Tim Bowen sheds some light on the origins and definition of the phrase to start the ball rolling.

The expression to start the ball rolling (also set the ball rolling) is frequently used to describe the commencement of an activity or series of activities. It is often used at the start of a meeting, as in, 'Right. Who would like to start the ball rolling?' meaning who would like to have the first word or bring up the first topic. It can also be used to describe a set of events, either positive or negative, as in, 'That was the incident that started the ball rolling and now things have got out of hand.'

Unsurprisingly, given the use of the word ball, this expression has its origins in sport, but not in one of the more mainstream sports such as football or tennis. To start the ball rolling is believed to originate in the genteel 19th century English pastime of croquet, a fairly simple game the aim of which is to hit a ball with a wooden mallet through a series of hoops. One weakness of the game is that the person starting first can win, if they are a good enough player, without the other person having a go. So starting first is a distinct advantage. The person winning the toss of a coin starts first and starts the ball rolling.