A consequence of this high intensity pressing, or the next step if you like, is to keep possession better in the first place. The more we keep the ball, the less we're pressing to win it back.
But as has been said, it's intelligent running. Pressing in pairs or reducing the options to the man on the ball. That's what forces mistakes. It's no good one player pressing when the man on the ball can just turn and pass to a team mate. We're pressing intelligently so that we win the ball back or force a mistake quickly. The quicker we do that the sooner we can stop pressing and start playing. It's hard work I'm sure but it's highly effective.