According to an article by Marc Bussanich for citylimits.org:
Swing by Randall’s Island on a given night, and just a little of New York City’s sports diversity will be on display. Rugby on one field, soccer on another. Gaelic football over here, maybe Australian rules football over here. On a weekend day, the parade field at Van Cortlandt Park might offer a similar mix of team equipment: cricket bats, softball gloves, hurling sticks, frisbees.
All those teams and players combine to offer the city’s players an array of athletic options. But they also compete for access to that space.
In 2017, the city’s Parks Department issued 8,100 athletic permits for 877,000 hours of athletic time on its 800 ballfields—satisfying most but nowhere near all the demand for space. According to testimony at a 2018 City Council hearing on athletic field access, 600 athletic permit applications were turned down, representing 24 percent of requests.
Read more here