense). The range of attack could fluctuate from 100% to 75%."

The good thing about EW5 is that all alterations (bonus damage and reduction such as Accuracy, Assault, Armor Master, etc) are done multiplicatively. Damage (D) becomes Damage including all Multipliers (mD) after applying them. This allows us to easily isolate the critical hit mechanics and look at average damage (avD):

avD=mD*(1-cc)+mD*cc*cd

cc is critical chance and cd is critical damage.

By dividing avD/mD we get the combined crit multiplier (ccm):

1-cc+cc*cd    or   1+cc*(cd-1)

An example: Let's say mD= 1000 and we take a standard general who has 5% critical chance (cc=0.05) and 120% critical damage (cd=1.20). This leads to an average damage of 1010 which equals a 1.01 multiplier.

Here are more examples: [ccm can be seen directly if we put a '.' after the '1' of the results]

As you can see, the highest results are on the diagonal. However, if we start as a blue general with friendliness bonuses, +10 cc will get him to the same value that +20 cd would.

-The effect of critical chance and critical damage as a whole can be packed into a single, combined crit multiplier.

ccm = 1 + cc * (cd - 1)

Given a limited number of points in cc and cd, it's best to distribute them equally.

-The effects of cc and cd from equipment depend on where a general starts from. Looking at their base stats, all generals are below the diagonal, so increasing their critical chance should take priority.

This is tricky, because we need the defender's defense stat and the attacker's attack

So let's use an approximation. For this we need to divide numerator and denominator of the damage formula by 'attack' which yields:

Damage = atk/(1+def/atk)

Now, we can assume that def is usually < atk, which makes the denominator range from 1 to 2 (2 if def=atk). So, in first approximation we can say damage is atk divided by a constant.

In order to "force" an equipment's attack stat increase into a multiplier (atkm) we need to calculate (atk without this equipment + atk from this equipment)/(atk without this equipment).

Probably an example would be useful:

Solar Sword (199 atk, 0.13 cc, 0.37 cd) vs. Thunder (180 atk, 0.20 cc, 0.26 cd) on a general with 800 atk, 0.05 cc, 1.20 cd (without this equipment).

combined crit multiplier (ccm): 1.103 vs. 1.115

attack multiplier (atkm): 1.249 vs. 1.225

multiplying the multipliers: 1.378 vs. 1.366

Here, the Solar Sword is the better weapon, and for them to break even, a base atk of >1000 would be needed. Even for "Napoleon" (800 atk, 0.15 cc, 1.35 cd) the Solar Sword is still superior.

As we've learned, for both ccm and atkm we always have to keep the "starting point" in mind, so when calculating whole sets of equipment it's wise to chose a general's base stats (with friendliness and without equipment), then sum up all the equipment bonuses for atk, cc, cd separately and calculate the approximated average damage with their totals. We don't need to care about other multipliers because we compare the same general in the same hypothetical scenario.

This is how it could look like for Napoleon:

Napoleon: once again, pure damage wins even though the first set up has a significantly higher ccm. But the difference in approximated avD is very small.

Nobunaga: Here, better atk is beaten by a much higher ccm. We want him to have an artifact and with his low base cc of 0.05 he'll make good use of Thunder.

There are also tactical arguments to consider:

-If save/loading or restarting multiple times at the beginning of a short scenario is your thing, then aiming for high Critical Damage (max=200% for Napoleon and Washington) is the way to go.

-The best Critical Chance we can achieve is 53% for Napoleon, most generals will have ~48% at best. If we plan for cavalry and some archers to deal the killing blow and then use their 'attack again' ability, 48% is too much of a gamble. If we settle for the non-critical damage, then a critical hit would be wasted. So artillery and archers are more suited for a critical build.

-Critical Hits multiply the damage. We're better off increasing cc and cd of generals who have high base atk. So we're left with Napoleon, (Li Shimin,) Washington, Nelson, Nobunaga, Yi Sun-sin and (Li Hongzhang + Catherine).