In the main series of Pokémon games, since Generation V, there has been a mechanic related to capturing Pokémon called a "critical capture." When you get a critical capture, the thrown ball will make a distinct whistling sound, fall to the ground, then shake only once to determine whether the Pokémon is captured or escapes. This greatly increases one's chances of successfully capturing a Pokémon during an encounter.
As mentioned in my answer to this question, the critical capture mechanic has been implemented in Pokémon Go as of version 0.57.2 for Android and 1.27.2 for iOS.
What is the likelihood of getting a critical capture during a Pokémon encounter? Is it affected by anything such as badges earned or species caught (similar to the main series)?