Quantifying Complex Passives and Converting them into Simpler Terms: #2



Introduction



A while ago, I wrote this post, which broke down several of the complex mechanics in the game and converted them into an approximate percentage-based passive.

The response back then was quite positive, so I decided to do another another one. In this post, I'll be breaking down and converting the complex passives of some of the game's most powerful gasha LRs.

Specifically, I'll be breaking down the passives of the following units:


Note: The calculations in this post are designed to convert complex passives into the "+ X% ATK" passives that they roughly approximate.

This process is designed just to give a general idea how these passives stack up to more standard passives, and they are not exact approximations for all circumstances.

I will outline below what parameters these calculations need in order to provide the exact equivalent values. Outside of those parameters, the results will deviate, but they will remain roughly accurate in most cases.



Parameters for the Following Calculations to be Exact



For the following equations to work, I'm assuming several things:

  • Each unit is SA lvl. 10

  • Each unit is level 6 in the dupe system ability that boosts super attack damage

  • Each unit has no levels in either Critical Hit Chance or Additional Attack Chance.

As I said above, straying outside of these parameters will yield results that deviate slightly, but they will still be relatively close to the results below.



LR LSSj Broly



Passive:

When performing a Super Attack, ATK +80000 but DEF -20000, and launch an additional Super ATK


To accurately convert this passive, it's important to know how much ki LR LSSj Broly will obtain. On the Resurrected Warriors team, LR LSSj Broly will average 15 ki for two of his attacks and 20 ki for one of his attacks.

Here's the ATK calculation for his 15 ki attacks:

  • 20,080 (enhanced base ATK) x 4.4 (Golden Frieza (Angel) leader skills) = 88,352

  • 88,352 x 1.25 (SSj and SFB links) = 110,440

  • 110,440 + 700 (Saiyan Warrior Race link) = 111,140

  • 111,140 x 1.55 (15 ki multiplier) = 172,267

  • 172,267 + 80,000 (passive) = 252,267

  • 252,267 x 4.55 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK boost) = 1,147,814

  • 1,147,814 + 1,071,961 (second super attack w/ 12 ki multiplier) = 2,219,776

Here's the ATK calculation for his 20 ki attack:

  • 20,080 (enhanced base ATK) x 4.4 (Golden Frieza (Angel) leader skills) = 88,352

  • 88,352 x 1.25 (SSj and SFB links) = 110,440

  • 110,440 + 700 (Saiyan Warrior Race link) = 111,140

  • 111,140 x 1.8 (15 ki multiplier) = 200,052

  • 200,052 + 80,000 (passive) = 280,052

  • 280,052 x 6.0 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK boost) = 1,680,312

  • 1,680,312 + 1,071,961 (second super attack w/ 12 ki multiplier) = 2,752,273

Now to average those values out:

  • ( 2,219,776 + 2,219,776 + 2,752,273)/ 3 = 2,397,275

As you can see, LR LSSj Broly's average ATK is 2,397,275 (before crit is applied).


Now that his average ATK has been obtained, the next step is to determine what his average ATK would be without his passive.

Here's his 15 ki ATK equation without his passive:

  • 20,080 (enhanced base ATK) x 4.4 (Golden Frieza (Angel) leader skills) = 88,352

  • 88,352 x 1.25 (SSj and SFB links) = 110,440

  • 110,440 + 700 (Saiyan Warrior Race link) = 111,140

  • 111,140 x 1.55 (15 ki multiplier) = 172,267

  • 172,267 x 4.55 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK boost) = 783,814

Here's his 20 ki ATK equation without his passive:

  • 20,080 (enhanced base ATK) x 4.4 (Golden Frieza (Angel) leader skills) = 88,352

  • 88,352 x 1.25 (SSj and SFB links) = 110,440

  • 110,440 + 700 (Saiyan Warrior Race link) = 111,140

  • 111,140 x 1.8 (15 ki multiplier) = 200,052

  • 200,052 x 6.0 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK boost) = 1,200,312

Now to average those values out:

  • (783,814 + 783,814 + 1,200,312)/ 3 = 922,646


With LR LSSj Broly's average ATK with and without his passive now determined, we can convert his passive into a percentage by comparing the two numbers:

  • 2,397,275 (average ATK w/ passive)/ 922,646 (average ATK w/o passive) = 2.60

Therefore, LR LSSj Broly's passive is equivalent to:

ATK +160%



LR SSj2 Gohan



Passive:

ATK +18% for every Ki Sphere obtained, and Ki +1 whenever Ki is raised with Ki Spheres.


