Put simply, the Colosseum was an amphitheatre, not a hippodrome. The Roman hippodrome was the Circus Maximus.

The Circus' teams were at first Red and White, then Blue and Green were added, and Caligula (37-41) was alleged by Suetonius to have been a Green fanboy to such an extent that he apparently once gave one of the drivers two million sesterces worth of gifts. Domitian (81-96) added gold and purple teams during his reign (Suet. Domit. 7.1), which presumably stayed – the Circus could just admit the width of six four-horse chariots, and the population was still on the increase.

As an amphitheatre, the Colosseum was thus built for gladiatorial combats rather than chariot racing. Not only that, another racing venue would have been unnecessary. Livy alleges that the Circus had come into existence in rudimentary form not long after Rome's foundation, but the Colosseum was not completed until 80 AD under Titus. At 73,300 square metres for the Circus Maximus, an attempt to build a second hippodrome would be immensely difficult anyway – the Colosseum has a footprint of just 24,000.