The meaning of "palombella" in Italian includes "columbine", "wild pigeon", and (in water polo, or in other ball sports) "a parabolic shot to go over the goalkeeper and score a goal"/"a lob shot". So the original title of the film could be read as "Red Lob", which brings the sport and the politics -red obviously signifies the Communist Party- together.
The film featured throughout is Doctor Zhivago (1965). It is set in Russia circa World War I and the Russian Civil War of 1918-1922, and is based on the 1957 Boris Pasternak novel Doctor Zhivago. The novel was rejected publication in USSR because of its implicit rejection of socialist realism. The author, like Zhivago, showed more concern for the welfare of individuals than for the welfare of society. Soviet censors construed some passages as anti-Soviet. Pasternak sent several copies of the manuscript in Russian to friends in the West. In 1957, Italian publisher Giangiacomo Feltrinelli arranged for the novel to be smuggled out of the Soviet Union by Sergio D'Angelo. Despite desperate efforts by the Union of Soviet Writers to prevent its publication, Feltrinelli published an Italian translation of the book in November 1957. So great was the demand for Doctor Zhivago that Feltrinelli was able to license translation rights into eighteen different languages well in advance of the novel's publication. The Communist Party of Italy expelled Feltrinelli from their membership in retaliation for his role in the publication of a novel they felt was critical of communism.
The actor who plays the guru is none other than Raúl Ruiz who was an experimental Chilean filmmaker, writer and teacher whose work is best known in France. He directed more than 100 films.
In the scene where Michele punches another player in the head, the punch was real. Nanni Moretti, a perfectionist, shot multiple takes of the scene, always punching the other actor for real. In fact, in the final take, he punched him so hard that he broke his pinky finger. This is the take that was used in the movie.
Protagonist Michele Apicella plays for fictional water polo team Rari Nantes Monteverde. The team wears the same colors as Lazio Nuoto, the team that director Nanni Moretti used to play for. In the name, "Monteverde" is a reference to Monteverde Vecchio, the Rome neighborhood Moretti is from, while "Rari Nantes" is part of the name of several Italian swimming and water polo teams: it's Latin for "chosen swimmers" and a reference to the Aeneid.
Nanni Moretti: [diegetic music] A player on the visiting team starts playing "I'm On Fire" by Bruce Springsteen on a stereo. All characters pause to listen to it.