APL (Dyalog Classic), 16 13 12 bytes
-3 thanks to @Adám
⍳∘≢+.×3⌽⊢+⌊/
⊢+⌊/ arg + min(arg)
3⌽ rotate 3 to the left, i.e. 1 to the right
+.× inner product, i.e. multiply element by element and sum
⍳∘≢ the indices of the array: 1 2 3 4 (uses 1-based indexing, ⎕io←1)