Looking back over a few games, and it's clear that Milner isn't being played as a left back in the traditional sense.
It's also clear that Klopp plays him there not just for his ability to get up and down, but because coming onto his right foot when deep means an easier pass into the half space for both Firmino and Coutinho, because he has created the angle to play it in.
Further up, he is there to take advantage of Coutinho and Firmino doubling up in that defensive half space, making the FB come inside, and pulling the CB out of position to create more room in the box, for Milner to target when he overlaps.
It's still a work in progress, obviously, and without Coutinho it doesn't work nearly as well, but this tactic wouldn't work half as well with a left footed player on that side, when passing from a deep position.
Obviously, the overlap doesn't work as well as it would with a left footer, but it's swings and roundabouts really, and is a plan which has worked pretty well right up until the time Coutinho got injured.
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