Locking vs Retiring

Just ctrl+f 'Catch' to skip to the bottom. I know you're not going to look at the numbers.

      

              

These numbers will assume you automatically aim to make a 3 stage column with triggers if immediately able. These also assume the opponent's field identically mirrors the example field above (but is Link Joker, obviously), and that the opponent will try not to drop more than 15K shield or 3 cards if possible. Both decks use 12 Crits 4 Heals.

Locking the Vanguard Booster:

4 damage:

   Can't replace the unit

No Triggers: (22/49)

   10 1

   -Hit- 

      No Triggers (33/49)

      10 1

      Crit Trigger (12/49)

      5 1

      Heal Trigger (4/49)

      5 1

1 Crit: (33/98)

   10 1

   15 2

   -Hit-
      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)

2 Crits: (11/196)

   10 1

   15 2

   15 2

1 Heal: (11/98)

   10 1

   10 1

   -Hit-

      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)

2 Heals: (1/196)

   10 1

   -Hit-

      No Triggers (33/49)
      15 2
      Crit Trigger (12/49)
      10 1
      Heal Trigger (4/49)
      10 1

1 Crit, 1 Heal: (2/49)

   10 1

   20 2

   -Hit-

      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)

Damage: (22/49)*[(33/49)+(12/49)]+(33/98)*(45/49)+(11/98)*(45/49)+(1/196)*[(33/49)+(12/49)]+(2/49)*(45/49)=8325/9604, 0.87 damage.
Cards forced out: (22/49)*[2*(33/49)+2*(12/49)+2*(4/49)]+(33/98)*[3*(45/49)+3*(4/49)]+5*(11/196)+(11/98)*[2*(45/49)+2*(4/49)]+(1/196)*[3*(33/49)+2*[(12/49)+(4/49)]]+3*(2/49)*[(45/49)+(4/49)]=6121/2401, 2.5 cards
Shield forced out: (22/49)*[20*(33/49)+15*[(12/49)+(4/49)]]+(33/98)*25*[(45/49)+(4/49)]+40*(11/196)+20*(11/98)*[(45/49)+(4/49)]+(1/196)*[25*(33/49)+20*[(12/49)+(4/49)]]+30*(2/49)*[(45/49)+(4/49)]=22.4984381507705123, 22.5K shield

B.a.s.s. Value of 8325/9604 damage, and 22.5K shield in the form of 6121/2401 cards. (-5K shield, -1 card modifier if retire, continual +s if opponent is unable to recreate power line)

Replace the unit

No Triggers (22/49)
   15 2
   -Hit-


      No Triggers (33/49)
      10 1
      Crit Trigger (12/49)
        5 1
      Heal Trigger (4/49)
        5 1



1 Crit: (33/98)
   15 2
   15 2
   -Hit-
      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)
2 Crits: (11/196)
   15 2
   15 2
   15 2
1 Heal: (11/98)
   15 2
   10 1
   -Hit-

      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)

2 Heals: (1/196)
   15 2
   -Hit-

      No Triggers (33/49)
      15 2
      Crit Trigger (12/49)
      10 1
      Heal Trigger (4/49)
      10 1

1 Crit, 1 Heal: (2/49)
   15 2
   20 2
   -Hit-

      Non-Heal Trigger (45/49)
      Heal Trigger (4/49)

Damage: (22/49)*[(33/49)+(12/49)]+(33/98)*(45/49)+(11/196)+(11/98)*(45/49)+(1/196)*[(33/49)+(12/49)]+(2/49)*(45/49)=2216/2401, 0.92 damage.
Cards forced out: 3*(22/49)+4*(33/98)+6*(11/196)+3*(11/98)+(1/196)[4*(33/49)+3*[(12/49)+(4/49)]]+4*2/49=8522/2401, 3.5 cards
Shield forced out: (22/49)*[25*(33/49)+20*[(12/49)+(4/49)]]+30*(33/98)+45*(11/196)+25*(11/98)+(1/196)*[30*(33/49)+25*[(12/49)+(4/49)]]+(2/49)*35=27.4984381507705123, 27.5K shield

B.a.s.s. Value of 2216/2401 damage, and 27.5K shield in the form of 8522/2401 cards. -5K shield, -1 card modifier, continual +s if opponent is unable to recreate power line.

Kill a Frontrow Unit

Lock:

No Triggers (22/49)

15 2

-Hit-

   Non-Heal: (45/49)

   Heal: (4/49)

1 Crit: (33/98)

15 2

15 2

2 Crits: (11/196)

15 2

20 2

1 Heal: (11/98)

15 2
-Hit-
   Non-Heal: (45/49)
   Heal: (4/49)

2 Heals: (1/196)

15 2
-Hit-
   Non-Heal: (45/49)
   Heal: (4/49)

1 Crit, 1 Heal: (2/49)

15 2
20 2

Damage: (22/49)*(45/49)+(11/98)*(45/49)+(1/196)*(45/49)=4995/9604, 0.52 damage

Cards Forced Out: 2*(22/49)+4*(33/98)+4*(11/196)+2*(11/98)+2*(1/196)+4*(2/49)=281/98, 2.9 Cards

Shield Forced Out: 15*[(22/49)+(11/98)+(1/196)]+30*(33/98)+35*[(11/196)+(2/49)]=2155/98, 22K Shield

B.a.s.s. Value of .52 damage, and 22K shield in the form of 2.9 cards.