The bulk of LR SSj2 Gohan's passive is already a percentage, but it's important to not forget that his ki boost has a massive impact on his performance. In this conversion, I'll assess the boost obtained through the second part of his passive and combine it with the nuking portion of his passive.

As with all my posts, I'm looking at the ATK generated by each unit. As such, I won't be factoring in the orbs that Whirus provides.

Without the ki boosting portion of his passive, LR SSj2 Gohan would average roughly 17 ki. With his passive, he jumps up to 24 ki.

Here's his ATK equation with his ki boost factored in:

  • 18,975 (enhanced base ATK) x 3.6 (Ultimate Gohan leader skills) = 68,310

  • 68,310 x 2.17 (passive w/ 6.5 orbs gathered) = 148,232

  • 148,232 x 1.15 (SFB link) = 170,467

  • 170,467 x 2.0 (24 ki multiplier) = 340,935

  • 340,935 x 6.5 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK buff + 50% ATK buff) = 2,216,078

Here's his ATK equation without his ki boost factored in:

  • 18,975 (enhanced base ATK) x 3.6 (Ultimate Gohan leader skills) = 68,310

  • 68,310 x 2.17 (passive w/ 6.5 orbs gathered) = 148,232

  • 148,232 x 1.15 (SFB link) = 170,467

  • 170,467 x 1.65 (24 ki multiplier) = 281,270

  • 281,270 x 6.0 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK buff) = 1,687,623

Now I'll compare the numbers to convert the ki boost into a percentage:

  • 2,216,078 (ATK w/ ki boost)/ 1,687,623 (ATK w/o ki boost) = 1.31

Thus, LR SSj2 Gohan's ki boost provides a +31% ATK boost on top of the nuking portion of his passive.


To see his full passive, those numbers need to be multiplied together:

  • 2.17 (nuking passive w/ 6.5 orbs) x 1.31 (ki boosting passive) = 2.84

Therefore, LR SSj2 Gohan's entire passive (w/ 6.5 orbs gathered) is equivalent to:

ATK +184%



LR SSj Future Trunks



Passive:

ATK +120%; High chance for each attack to be a critical hit.


I still haven't seen any data to definitively prove what proc rate LR SSj Future Trunks' built-in critical hit has. However, minor anecdotal evidence has suggested it's around 50%, and because "high chance" usually means a 50% proc rate, I'll assume it's 50% for these calculations.

Luckily, because critical hit chance is a flat multiplier at the end of the damage equation, LR SSj Future Trunks' full ATK equation isn't necessary to see how much of an impact his critical hit chance makes. All I need to do is compare a number with a 50% critical hit chance to the same number using the average type modifier. Because Dokkan loves the number 7, I'll just use 777 as my base number for this comparison.

Here's the base number after it goes through a 50% critical hit chance:

  • 777 (base number) x 1.9 (critical hit multiplier) x 0.5 (critical hit chance) = 738

  • 777 (base number) x 1.015 (average type modifier) x 0.5 (non-critical hit chance) = 394

  • 738 + 394 = 1,132

Here's the base number when it's only multiplied against the average type modifier:

  • 777 (base number) x 1.015 (average type modifier) = 789

Now I'll compare the two numbers to see how much of an ATK increase is generated from LR SSj Future Trunks' built-in critical hits:

  • 1,132 (base number w/ 50% crit chance)/ 789 (base number w/ only the average type modifier) = 1.43

Thus, LR SSj Future Trunks's built-in critical hit chance generates a separate +43% ATK increase on top of the +120% ATK portion of his passive.


