Badge Map — Reroll Research

In the update 3.10, the badge reroll mechanic was introduced, which allows the option to change characteristics of badges created by the player, such as bonus conditions, badge position and sets. However, with this introduction, it was discovered that, when changing a characteristic of a badge, its location on the Badge Map changes, in a “random” manner. The community carried out some log collections in an attempt to better understand how such mechanic works, but did not reach conclusive results.
In the update 6.13, Natsu Dark, one of the contributors to the Badge Map, made another attempt to understand the mechanics of the badge map and came to some conclusions about badge rerolls.
== Jump Groups: The basis of the research==
The map used in the research was version 3 of the Badge Map.
The detailed version of the badge map adds the concept of Jump Groups (represented by the purple column) to the standard map, which initially specified information on the possible results of your badge when you use a Jump recipe. When performing a Jump in a specific location, the bonus condition of the badge created, if any, will belong to the specific Jump Group of that location.
As of Patch 6.13 (when the research was conducted), there were 2 Traits Condition Bonus groups, 2 Class Condition Bonus groups, and 8 Hero Condition Bonus groups (not shown on the map, as the groups are constantly changing). Therefore, the 8 Jump Groups represent the following groups:
CONDITION BONUS	1 	3 	5 	7 	2 	4 	6 	8
TRAIT 	Lucky, Strong, Marksman, Vigilant, Sure Shot, Defensive Stance, Follow Through, Punish, Critical Aim	Lucky, Strong, Marksman, Vigilant, Sure Shot, Defensive Stance, Follow Through, Punish, Critical Aim	Lucky, Strong, Marksman, Vigilant, Sure Shot, Defensive Stance, Follow Through, Punish, Critical Aim	Lucky, Strong, Marksman, Vigilant, Sure Shot, Defensive Stance, Follow Through, Punish, Critical Aim	Dodge, Iron Skin, Retaliate, Power Strike, Bullet Dodge, Ruthless, Perseverance, Revenge, Weakening	Dodge, Iron Skin, Retaliate, Power Strike, Bullet Dodge, Ruthless, Perseverance, Revenge, Weakening	Dodge, Iron Skin, Retaliate, Power Strike, Bullet Dodge, Ruthless, Perseverance, Revenge, Weakening	Dodge, Iron Skin, Retaliate, Power Strike, Bullet Dodge, Ruthless, Perseverance, Revenge, Weakening
CLASS 	Shooter, Bruiser, Scout 	Shooter, Bruiser, Scout 	Shooter, Bruiser, Scout 	Shooter, Bruiser, Scout 	Hunter, Warrior, Assault 	Hunter, Warrior, Assault 	Hunter, Warrior, Assault 	Hunter, Warrior, Assault
HERO 	Aaron 	Alpha 	Beta 	Carl 	Abraham 	Guardian Carol 	Beth 	Carol
HERO 	Daryl 	Eugene 	Gabriel 	Governor 	Dwight 	Ezekiel 	Glenn 	Hershel
HERO 	Jerry 	Maggie 	Merle 	Morgan 	Jesus 	Mercer 	Michonne 	Negan
HERO 	Princess 	Rosita 	Sasha 	Tara 	Rick 	Rufus 	Shane 	T-Dog
HERO 	Tyreese 	Huntsman Daryl 	Riot Gear Glenn 	Hilltop Maggie 	Yumiko 	Survivalist Rick 	Fighter Rosita 	Sniper Morgan
HERO 	Outlaw Negan 	Quinn 	Jadis 	Simon 	Connie 	Magna 	Simon (Yes, again) 	Protector Daryl
For example, if you use a Jump Recipe on 1L, you will create a badge. Since the Jump Group of 1L is 1, the badge will either be a badge dwithout a bonus, or n badge with one of the possible bonus conditions from Jump Group 1: that is, one of the 9 trait bonus conditions from Trait Group 1, either Shooter, Bruiser, or Scout, or one of the 6 options from Hero Group 1, so a total of 1 + 9 + 3 + 6 = 19 possibilities, which is less than the 73 total possibilities.
Jump Groups were the key concepts in the conclusions made regarding the 3 types of rerolls of badge characteristics.
== Research conclusions==
===1. Movement in rerolls===
When rerolling a badge's slots and sets, in version 3 of the Badge Map, your location tends to move back 1 full column. If you are in column 1 or 2, and return to column 8, your location moves down 1 row.
Example: if you are at 3K and reroll a Slot or Set, your new location tends to be 2K. Now, when rerolling a Slot or Set at 1K, your new location tends to be 8L, from the K row down to the L row.
For bonus condition rerolls, instead of moving back 1 full column, it moves back 2 columns instead.
However, there are situations that make this tendency change:
===2. Result generation===
When you change your location, a reroll result is generated that, based on research, is based on the Jump Group of the location above your new location.
In Bonus Condition Rerolls, a bonus condition is chosen to match the Jump Group of the position above your new location.
Example: If the new location is 2K, the Jump Group of 2J (the position above) is checked. Since 2J belongs to Jump Group 2, then one of 18 specific possibilities will be generated, selecting from Trait Group 2’s nine bonus conditions, or from Hunter, Warrior, or Assault, or one of the six Hero Group 2 options, being in total 1 of 18 options.
In slot rerolls, the result comes out in a position opposite to the Jump Group of the location above the new location: if the Jump Group is even, the result will be odd, and vice versa.
Example: if your new location was 2K, the Jump Group of 2J, the location above 2K, is checked, and an opposite result is generated with the Jump Group of 2J. Since the Jump Group of 2J is 2 (an even number), a result will be generated in the odd position.
Unfortunately, no pattern was found in the result-generating behavior of set rerolls. It is theorized that such randomness is due to the odd number of possibilities (5 sets).
===3. Checking the result===
When the result is generated, it is then checked to see if the result obtained has already been obtained previously on that same badge (since in update 3.12, a restriction was added to rerolls, so that, for Slot and Set rolls, the results are restricted until all options have been generated, and for bonus rerolls, only the 10 previous results would be restricted).
If the result obtained was not previously generated on that badge, the result then becomes the final result.
If the result obtained was previously generated on that badge, then process 1, 2, and 3 is generated again, moving its location back, generating another result based on its new location, and checking whether the result was previously obtained or not. This repeats until a result is generated that has not been generated previously.