It is often said that LFC's defensive personnel has underwhelmed this season. I believe that assessment is in error.
In honor of Rafa's return to Anfield, let's start with some facts (stats are BPL only):
1. This season LFC has the second-most clean sheets in the league (to Man City) and the second-highest clean sheet percentage. Unlike Man City, LFC typically does not play with two out-and-out defensive midfielders in a 4-2-3-1. This despite the fact that their first-choice keeper has missed 7 games and been wonky in others. This despite the fact that injuries and lack of depth have forced Downing, Henderson, and Wisdom into the back line, and Joe Allen to play out of position for much of the first half of the season.
2. However, LFC has conceded only the fifth-fewest goals in the league. This indicates that when they give them up they give them up in bunches.
3. LFC is much better in terms of goal prevention at home than away: they have conceded 0.88 goals/game at home, and 1.53 goals/game on the road. This suggests that they have major problems with goal prevention away from home.
4. LFC has lost 14 points from games in which they held a lead (4 draws, 2 losses), seventh in the league. This suggests that LFC has a problem consolidating wins.
5. LFC has taken maximum points in only 3 of 15 games against top-half competition (6 draws, 6 losses), which is 11th in the league (8th on a ppg basis), but is 5th in the league in terms of points against bottom-half opposition.
So what can we take away from these? I believe it is Rodgers' strategy more than personnel.
Rodgers gives the team an attacking intent no matter the context. He plays with one holding midfielder -- who has either been injured or recovering from injury most of the year -- and three forwards (sometimes four). His fullbacks are more like wingbacks, and he plays a quite high defensive line. His strategy is to defend by attacking: keep possession, keep the opposition pinned deep and on their heels, pressure the ball as soon as it conceded. If they never have the ball in your half they'll never score. Play wide in attack, but get compact on defense and press hard.
When it works this strategy really works: LFC keeps a clean sheet and looks great doing it. This strategy is more likely to work at home and against weaker opposition, when opposing teams will be more likely to field a defensive lineup. And LFC dominates in those situations (at least on defense... sometimes they still have trouble scoring). Against stronger teams and more offense-minded teams, however, it leaves LFC open to goals on the counter-attack. Sometimes this will look like a defensive blunder -- somebody failing to cover someone on the break -- but whenever you ask defenders to go one-on-one with attackers on a regular basis you are asking for trouble. Whenever you ask defenders to mark attackers who are operating in space you are going to get burned eventually. Whenever you ask the last man to play with the ball in the middle of the park you are increasing the odds of a costly error that culminates in a goal.
But is this actually a blunder, or is it a calculated risk? I contend that it is the latter. It is part of the overall strategy, which is to be a team which constantly attacks, constantly creates chances, and turns those chances into goals. When your fullbacks say to the media that they think of themselves as strikers in Rodgers' system, then it is clear that the emphasis is not on goal-prevention. The gamble was even more severe earlier in the season, when at least one (and usually several) of Lucas, Johnson, and Enrique were not in the lineup through injury or disfavor.
This is probably the correct strategy -- you don't win the league by preventing goals -- but it leads to feast-or-famine: either LFC wins the game handily, or they drop points. 9 of LFC's 13 wins have come with clean sheets. The other four have been blowouts -- 5-2 v. Norwich -- or they've benefited from an own goal or a late penalty. They aren't grinding out many 2-1 or 3-2 victories; they are suffering from a ton of 1-1 and 2-2 draws.
When LFC encounters teams that can play well on the counter, or absorb pressure without conceding, LFC struggles to secure full points. LFC is a decent attacking team -- fifth in the league -- but they are not an elite attacking team. This strategy requires them to be an elite attacking team, since they are throwing nearly everything into the attack. They should average 2 goals per game with this style of play, and they average 1.7.
So why have things looked better since Carra's been back? Simple. They've abandoned one element of the system: a high line. Carra can't play a pressing style far up the pitch, so the team has adjusted. (At least by perception; I don't know of a stat for this.) But this doesn't mean that Carra is any better than Skrtel, or that Skrtel has to go. It simply means that when your defensive strategy becomes more risk-averse you are more likely to not suffer as many defensive lapses. Early in the season, Skrtel was being forced into playing in a high line that he clearly was not comfortable with; lately Carra hasn't been asked to do the same thing, so he's looked better.
Moving forward, and looking to next year, Rodgers will need to decide what strategy to take. If LFC stays dedicated to an attack-minded strategy they need to score more: this year, they're scoring half a goal less per game than Man United (and are, in fact, below all of the top four). They are not an elite attacking team, but they are playing a strategy designed for an elite attacking team. They're going to need to get a CB that can hold a high line with Agger and press better. If they are going to try to more consistently limit the other team's goals, then they'll need to adopt formations and/or positioning that will accommodate that (all of the top-4 are better at that too). RIght now they're kind of in between; they're good enough to dominate below-average teams, but not good enough to boss around above-average teams.