The text of this page written by ShantyTown of the pret discord server. Used with permission.
An Extra Ball is probably the most valuable thing to achieve while playing a round of pinball. When the player has an active "Extra Ball", losing a ball below the bottom of the screen will not result in a lost ball life. Up to 10 Extra Balls can be active at a time. This means that the player could lose a ball 10 straight times without losing a ball life. If an 11th Extra Ball would have been received, the player is awarded 10 million points instead. When an Extra Ball is active, the "AGAIN" light above the flippers is lit.
There are many ways to receive an Extra Ball, and all of these methods apply ONLY to a single ball life, except for the Slot Reward. (When the player loses a ball life, these associated counters reset back to 0.)
The player receives an Extra Ball every 10 Pokemon caught.
An Extra Ball is a rare reward from the Slot roulette. It only appears as a reward option in the 25th unique Slot reward set; see Slots.
Both Red and Blue fields use a Bonus Multiplier system, which is increased when the pinball hits certain field objects. An Extra Ball is received whenever the Bonus Multiplier value is increased to x25, x50, or x75. The Slot roulette's Bonus Multiplier reward can also increase the Bonus Multiplier, which will follow the same rules for granting an Extra Ball.
Every 10 times the Pikachu Saver is used, an Extra Ball is received. This counter has a maximum of 100, so 10 Extra Balls can be received from this.