Super Robot Wars Z

byBrunom1, Dr. Pepper, Caphi

Part 35: Dr. Pepper's Math Corner (regarding various in-game calculations)

Extra Chapter: Numbers and what they mean

So I think it’s high time to actually talk about math in this game. Super Robot Wars Z is a game with a lot of calculations going on behind the scenes. So get ready for a lot of talk about numbers!

Yeah that’s the stuff right there. Setsuko will serve as our example for this lecture. Z has a lot of stats involved. Both the pilot and the mech have a set of stats that are used to determine how it all goes. First let’s look at the pilot stats, and how they function.

Lv: Level. Obvious for any RPG. The higher it is the better your stats are. 99 is the Level cap.

The cap for all those stats is 400. You’re not going to reach the level cap or any stat cap in normal play. Next let’s look at the mech stats.

HP: Hit Points. A mech loses hit points every time it’s hit by an attack, if HP reaches 0 the mech is destroyed that stage.
EN: Energy. A mech uses 5 energy to move through Air or Space Terrain. Some weapons require energy to use.

Obviously the mech’s stats are upgraded using cash rather than EXP. Each stat can be upgraded 10 times normally. If you’ve unlocked Special Mode, they can be upgraded 15 times.

Finally, there’s terrain rankings. These tell you how well the mech does in each of the four terrain types in the game.

Pilots, Mechs, and Weapons all have their own ranks in each terrain. The ranks are D, C, B, A, and S. D rank mechs or weapons can not function at all in that terrain. To determine the rank, the pilots rank and weapon/mech rank is added and rounded down. C+B=C, C+A=B, C+S=A and so on. Pilot rank can be upgraded with PP, while upgrading mech and weapon ranking requires either a part equipped or a ton of money to upgrade every stat of the mech.

Of course, those are just a bunch of numbers. It’s meaningless to just tell you them if I don’t show you how they interact. And oh boy do they interact. The formulas for this game are fairly complex with a lot of fiddly bits. Still, let’s start by seeing how the game calculates Attack and Defense.

Damage Formula
• (Melee or Range+Will)*(Weapon Attack*Weapon's Terrain Rank)/200=Attack

Rank effects
• S=110%,A=100%,B=80%,C=60%

Defense Formula
• [(Defense+Will)*Mech's Armor]/200=Defense

As you can see, the way the game works is that the pilot stats are used to create multipliers that affect the mech’s stats. Also note the way Will works in the damage calculations. A point of Will is equal to a point of Melee, Range, and Defense simultaneously. Incidentally, Will Limit Break costs 500 PP. To buy 20 points of Melee, Ranged, and Defense stats costs 3000 PP. I think we know which one is the better deal.

But of course one you have the Attack and Defense how does it come together? With a lot, and I mean a lot of fiddly modifiers

Final Damage

Terrain Modifiers

Ground, Water, and some Space Terrain will often have effects. Shown as a percentage, any attacks final damage will be reduced by the percentage shown.

Size Modifier

Each mech has a size, which is represented in the formula as a number. Small:1, Medium:2, Large:3, 2Large:4. The size modifier works as a percentage. The formula is as follows.
• 1+(Attacker's Size-Defender's Size)*10=Size Modifier Percentage
If the Pilot has the Ignore Size Difference Skill, ignore any negative size modifiers

Ability Modifiers

There are quite a few abilities that can modify damage.
• Any mech with a Shield whose Pilot triggers the Blocking skill will use Shield Defend and reduce damage by 60%
• Any pilot with the Guard skill whose Will is over 130 will reduce damage by 20%
• Any pilot with the SEED skill whose Will is over 130 will increase damage by 10%
• Any mech with the Mazin Power ability will increase damage by 25% once the pilot is over 130 Will
• Any mech with the Dizer Full Power ability will increase damage by 25% once the pilot is over 130 Will.

There are a lot of Squad Leader Bonuses that increase or decrease damage done. That is all.

Formation Modifier
If the Attacking Formation has an advantage over the defending formation, 10% more damage is done. Each Formation has an advantage over another one, the chain is:
• Tri Formation > Center Formation > Wide Formation > Tri Formation.
Barrier Effect

Unlike other defensive measures, Barriers don’t add a negative damage modifier to the final damage. Instead they just subtract a flat number from the final damage.

