How effective are Razz Berries, quantitatively?

It will increase the chance to keep the Pokémon inside the ball for one try. I'm not sure by what rate, since there is no data about this in the datamined file. If it gets out of the ball you'll need a new berry and if you miss the Pokémon the berry is not consumed. It'll be consumed once the Pokémon is in the ball.

The other values are most likely unaffected and there is no laser guide or crosshair/scope/etc.
Since the effect is gone, after the Pokémon breaks out of the ball I don't believe the escape chance (end of fight) is affected. The other ones are based on your skills (aiming) and timing (dodging). The berry can't affect those.