Critical hits deal more damage. It’s what they do. Most of you know that normal damage is tripled during a crit, but some might be surprised to hear that it didn’t work like that in the Jugdral games (FE4 and FE5). There, crits double your attack power before subtracting defense.

How does this affect gameplay? To answer this question, we need to dive into the wonderful world of math. Crit damage is calculated like this:

Jugdral Crit Dmg = 2Atk - Def

Normal Crit Dmg = 3Dmg = 3Atk - 3Def

(For simplicity’s sake, I’m gonna call Jugdral Crit Dmg “JCD” and Normal Crit Dmg “NCD” from now on.)

Normally, if you deal no damage to an enemy (your Atk stat is equal to or lower than their Def stat), a crit won’t do anything to help you. After all, 0 x 3 = 0. But that changes in Jugdral. Imagine Atk is 20 and Def is 30. With a crit, Atk becomes 40 but Def stays the same. Result? 10 damage dealt instead of 0.

**Jugdral crits help overcome the target’s defenses. They can convert 0 damage into real damage.**

But this doesn’t mean Jugdral crits always deal more damage. Why? Take a look at this graph, where the red solid line represents NCD and the green broken line represents JCD.

Horizontal axis is Atk, and vertical axis is crit damage. Assuming Def is constant at 10, JCD is higher when Atk < 20, while NCD is higher when Atk > 20. Notice how the trend reverses at 20, which is not a coincidence: it’s Def x 2. For comparison, see the graph when Def is constant at 20:

Here, JCD is higher when Atk < 40, while NCD is higher when Atk > 40. Again, the point of reversal is Def x 2.

This isn’t the only way to look at the situation, though. We can plot Def against Crit Dmg:

Assuming Atk is constant at 10, NCD is higher when Def < 5, while JCD is higher when Def > 5. If Atk is 30, NCD is higher when Def < 15, while JCD is higher when Def > 15. Point of reversal: Atk / 2.

Finally, we can plot Dmg vs Crit Dmg:

Assuming Def is constant at 0, NCD is always higher than JCD regardless of Atk values. This is because normal crits triple Dmg while Jugdral crits double Dmg and add Def, which is zero in this case. Interesting, but you will rarely see enemies with 0 defense in Fire Emblem, so let’s move on to something more realistic.

Here, Def is constant at 10. JCD is higher when Dmg < 10, while NCD is higher when Dmg > 10. Point of reversal is 10, which is just the Def value. In fact, if you look at the functions, I wrote them specifically as (2Dmg + Dmg) and (2Dmg + Def) to make it clear that, if you want to know which formula gives higher damage, you just need to know whether Dmg is bigger or Def is bigger. A similar graph can be made using Atk as a constant instead of Def, but I like this one because the reversal point is slightly easier to find (the other has the reversal point at Atk/2).

We can also deduce some things with algebra instead of graphs. Jugdral crits deal more dmg when:

2Atk - Def > 3Atk - 3Def

3Def - Def > 3Atk - 2Atk

2Def > Atk

2Atk - Def > 3Dmg

Atk + Atk - Def > 3Dmg

Atk + Dmg > 3Dmg

Atk > 3Dmg - Dmg

Atk > 2Dmg

Now we can summarize how to know under which circumstances one formula yields more damage than the other.

Jugdral crits do more damage when:

· Atk < 2Def

· Def > Dmg

· Atk > 2Dmg

Normal crits do more damage when:

· Atk > 2Def

· Def < Dmg

· Atk < 2Dmg

In layman’s terms, Jugdral crits are better when Dmg is very low. Meanwhile, normal crits either yield low damage if you’re not doing much to begin with, or yield exorbitant amounts of damage if you’re already doing a lot of it. The rich get richer, if you will. Jugdral’s formula is more balanced, and the normal formula is more exaggerated at the extremes.

Jugdral’s formula has serious implications for tanky units. You may think that your armor knight is safe because he takes so little damage from all these enemies. But surprise, this myrmidon just did 15 out of nowhere! Oops. Now high-crit units can pierce through defenses easily. It’s a boon for myrmidons, but a bane for thicc bois.

You might also be wondering, “What about the battle forecast? How are we gonna know how much damage a crit will do? Normally we just multiply dmg by 3, but with Jugdral’s formula we have to multiply atk by 2 and it’s nowhere in the forecast!”

That’s a good point, but! Fire Emblem streamlined damage calculations from FE6 onwards. In Jugdral, the forecast showed the Atk and the Def values, and you had to math out the damage yourself. With the old-fashioned forecast you can deduce JCD easily. If we were to implement Jugdral crits in modern games, though, we should include the possible crit dmg further down the list. In the meantime, you can calculate JCD in modern games by adding Dmg and Atk. A bit cumbersome because it’s not all on the same screen, but it can be done. Alternatively, you can go to Options and change the battle forecast. Now it looks just like in Thracia 776.

In conclusion: the Jugdral games had a formula that benefited those who struggle to do damage, but didn’t produce overkill amounts of it when you were ahead - at least not as much as the normal formula. It makes defensive units worse off and rewards those with high skill. Considering armor knights are seen as underwhelming most of the time, this only digs their grave deeper. If need be, the player can attack the other defensive stat (resistance) to overcome the enemy’s bulkiness. Or the other way around, if it’s a magical enemy with high res. On the other hand, myrmidons are usually underwhelming as well, and this type of crit calculation would make them more useful.

What do you think? Discuss.

(Fun fact: Thabes Labyrinth in Echoes has enemies with almost 100 HP, and you are thankful for the massive amounts of dmg produced by the normal formula. They would be harder to kill with Jugdral’s.)