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 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.
The night scenes were filmed as late as 5 AM. Around 4 AM, the three hundred extras playing the audience would start calling for the end of the shift, chanting "Moretti! Moretti! vogliamo li cornetti!" ("Moretti! Moretti! we want the croissants!"; it rhymes in the original Italian).
Soon after its release, a critic with the Communist Party of Italy (PCI) criticized the movie for presenting an outdated view of the party, and a crisis of identity that it had already gotten over. Two months later, the Berlin Wall fell. A little over a year later, the PCI itself was dissolved.
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.