How can a player likened to Fernando Torres 12 months go, suddenly become a throw-away makeweight in a deal for a 29 year-old fullback?
That cash and Alex Kacaniklic also went in the opposite direction for Paul Konchesky, who was inside the final year of his Fulham contract, makes the Finn's trade even more baffling.
Throw in Hodgson's comments about not knowing enough about Dalla Valle to make an assessment - even though he had been coach of Finland less than four years ago - and this transfer simply doesn't make sense.
It particularly rings true when you consider the quiet and considered overhaul Hodgson has performed on Liverpool's transfer policy since taking over.
Along with Konchesky, Hodgson managed to land this summer's hottest Bosman, Joe Cole, sending the club's website into meltdown as a result. He also secured the commitment of Steven Gerrard and Fernando Torres with Europe's biggest clubs circling and outbid Manchester United to bring Raul Meireles to England.
The new manager managed to steer Liverpool into the Europa League group phase with a shadow team and gave an already rejuvenated support a glimpse into the future by introducing youngsters like Raheem Sterling and Jonjo Shelvey in preseason senior action.
It's been an impressive first summer market under Hodgson - which is why allowing Dalla Valle to leave just doesn't jive.
The only doubts about the player have come from Finnish fans, who have emailed tribalfootball.com in recent months about Dalla Valle's apparent decision to commit his international future to the country of his father, Italy. But that still doesn't explain the decision to cut him loose to Fulham.
Reds legend Sami Hyypia welcomed his fellow Finn four years ago, declaring the move to Liverpool "the best he could make".
A little over a year ago, Steve Claridge, the former Birmingham City striker, said of Dalla Valle: "Everything he does comes naturally. Some things can't be taught – qualities that separate ordinary players from very good ones – and even at his age his positioning in build-up play and knowledge of where to stand when the ball comes into the box seems spot-on.
"Little wonder his signature was coveted by so many big clubs. As a 15-year-old he chose Internazionale but then moved back home to Finland after only a year in Milan. At 17 sometimes the choices you make off the pitch can be as important as the ones you make on it and his decision to go to Liverpool, which looks a perfect match, means he's got both just about right."
So why would Hodgson allow such a talent leave for Fulham on a virtual 'free'? Has his good mate Elias got one over on him?
It smacks of Ron Atkinson rejecting a young Peter Beardsley at Manchester United. United lived to regret that decision throughout the 1980's - and Liverpool could be doing the same for the next ten years.