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While I don't think that head coach Les Miles is dependent on any one player or thing (including water, shelter, or common sense), they LSU Tigers did have a couple notable losses.
Leading running back Stevan Ridley joined the New England Patriots in the NFL draft, while top wide receiver Terrence Tolliver is awaiting for the NFL lockout to end so he can be signed by a team as an undrafted free agent.
Ridley was a powerful running back, which provided LSU a great go-to option with Miles' trick plays weren't clicking.
Tolliver was a four-year contributor, really coming into his own the last two years. Replacing his 14.1 yards per catch average will be a top priority for quarterback Jordan Jefferson.
Patrick Peterson, star cornerback and return man was lost to the draft as well in the first round. Such players are hardly ever replaced quickly.