The phrase "to put the ball" means to take control or responsibility for a situation or task. It implies being in charge and making decisions. Full definition
I don't care what his statistical averages are over the lifespan of his last second shots, I'm comfortable in putting the ball in his hands to close the game. (sbnation.com)
They built up a 4 - 1 lead with a dose of steady offense and just putting the ball on net. (allsportsseries.com)