You might be interested to read about the chariot races, which were very factional and competitive, not unlike modern sports teams. Chariot racing was actually the most popular public event in the Roman world, surpassing the spectacles in the Coliseum. The races were held in a long stadium called a circus, in Rome the primary one was called the circus maximus. The track was long and thin with very sharp turns at each end, which made the races actually quiet deadly, more deadly than gladiator fights in fact. In Rome there were four factions, the Blue, Green, Red, and White teams. Each team could submit three racers in each race and they would wear their team colours to signify their allegiance. And they were very popular with the people. There are instances of graffiti from Pompeii in support of the various factions and even individual racers which could become very famous and very rich - potentially the highest paid sports stars ever. Diocles was the most successul, having won 1, 462 races and earning nearly thirty-six million sesterces, estimated to be about US$15billion.

As far as I am aware the Coliseum games were more for the spectacle rather than faction competitions. The Coliseum was for beast fights and for mass executions of Christians, while the circus was for sport.