The game influence is a scoring combinatorial game that has been introduced in 2021 by Duchene et al [DGP + 21]. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss his turn. New general results are first given for this universe, by transposing the notions of mean and temperature derived from non-scoring combinatorial games. Such results are then applied to influence to refine the case of unions of segments started in [DGP + 21]. The computational complexity of the score of the game is also solved and proved to be PSPACE-complete. We finally focus on some specific cases of influence when the graph is bipartite, by giving explicit strategies and bounds on the optimal score on structures like grids, hypercubes or tori.