Retire: (Move the Rear-Guard to the Front)

No Triggers (22/49)

15 2

-Hit-

   Non-Heal: (45/49)
   Heal: (4/49)

1 Crit: (33/98)
15 2
15 2
2 Crits: (11/196)
15 2
15 2
  5 1
1 Heal: (11/98)
15 2
  5 1
-Hit-

   Non-Heal: (45/49)
   Heal: (4/49)

2 Heals: (1/196)
15 2
-Hit-
   No Trigger: (33/49)
   10 1
   Critical Trigger: (12/49)
     5 1
   Heal Trigger: (4/49)
   -Hit-

      Non-Heal: (45/48)
      Heal: (3/48)

1 Crit, 1 Heal: (2/49)
15 2
15 2

-Hit-

   Non-Heal: (45/49)
   Heal: (4/49)

Damage: (45/49)*(2/49)+(1/196)*[(45/49)+(4/49)*(45/48)]+(11/98)*(45/49)+(22/49)*(45/49)=0.5579706372344856, 0.56 damage
Cards Forced Out: 2*[(22/49)+(1/196)*(4/49)]+3*[(11/98)+(1/196)*(45/49)]+4*[(2/49)+(33/98)]+5*(11/196)=7300/2401, 3 cards
Shield Forced Out: 15*(22/49)+30*(33/98)+35*(11/196)+20*(11/98)+(1/196)*[25*(33/49)+20*(12/49)+15*(4/49)]+30*(2/49)=22.3875468554768846, 22.4K shield

B.a.s.s. Value of 0.56 damage, and 22.4K shield in the form of 3 cards. -5K shield, -1 card modifier, continual +s if opponent is unable to recreate power line.


Retire: (Replace the unit)

No Triggers (22/49)

15 2

-Hit-

   No Trigger: (33/49)

   10 1
   Critical Trigger: (12/49)
     5 1
   Heal Trigger: (4/49)
   -Hit-

      Non-Heal: (45/48)
      Heal: (3/48)

1 Crit: (33/98)
15 2
15 2
-Hit-
   Non-Heal: (45/49)
   Heal: (4/49)
2 Crits: (11/196)
15 2
15 2
15 2
1 Heal: (11/98)
15 2
10 1
-Hit-

   Non-Heal: (45/49)
   Heal: (4/49)

2 Heals: (1/196)
15 2
-Hit-

   No Trigger: (33/49)

   15 2
   Critical Trigger: (12/49)
   10 1
   Heal Trigger: (4/49)
   -Hit-

      Non-Heal: (45/48)
      Heal: (3/48)

1 Crit, 1 Heal: (2/49)
15 2
20 2
-Hit-
   Non-Heal: (45/49)
   Heal: (4//49)

Damage: (22/49)*(45/49)+(22/49)*(4/49)*(45/48)+(33/98)*(45/49)+(11/98)*(45/49)+(1/196)*(45/49)+(1/196)*(4/49)*(45/48)+(2/49)*(45/49)=0.9015774677217826, 0.9 damage
Cards Forced Out: 3*(22/49)*(45/49)+2*(22/49)*(4/49)+4*(33/98)+6*(11/196)+3*(11/98)+(1/196)*(33/49)*4+3*(1/196)*(12/49)+2*(1/196)*(4/49)+(2/49)*4=8433/2401, 3.5 cards
Shield Forced Out: 25*(22/49)*(33/49)+20*(22/49)*(12/49)+15*(22/49)*(4/49)+30*(33/98)+45*(11/196)+25*(11/98)+30*(1/196)*(33/49)+25*(12/49)*(1/196)+15*(4/49)*(1/196)+35*(2/49)=27.3110162432319867, 27.3K shield

B.a.s.s. Value of 0.9 damage, and 27.3K shield in the form of 3.5 cards. -5K shield, -1 card modifier. Continual +s if opponent is unable to recreate power line.





Catch

Okay, so this is slightly unfinished because I only have one example, but there's something important I want you to notice here. Ignoring the damage for a second, if your opponent isn't able to replace their Rear-Guard because it's locked or they don't have a unit to call out, Locking and Retiring are virtually even in terms of their B.a.s.s. values, that is, the combined minimum net amount of shielding and cards necessary to guard every attack optimally. To put it simply, you save the same amount of cards in both scenarios, which is expected, of course. However, the opponent also has permanently lost 5K shielding and 1 card, or if you don't think calling/needing to replace boosters is a loss in 5K shield, is still dragging out 1 more card. This basically means that if the opponent is unable to replace their unit, retiring is strictly better than locking. In the next scenario, which necessitates that you retired, you lose 5K more shield and one more card. However, because the opponent must have that 5K shield, 1 card loss, this means from a net perspective, that scenario is the exact same as having locked the unit. Considering the last possible scenario with retiring, this means that retiring is either equally as powerful, or even more so than locking.

This was made on the fly in response to a weird little 'lock vs retire' argument I came across. If you want me to finish these numbers with more examples (like 5 damage perspective, hitting different targets, etc.), then please ask. And to note, this is not a Link Joker vs Kagero/Narukami argument. These numbers are completely representative of the mechanics at work and not the cards that have access to them. At that however, these numbers would mean that retiring is the superior mechanic from being equally as powerful or even better than locking.

Targeting a Frontrow Unit

Much like hitting the Vanguard booster, it seems that the pattern remains present.

If you aren't able to replace it right away, even despite the fact that you can slide the booster up to the frontrow, the B.a.s.s. value of a retired field is identical to that of the locked field. After considering the retire modifier, this means that once again, if you're unable to replace the unit, retiring is strictly better than locking. In the case that you are able to replace it, the modifier creates a surprising turn of making a replaced field force out less net cards, however it is bound to deal more damage, which I'll just take as a fair trade. What this basically means is that between retiring a frontrow unit and locking it, once again Retiring and Locking can be equally powerful, but in the case that you aren't able to replace it, retiring is even more powerful than Locking.