Pat Smith, spokesperson for the airport, says the pilot was making his way from a runway to a taxiway to pick up the team for their charter flight home.
The pilot took the turn too wide and put a wheel and nose of the plane into the mud.
Only the crew was on board; there are no injuries.
Air traffic is not affected because the incident happened off the taxiway.
Airport crews are in the process of getting the plane out of the mud.
The team will take busses back to New York.
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