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I found Chelsea a very difficult team to extract one most important player from. They have no one individual that sticks out from the rest, in my mind.
Anelka, when not benched inexplicably for Drogba, was clinical. But, in many ways, as the sole striker, he was the beneficiary of what happened behind him.
It may seem logical to work from the ground up. But I am not a particular fan of Terry or Carvalho, and I find them hard to differentiate.
The midfield is the most important part of the formation for Chelsea. They play five there, essentially, and seem to focus their style around their midfield players.
It is the midfield that has to be blamed in large for the lack of dynamism plaguing Chelsea of late. Deco and Ballack have been subpar, Obi Mikel has done his job, but not extraordinarily so. Lampard has been fine, not horrible, but not his shining best either. Anyway, I never felt like he defined that team, even if the media wished it so.
The most important player for Chelsea, much like Arsenal, is injured at the moment. It is Michael Essien. He is the type of multi-talented center midfield player that can make a world of difference for a team.
His combination of work ethic, defensive ability, and occasional and timely attacking panache was massive for Chelsea in years past. His flexibility was of great value as well, patching holes where they existed and allowing Chelsea to retain a fluid, stable form.
Perhaps I am wrong, but Essien would make an enormous difference for Chelsea were he playing, and in fact, I think he is their most important player.
Side note: is it coincidental that the two teams whose listed most important player, Arsenal and Chelsea, are the two clubs struggling most? It obviously does not explain everything, but it is interesting.
Other possibilites: Frank Lampard, John Terry, Ricardo Carvalho, Nicolas Anelka, Jose Bosingwa