An unusual aspect of the N.H.L.’s two outdoor games at Yankee Stadium is that the Rangers have been designated the road team for both games, even though their opponents, the Devils and the Islanders, come from outside New York City.

The reason seems to lie in the special exemption that has freed Madison Square Garden from paying property taxes since 1982.

A provision of that 1982 agreement stipulates that if the Rangers or the Knicks play a home game outside the Garden, the exemption is forfeited. The city’s Independent Budget Office said last fall that the exemption was worth $17.3 million in fiscal 2014. The 1982 state law granting the Garden a pass on paying taxes stated it “shall continue with respect to such property as long as both of said teams play their home games therein and no longer.”

The law went on to say, “If one or both of said teams shall cease to play their home games in said property at any time, the tax exemption provided herein shall cease immediately and said property shall immediately be restored to the tax rolls.”