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Fleets will start from level 0 as your fleet goes on expeditions you will gain experience and level up, the level of your fleet will improve your rewards as you progress through the levels.
You get 5 experience points in a linear way for each expedition you attend (win or lose).
There are currently 5 Tiers of experience, which once you progress from one Tier to another you will get a greater benefit in rewards for achieving this milestone.
In order to progress in an optimal way, you will have to climb between Planets, as you go up each experience Tier (to levels 6, 11, 16, 21, and 25) the amount of experience received in lower planets decreases. For example, if your fleet is level 21, the experience you will get on Planet 1 will be 0.5 per expedition.
In the following table you can see the amount of experience required per level, and the amount of expeditions needed to achieve that experience, for example, for level 13 you will need 18 days starting from level 0.
Fleet's Experience Table