I also like Sakho and Skrtel. I think we have quality CBs, good enough for where we want to be. The problem comes from elsewhere. Training and coaching staff maybe? We need a good defensive coach.
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We excelled at defending in games where we fielded a compact 4-3-3, a formation which we yield powerfully in attack too. We were never able to carry this game plan over succesfully to our away fixtures, where we sought a more expansive system (diamond formation etc). Though the latter produced goals it was a shambles defensively. The shambles was too consistent to be pinned down on concentration errors alone, so you're right, defensive tactics were either weak or ill-suited to our defenders, or both. I still favour taking the 4-3-3 about 15 yards higher when facing parked buses, but BR seems reluctant to go to a high d-line consistently. Implementing that system requires too better defensive coaching.
I don't think it is Rodgers plan. I believe he does want a high line - Sakho signing would imply this as he is a naturally aggressive, front foot defender. Skrtel on the other hand looks dropping and defending on the 18 yard line and that is the problem. Personally, I think it's naive to blame the tactics - far too many individual mistakes have been made by senior members. The number of own goals as well indicates the confusion amongst our defence.