After some investigation and research I came to the following conclusions. Take them with a grain of salt, as they might still be wrong, but they are good enough for me to change my strategy to the one listed below.
- There is a clear differentiation between recovering your own ships versus enemy ships. Your own benefit from officers and skills, while enemy ships ignore this.
- Recoverability of a ship is usually up to chance. The main factors are: size of a ship, modifiers (D-mods / S-mods) and its status (disabled / destroyed). In general repeating the encounter yields different results. Very few ships have flags that change the probability to always (Ziggurat) or never ([Redacted]).
- As far as I understand, the bigger the ship the less likely the recovery. The size of a ship is dependent on the DP in relation to the type (frigate, destroyer, carrier etc.) This is why it's easier to recover an Onslaught versus a Paragon.
- The more D-mods the less likely the recovery. The status of the ship after the encounter is relevant, so after potential new D-mods. A ship can get 0-3 new D-mods per encounter.
- A destroyed ship halves the probability of recovery compared to a disabled ship.
- Ships usually get disabled if they are killed, but can receive additional damage. This "overkill" triggers the destruction. Overkill is 2-3 times the ships HP but without armor / shield bonuses.
- The probability of ship recovery is proportional to participation rate of the payer.
- There is an upper limit of recoverable ships which is around 20ish
In summary the best strategy seems to be:
Save before the fight. Fight the enemy alone (100% participation) and control the takedown of a ship. Don't use huge burst damage in the final attacks. Use the "claim victory" option when there are many ships in the encounter. Retry the fight if the ship you wanted is not recoverable.
There are two strategies with very big fights to increase the chance of getting the ship you want.
1. Kill the ship in the main encounter, claim victory early and don't pursue to limit the amount of ships disabled or destroyed.
2. Let the ship you want retreat and take down as many remaining ships, but don't pursue. Try to get the ship you want in a second encounter with a reduced enemy fleet.
Additionally, check the "salvage" as a ship might be recovered in this interaction as well. More fights mean more salvage opportunities.
Let your allies / other parties kill your enemies if your fleet is not good enough to contribute to a fight significantly. Don't participate in the fight as this seems to reduce the chance for recovery due to low participation.