
First off, let’s get things straight – it wasn’t a beachball, or not one in the traditional sense. However, the world is laden with examples of not-quite-correct terminology, so this intervention isn’t going to change the name of ‘the beachball game’.
It’s an easy shorthand for a memorable, unusual incident, Darren Bent’s winning goal for Sunderland against Liverpool in 2009. It helped to overshadow the unorthodox kit worn by the visitors at the Stadium of Light that day.
In the summer of 2009, Liverpool launched this change kit:

While they have rarely deviated from all-red when shorts- or socks-clashes have arisen, there haven’t been such reservations with change strips and so, for the trip to Sunderland, the dark grey shorts and socks were deemed to clash with the hosts’ black items.
As a result, they looked like this:

Despite the lack of fond memories of this combination, it was seen again at Old Trafford in March, when just a socks-swap would have sufficed.
However, since that season, as far as we can ascertain, for competitive first-team games Liverpool have only used alternative socks with dark change shirts when required – the Premier League allows shorts-clashes and they have taken advantage of this.
Liverpool used change socks wearing a white top away to arsenal in the 2013/14 season. The normal pair is white and the change socks were black
Yeah, they’ve worn alternative socks, but it’s shorts-changes with dark away shirts that they haven’t used since then