To see his full passive, those numbers need to multiplied together:

  • 2.2 ("+120% ATK" portion of his passive) x 1.43 (built-in critical hit chance portion of his passive) = 3.15

Therefore, LR SSj Future Trunks' entire passive is equivalent to:

ATK +215%



LR Goten and Trunks



Passive:

ATK +120% when SA is launched; Randomly gain between 3-9 ki at the beginning of the turn.


Although their passives may seem different on the surface, LR Goten and Trunks' passive is similar in overall function to LR SSj2 Gohan's passive. Both passives give an ATK boost alongside a ki boost. As such, I'll follow the same procedure I did when converting SSj2 Gohan's passive.

Again, there hasn't been any data to definitively say how LR Goten and Trunks' passive works. Based on the wording, each possible amount of ki gained has an equal chance, which means the average ki gained per turn is 6. On the Mixed Blood team, LR Goten and Trunks average 22 ki after their passive is factored in. Without their passive's ki boost, they'd average 16 ki. To see how much their ki boost increases their ATK, I'll compare the ATK with and without the ki boost factored in.

Here's their ATK equation at 22 ki:

  • 18,040 (enhanced base ATK) x 3.6 (Ultimate Gohan leader skills) = 64,944

  • 64,944 x 1.15 (Z Warriors link) = 74,685

  • 74,685 + 5,000 (Legendary Power link) = 79,685

  • 79,684 x 1.9 (22 ki multiplier) = 151,402

  • 151,402 x 2.2 (passive) = 333,085

  • 333,085 x 6.5 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK buff + 50% Average ATK buff) = 2,165,052

Here's their ATK equation at 16 ki:

  • 18,040 (enhanced base ATK) x 3.6 (Ultimate Gohan leader skills) = 64,944

  • 64,944 x 1.15 (Z Warriors link) = 74,685

  • 74,685 + 5,000 (Legendary Power link) = 79,685

  • 79,684 x 1.6 (16 ki multiplier) = 127,494

  • 127,494 x 2.2 (passive) = 280,487

  • 280,487 x 4.25 (SA lvl. 20 multiplier + 30% dupe system bonus + 30% ATK buff – 30% ATK debuff) = 1,192,072

Now I'll compare the numbers to convert the ki boost into a percentage:

  • 2,165,052 (ATK w/ ki boost)/ 1,192,072 (ATK w/o ki boost) = 1.82

Thus, LR Goten and Trunks' ki boost provides a +82% ATK boost on top of the "+120% ATK" portion of his passive.


To see his full passive, those numbers need to be multiplied together:

  • 2.2 ("+120% ATK" portion of his passive) x 1.82 (ki boosting passive) = 4.00

Therefore, LR Goten and Trunks' entire passive is equivalent to:

ATK +300%



Conclusion



For the sake of easy viewing, here are all converted passives:


IMO, the thing that's illustrated best by these conversions is how important extra ki is on LRs that only have Colossal damage for their 12 ki SA.

The reason LR Goten and Trunks' converted passive is so ridiculously high is their 12 ki SA is garbage compared to thei 18 ki SA. Their built-in ki boost enables them to always reach their 18 ki SA, so it's a massive boost in ATK.

On the other hand, LR SSj2 Gohan has Mega-Colossal damage for both of his supers, so his built-in ki boost ends up having less value because it doesn't have as large of an impact on his ATK. As such, his converted passive seems quite small compared to LR Goten and Trunks', even though it has similar functionality.


The other thing those numbers made clear is how much potential LR SSj Future Trunks has.

His built-in critical hit chance is an extremely powerful mechanic. However, he's been held back on both of his teams due to not being able to consistently reach 18 ki on each of his turns.

If he ends up on a team where he consistently reaches 18 ki on every turn, he has a very good chance at becoming the hardest hitting unit in the game.


I hope you all enjoyed this post.

If you notice any errors or have any questions, please let me know.



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