Once you do all that math, the game finally spits out the final damage number!

Of course, first you have to hit the mech first. Which means, thats right, more math! First we need to how well an attack can hit

Hit Rate Formula
• ([Pilot Accuracy/2]+Mech Accuracy)*(Terrain Rank)+(Weapon Hit Rate)=Hit Rate
Rank effects
• S=110%,A=100%,B=80%,C=60%
Whether the attack uses the attackers terrain or the defenders terrain is weird and complex. Far as I can tell, if the attack animation shows the attacker’s mech getting close to the defender then it uses the defenders terrain, if not then it uses the attacker. (Example: The Virgola 1’s Hard Strike would use the enemy’s terrain for Terrain Rank calculations, while it’s Ray Straight Turret would use the terrain it’s standing on for Terrain Rank calculations.)

Evasion Rate Formula
• ([Pilot Evasion/2]+Mech Mobility)*(Terrain Rank)=Evasion
The same basic numbers apply, though thankfully the defender always uses it’s own Terrain to determine ranking. Now to do the math for these numbers

Final Hit Rate
• (Hit Rate-Evasion)*(Size Modifier)+(Distance Modifier)+(Terrain Effects)+(Commander Aura Modifier)+(Skill Modifiers)+(Squad Leader Bonus Modifiers)+(Formation Modifiers)+(Spirit Command Modifiers)
Distance Modifier

Basically the closer you are to the target the more accurate you are. The formula is:
• (5-Number of Squares between units)*3
Size Modifiers

The size modifier is based off the defenders. 2Large doesn’t have it’s own Modifier for hit rate, just using Large’s
• Large=120%, Medium=100%, Small=80%
Commander Aura Modifier

If a unit is in the “Command Aura” of an allied unit with the Command Skill they get a bonus to Hit and evasion. The amount is dependant on the level of the skill, and how close they are to the ally.

At level on the Commander’s Aura is 3 squares around the unit, it increases by one square per level and the maximum level of the skill is 4. The amount the hit and evasion is increased is shown below.
• Level 1: +12 | +10 | +5
• Level 2: +18 | +15 | +12 | +9
• Level 3: +24 | +20 | +16 | +12 | +8
• Level 4: +30 | +25 | +20 | +15 | +10 | +5

Skill Modifiers

There are so many skills that effect hit rate and evasion that they’re getting their own section.

No.

Formation Modifiers

If in Tri Formation, the Squad Support members get a +20 bonus to their evasion.

If in Center Formation, the Squad Leader gets a +20 bonus to Accuracy.

Spirit Command Modifiers

Naturally, a few spirit commands affect hit and evasion.

Focus adds 30 to hit rate and subtracts 30 from evasion rate.

If an opposing pilot casts Confuse then all hit rates for that turn are halved.

Once the final number is made with all these fiddly bits, the game rolls a random number between 1 and 100 for the attacker. If the result is good, the attack hits, if not it misses. Once the damage has been calculated the game checks for a critical hit. The formula is a bit less fiddly.

Critical Hit Rate
One the rate has been found, the RNG is summoned again. Critical hits multiply final damage done by 1.5.

Skill Details

We’re not done yet though! Far from it, there are a ton of skills that affect accuracy and evasion and whole bunch of other stuff.

Blocking

Blocking can only be used with a mech that has a Shield or Sword Equipped. Sword cut just negates melee attacks, while Shield Defense reduces damage by 60% Both have the same activation rate.
Two more things about Blocking. There’s a floor on the activation rate, if the result is less than 10, then it’s increased to 10. Also, enemy units have the final activation rate cut in half, with a floor of 5.

Counter

Counter lets the defender attack first on the opposing phase. The activation rate is a bit complex.
• [(Defender’s Skill-Attacker’s Skill)/8+(Counter Level)]/16
Predict
• +10 to Hit, Evade, and Critical Rate at 130 Will
The only drawback free skill to effect Hit, Evasion, or Critical Rate that can be bought. It does give a bit of an extra oomph.

