When you battle a Pokémon in the wild, you will notice a number by it listing its "CP", otherwise known as Combat Points. This is essentially the calculation of the strength of the Pokémon. Each Pokémon has got a base Combat Points level and their maximum varies depending on species, size and your own trainer level. As your trainer level gets higher, you will encounter more higher levelled Pokémon.
Combat Points are the power of the Pokémon and help determine how much damage your Pokémon does in battle when against a Gym. The higher the CP compared to the opponent, the more damage inflicted.
However, aside from all that, the CP is determined based on the power of your Pokémon. This is shown by a scale running in a semicircle at the top of the Pokémon status screen. This circle essentially shows what could be considered as the Pokémon's Level and can be increased. When a Pokémon evolves, the placement in the semi circle will remain the same, but the Pokémon's CP will likely increase based on the Pokémon's base stats.
When the trainer level increases, the Pokémon you already have will not have their CP increase but will gain access to more on the scale. For each level you're at as a trainer, you can Power Up your Pokémon twice.
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