Nationals fans make their way to the stadium near the Navy Yard Metro station in this file photo. (Marlon Correa/The Washington Post)

American University has agreed to pay for late-night Metro service from the Navy Yard­Ballpark station after Washington Nationals postseason games in October. However, because fare revenue is expected to cover much of the cost of keeping the subway open, AU’s expense probably will be relatively small, according to Metro.

For Nats fans getting ready for a playoff series this week, the arrangement means that after any games on Sundays through Thursdays, a subway ride home from Nationals Park will be available as late as 12:20 a.m. — or 1:30 a.m. if a game is delayed by rain or goes into extra innings, officials said Monday.

Normally on those nights, the last Green Line train with guaranteed connections to other subway lines leaves Navy Yard-­Ballpark at 11:20 p.m. On Friday nights into Saturday and Saturday evenings into Sunday, Metro already stays open until 3 a.m., with the last connecting trains leaving the ballpark at 2:20 a.m.

“American University is pleased to extend our partnership with the Nats into the postseason,” AU President Cornelius M. “Neil” Kerwin said in a statement Monday.

In an existing sponsorship arrangement with the Nats, AU has been the team’s higher-education partner since 2012, said Teresa M. Flannery, an AU spokeswoman. That gives the private university high visibility inside the ballpark through signs, T-shirt giveaways and other promotional activities, she said.

Nationals fans make their way to the stadium near the Navy Yard Metro station in this file photo. (Marlon Correa/The Washington Post)

This postseason, barring rain delays or extra innings that might force a second extra hour of service (until 1:30 a.m.), it appears that AU’s cost for the first extra hour of service (until 12:30 a.m.) could be negligible, Metro said.

Postseason baseball games that are played at night usually start later and last longer than regular-season games. At most, the Nats could play 10 home games this October (or just two home games if they make an early exit from the playoffs). And the Nationals’ first two postseason games, on Friday and Saturday, begin in the afternoon and presumably would not need extra service on the Metro.

Under AU’s agreement with Metro, the transit agency puts the cost of an extra hour of service at $29,500 and assigns a $5.36 fare value to each rider entering the Navy Yard-Ballpark station during that hour, Metro spokesman Dan Stessel said.

AU will post a $29,500 deposit for the first extra hour. If 5,504 or more people leaving the 42,000-seat Nationals Park board the subway during that added hour of service, at a revenue value of $5.36 per person, Metro would consider that it has recouped the $29,500. AU, owing nothing, would get back its entire $29,500 deposit.

The university will be refunded $5.36 for every rider up to its total $29,500 deposit. If, for example, just 4,500 riders leaving the ballpark use Metrorail in the extra hour of service, AU would get back $24,120 — meaning its cost would be $5,380.

The formula is a standard one that Metro uses regularly with event organizers, Stessel said. “In the case of most major sporting events, certainly postseason sporting events, we expect that ridership will defray a significant portion, if not all, of the cost of the deposit,” he said.

For any Nats night games on Sundays through Thursdays, AU will put down two $29,500 deposits, for a total of $59,000, in case a rain delay or extra innings create the need for a second extra hour of service, Stessel said. If a second hour of service turns out not to be necessary, the $29,500 deposit for that second hour will be returned to the school.

However, if a second hour does become necessary, AU could be on the hook for a significant sum. If, say, 5,000 people left the ballpark on the subway during two extra hours of service, at a revenue value of $5.36 per person, $26,800 would be refunded from AU’s $59,000 deposit. So the university’s cost would be $32,200.

Metro said other teams, including the Washington Redskins and Washington Capitals, routinely subsidize extra-hours Metro service. The transit agency said the Nationals have declined to chip in financially.

Asked why the team won’t foot the bill for extra subway service after its games, a Nationals spokeswoman said, “What matters is that our fans will be able to ride Metro to and from postseason games and not have to worry about missing a second of the action.”

Two years ago, when the Nats were last in the postseason, the team steadfastly declined to finance Metro service. The Web-based daily-deals company Living Social eventually entered into an arrangement with Metro similar to the one to which AU has agreed.