Regulators help manage the air used for each shot. For example, if you set the regulator at 130 BAR, the output pressure flows at 130 BAR every time you pull the trigger.
Having consistent pressure provides more accurate shot strings.
In the example shot string, the airgun equipped with the regulator has a minor change in pressure between shots compared to the airgun without a regulator.
Having a regulator provides a more consistent shot string than an unregulated model, but this is usually sacrificed for power and velocity.