Definition of tensor product of graded maps

Question

The tensor product of $\mathbb{Z}$-graded vector spaces $V = \bigoplus_iV_i$ and $W = \bigoplus_iW_i$ is $$ V\otimes W = \bigoplus_i(V\otimes W)_i, $$ where $$ (V\otimes W)_i=\bigoplus_{j\leq i}(V_j\otimes V_{i-j}). $$ Hence $V_i\otimes W_j\subset (V\otimes W)_{i+j}$. The tensor product of graded maps $f,g:V\to W$ must then satisfy $$ (f\otimes g)(v_i\otimes v_j) \in \bigoplus_{k\leq i+j}(W_k\otimes W_{i+j-k}). $$ A natural definition would be $$ (f\otimes g)(v_i\otimes v_j) = f(v_i)\otimes g(v_j)\in (W\otimes W)_{i+j}. $$ However, the usual definition for the tensor product of graded maps has an additional minus sign: $$ (f\otimes g)(v_i\otimes v_j) = (-1)^{|f||g|}f(v_i)\otimes g(f_j). $$ Why is the minus sign there in the usual definition?