Prevail

This skill is a bit complex. It increases Hit and Evasion, the Mech's Armor, and Critical rate as the mech's HP goes down. How much it increases and when it starts increasing it depends on the level of the skill. At Level 1 Prevail only gives a tiny boost, and only when the mech has lost 90% of its HP. At Level 2 the skill instead gives a tiny boost at 80%, gives a larger one at 90% and so forth. At level 9 the boost starts at 90% HP and goes from there. Here's the rates of increase:

code:
``````+------------+---+---+---+---+---+---+---+---+---+
|HP Remaining|90%|80%|70%|60%|50%|40%|30%|20%|10%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 1    |   |   |   |   |   |   |   |   | 5%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 2    |   |   |   |   |   |   |   | 5%|10%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 3    |   |   |   |   |   |   | 5%|10%|15%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 4    |   |   |   |   |   | 5%|10%|15%|20%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 5    |   |   |   |   | 5%|10%|15%|20%|25%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 6    |   |   |   | 5%|10%|15%|20%|25%|30%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 7    |   |   | 5%|10%|15%|20%|25%|30%|35%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 8    |   | 5%|10%|15%|20%|25%|30%|35%|40%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 9    | 5%|10%|15%|20%|25%|30%|35%|40%|45%|
+------------+---+---+---+---+---+---+---+---+---+``````
Armor Increase:
code:
``````+------------+---+---+---+---+---+---+---+---+---+
|HP Remaining|90%|80%|70%|60%|50%|40%|30%|20%|10%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 1    |   |   |   |   |   |   |   |   |10%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 2    |   |   |   |   |   |   |   |10%|20%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 3    |   |   |   |   |   |   |10%|20%|30%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 4    |   |   |   |   |   |10%|20%|30%|40%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 5    |   |   |   |   |10%|20%|30%|40%|50%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 6    |   |   |   |10%|20%|30%|40%|50%|60%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 7    |   |   |10%|20%|30%|40%|50%|60%|70%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 8    |   |10%|20%|30%|40%|50%|60%|70%|80%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 9    |10%|20%|30%|40%|50%|60%|70%|80%|90%|
+------------+---+---+---+---+---+---+---+---+---+``````
Critical Rate:
code:
``````+------------+---+---+---+---+---+---+---+---+---+
|HP Remaining|90%|80%|70%|60%|50%|40%|30%|20%|10%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 1    |   |   |   |   |   |   |   |   | 8%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 2    |   |   |   |   |   |   |   | 8%|16%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 3    |   |   |   |   |   |   | 8%|16%|24%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 4    |   |   |   |   |   | 8%|16%|24%|32%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 5    |   |   |   |   | 8%|16%|24%|32%|40%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 6    |   |   |   | 8%|16%|24%|32%|40%|48%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 7    |   |   | 8%|16%|24%|32%|40%|48%|56%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 8    |   | 8%|16%|24%|32%|40%|48%|56%|64%|
+------------|---|---|---|---|---|---|---|---|---|
| Level 9    | 8%|16%|24%|32%|40%|48%|56%|64%|72%|
+------------+---+---+---+---+---+---+---+---+---+``````
As you can see, Prevail is a fairly backloaded skill. You don't really start to get decent results with it until level 7. Still, character with a high level Prevail and at low HP can be scary, with a massive boost to hit and evade, nearly doubling their armor, and pretty much never not critting. This makes Prevail pretty dangerous on bosses, who will have large amounts of HP to trigger it with.

