How do Fragtrap's Subroutines work?

Solution 1:

General description, see math below

Skills in Fragmented Fragtrap tree give immense bonuses to certain weapon types, while penalizing all others, incentivizing the player to switch weapons to match the current Subroutine.

Subroutines are time-based, each one being active for 100 seconds. Frag Stacks are basically units of time - you are granted 100 Frag Stacks at Subroutine activation, and they decay at a rate of one per second. Down the skill tree there are skills that allow the player to prolong or shorten a Subroutine's duration as follows:

• Grenade Vent adds up to 5 Frag Stacks per Grenade thrown
• Cryogenic Exhaust Manifold subtracts up to 5 Frag Stacks on a Slam
• Float like a Bee adds up to 5 Frag Stacks on a Melee Kill

There are four skills that unlock different Subroutines, first two of which are mandatory, while other two are optional. Only one Subroutine is active at any time, and learning more skills just adds new Subroutines to the pool they are randomly picked from.

• Gun Subroutines increase Damage, Fire Rate and Reload Speed of a single gun type, while decreasing Damage of other gun types. Grenades and Melee are not affected.
• Defensive Subroutines increase Capacity and Regeneration of either Health or Shields, while decreasing Damage with all guns. Grenades and Melee are not affected.
• Melee Subroutine drastically increases Melee Damage, while decreasing Damage with all guns. Grenades are not affected.
• Elemental Subroutines increase Damage of a single element, while decreasing Damage of other elements. Grenades are affected, non-elemental guns and Melee are not.

The bonuses are pretty modest until you get Tripleclocked skill at level 14. It multiplies all bonuses and penalties of Subroutines by a varying factor of up to 3 depending on Frag Stack count - multiplier is x1 at 100 Frag Stacks and reaches x3 by Subroutine expiration.

Fortunately, negative modifiers in Borderlands are handled by an asymptotic formula of 1/(1-x) - that means that a penalty of -75% does not leave 25% of a value ("4 times less"), but 1/(1+0,75) = 57%. Considering this, here is a table of all possible bonuses or penalties of Subroutines:

                        Gun Damage  Fire Rate  Reload Speed  Wrong Gun Damage
Gun Subroutine             +25%        +20%        +20%            -13%
 Tripleclocked Max         +75%        +60%        +60%            -31%
                         Capacity  Regeneration                 Gun Damage
Defensive Subroutines      +35%      +2.5%/sec                     -13%
 Tripleclocked Max        +105%      +7.5%/sec                     -31%
                       Melee Damage                             Gun Damage
Melee Subroutine          +150%                                    -20%
 Tripleclocked Max        +450%                                    -43%
                      Element Damage                       Wrong Element Damage
Elemental Subroutines      +32%                                    -14%
 Tripleclocked Max         +96%                                    -32%

Note: Tripleclocked Health and Shields always receive +105% Capacity, only Regeneration ramps up with Frag Stacks.

Oh, and one more bit of math:

                        Gun DPS   Wrong Gun DPS
Gun Subroutine            +50%        -13%
 Tripleclocked Max       +180%        -31%