Centuries in the past, life was often brutal and short. In hard times, efforts concentrated on survival; the struggle for food and shelter sometimes took all the energy that people had. But not always. Sometimes there was time for play, time to run and dance, time to show off physical prowess.
Was this a way to attract members of the opposite sex? Maybe that was part of it but religion also played a part. In Mesoamerica playing the game of ball was an act that related to their mythology. In some cases, this could be taken to extremes with the losing team’s captain, or even the whole team, being sacrificed at the end of the game. There’s winning incentive for you.
The Olympic Games in Ancient Greece also had a religious background. The city states competed with each other to honour Zeus and the origin of the games was attributed to the gods.
In the western world religion also played a part in the sporting calendar. In Britain, the medieval sporting year began at the time of the spring fertility rituals and games were played on holy days, which were the only times that most people were free from work. Some activities like animal baiting are associated with the period, but others that were popular in medieval times are still around today. Think of bowls, wrestling, tug-of-war, football and tennis. Many other sports have their original far in the past as well. These include ball games similar to those of the Maya and traditional Olympic games such as discus throwing, running and chariot racing.
Brailsford, Dennis. British Sport: A Social History, The Lutterworth Press, Cambridge, 1992.
The Ball Game of Mesoamerica http://www.ancient.eu/article/604/