Genius
• +20 to Hit, Evade, and Critical Rate
It’s like Predict but better.

Newtype/Newtype X

Far as I can tell, these skills are identical. They increase hit and evasion and grow more potent depending on the level of the skill. Some weapons require this skill to be used.
• Level 1: No Bonus
• Level 2: +5%
• Level 3: +10%
• Level 4: +15%
• Level 5: +20%
• Level 6: +25%
• Level 7: +25%, increases the range of weapons requiring this skill by 1.
• Level 8: +30%, increases the range of weapons requiring this skill by 1.
• Level 9: +30%, increases the range of weapons requiring this skill by 2.
Enhanced Human/Artificial Newtype

Increases Hit and Evasion and counts for weapons requiring the Newtype skill.
• Level 1: No Bonus
• Level 2: +4%
• Level 3: +8%
• Level 4: +12%
• Level 5: +15%
• Level 6: +20%
• Level 7: +20%, increases the range of weapons requiring this skill by 1.
• Level 8: +25%, increases the range of weapons requiring this skill by 1.
ESP

Increases Hit and Evasion. Like Newtype but not as potent.
Extended

Increases Hit, Evasion, and Critical Rate. This skill is actually enemy only, only had by the Extended Phantom Pain kids.
• Level 1: +3% Hit/Evade, +2% Critical
• Level 2: +6% Hit/Evade, +4% Critical
• Level 3: +9% Hit/Evade, +6% Critical
• Level 4: +12% Hit/Evade, +8% Critical
• Level 5: +15% Hit/Evade, +10% Critical
• Level 6: +18% Hit/Evade, +12% Critical
• Level 7: +21% Hit/Evade, +14% Crtiical
Category F

Increases Hit, Evasion, and Critical Rate. Another enemy only skill. The only pilots with this are the Frost Brothers.
• Level 1: No Bonus
• Level 2: +4% Hit/Evade; +3% Critical
• Level 3: +8% Hit/Evade; +6% Critical
• Level 4: +12% Hit/Evade; +9% Critical
• Level 5: +15% Hit/Evade; +12% Critical
• Level 6: +20% Hit/Evade; +15% Critical
• Level 7: +20% Hit/Evade; +18% Critical
• Level 8: +25% Hit/Evade; +21% Critical
• Level 9: +30% Hit/Evade; +24% Critical
Oversense

Increases Hit and Evasion rate, adds to a Weapons Attack Power, and increases the amount of damage an Overman’s Photon Mat Barrier defends against. Furthermore, each Overman has a unique Overskill which activates at 130 Will. In order for the Overskill to activate the pilot must meet an Oversense level requirement.
• Level 1: +2% Hit/Evade, +50 Attack Power, +100 Photon Mat Barrier Defense
• Level 2: +4% Hit/Evade, +50 Attack Power, +200 Photon Mat Barrier Defense
• Level 3: +6% Hit/Evade, +100 Attack Power, +300 Photon Mat Barrier Defense
• Level 4: +8% Hit/Evade, +100 Attack Power, +400 Photon Mat Barrier Defense
• Level 5: +10% Hit/Evade, +150 Attack Power, +500 Photon Mat Barrier Defense
• Level 6: +12% Hit/Evade, +150 Attack Power, +600 Photon Mat Barrier Defense
• Level 7: +14% Hit/Evade, +200 Attack Power, +700 Photon Mat Barrier Defense
• Level 8: +24% Hit/Evade, +200 Attack Power, +800 Photon Mat Barrier Defense
• Level 9: +27% Hit/Evade, +250 Attack Power, +900 Photon Mat Barrier Defense
Lift Technique

Increases Hit Rate and Critical Rate. Also provides an Afterimage effect, allowing the mech to automatically dodge an attack regardless of evasion rate.
• Level 1: +2% Hit, +3% Critical; 4% Afterimage Activation Chance
• Level 2: +4% Hit, +6% Critical; 8% Afterimage Activation Chance
• Level 3: +6% Hit, +9% Critical; 12% Afterimage Activation Chance
• Level 4: +8% Hit, +12% Critical; 16% Afterimage Activation Chance
• Level 5: +10% Hit, +15% Critical; 20% Afterimage Activation Chance
• Level 6: +12% Hit, +18% Critical; 24% Afterimage Activation Chance
• Level 7: +14% Hit, +21% Critical; 28% Afterimage Activation Chance
• Level 8: +16% Hit, +24% Critical; 32% Afterimage Activation Chance
• Level 9: +18% Hit, +27% Critical; 36% Afterimage Activation Chance
There. That is every pertinent number involved in this game. This game is does a ton of insane math behind the scenes, even though it’s a pretty simple game to play. Still, hopefully this helps give a better understanding of how it all comes together.m