The frequent Long Island Rail Road disruptions that have been plaguing commuters — including three over four days last week — have occurred as the agency released statistics saying trains are running on time more often than they have in three years.

Commuters and advocates, however, say the LIRR’s 93.7 percent on-time performance for the first half of 2016 is at odds with what they deal with on a regular basis.

“Those numbers don’t reflect the commuters’ experience. I can tell you that,” LIRR Commuter Council chairman Mark Epstein said. “I don’t know if perception is reality or reality is perception. Either way, it doesn’t jibe with what people are feeling.”

The LIRR has suspended service on one or more branches 13 times this summer. On five occasions, the railroad has completely shut down service into and out of Penn Station.

Numerous other rush hours have been snarled by heavy delays and widespread cancellations — made worse, commuters say, by unreliable service updates, shoulder-to-shoulder crowds on trains and in stations, and poor contingency planning, including providing alternate modes of transportation when service is down.

At the same time, the railroad has released statistics showing from January through June there were 7,734 individual train delays, compared with 10,642 in the same period in 2015 — a 27.3 percent improvement.

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The LIRR benefited from a milder winter than in 2015, and also said improved train and track maintenance, infrastructure investments and other initiatives made service more reliable.

LIRR officials acknowledge that it’s been a challenging summer, and July’s on-time performance, not officially published yet, dipped to 89.3 — the worst of any month this year, but they stand by their latest Operating Report, which showed improvement in nearly every metric through June.

Morning and evening rush-hour trains had their best on-time performance in four years, fewer trains were canceled, and delays fell on every LIRR branch. The average length of delays, 12.8 minutes, was the same as last year, but the number of delays lasting 15 minutes or more dropped 35.5 percent, to 1,323 from 2,052.

Overall, it was the best first half of a year since 2013. And the improvements came despite the LIRR carrying 1 million more riders than in the first half of 2015.

The LIRR considers a train late if it arrives at its final destination six minutes or more after its scheduled time. It is the industry standard shared by other major commuter railroads, including sister Metropolitan Transportation Authority railroad Metro-North, SEPTA in Philadelphia and Metra in Chicago.

MTA Chairman Thomas Prendergast said the new stats show the LIRR’s commitment to improvement.

“The old adage of ‘You’re only as good as your last storm or your last rush hour’ is something that’s first on the mind of everyone who runs these organizations,” said Prendergast, a former LIRR president. He called the railroad “one of the most difficult MTA agencies to operate” because of its bottleneck design of seven branches all converging into a single line into and out of Penn Station.

Commuters are not sympathetic.

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Twenty-year commuter John Dillworth of Northport said he believes the stats are “just not accurate.” Dillworth, 51, who commutes from Huntington to Penn Station, is among many riders who have taken to Twitter in recent months, using the hashtag #WeDeserveBetter, to express their dissatisfaction with what they say is deteriorating service.

“I think they’re worse than ever,” said Dillworth, a project manager for the City of New York. “Every time you see [the LIRR report] that a train is 12 minutes late, you can double that.”

The problem is not with what’s in the LIRR stats, but what is not, said Epstein, of the LIRR Commuter Council.

Delays of up to 5 minutes and 59 seconds are not included in the stats, but are routine and could result in commuters being delayed by much more than that, especially if they miss other transit connections, Epstein said. He wants to meet with LIRR officials to discuss the methods behind their on-time performance measurements.

The numbers also don’t take into account the many other frustrations inherent in LIRR service disruptions, Epstein said.

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“The communication problem is still really poor,” said Epstein, who called on the railroad to implement technology to allow riders to get audio updates directly from the LIRR’s operations control center. “The situation might not be under their control, but how they handle it is under their control.”

Ronkonkoma commuter John LaPlante, who started the #WeDeserveBetter social media campaign, also had difficulty accepting the LIRR’s improved on-time performance numbers in a year in which he said major service problems have become common.

“Just observationally, I can’t recall a year when the gates have been pulled down in Penn Station as often as they have been this year. It’s been insane,” said LaPlante, 36, referring to the MTA Police’s practice of closing off access to the Manhattan terminal during serious service disruptions to reduce crowding. “You see these numbers and it looks like things are getting better. But it doesn’t feel like they are.”

LaPlante said that many of the inconveniences faced by commuters during a service issue are not easily measured, such as crowded trains on a hot summer day, poor mobile phone connectivity for riders trying to reach others or get service updates, and the “real-world implications” of being even five minutes late to a job or medical appointment. “Those are things that these numbers will never show,” LaPlante said.

LIRR President Patrick Nowakowski, in an email statement, said on-time numbers don’t tell the full story of the agency’s performance.

“I believe you should also look at categories such as the average length of delay and the number of train delays for significant periods — both are among the statistics we report publicly to the MTA Board every month,” Nowakowski said. “Most customers are not concerned about the train which is six minutes late but greatly concerned with a 60-minute delay. Remember they are both one late train.”

Nowakowski said several initiatives have helped improve the railroad’s punctuality, including stepped-up efforts to cut vegetation and lessen the likelihood of debris in front of a train during a storm, hardening electrical systems post-superstorm Sandy, and improving maintenance standards on trains to reduce breakdowns.

Milder weather last winter was also a key factor in the LIRR’s on-time gains. Of the 2,908 additional delays the LIRR had through the first half of last year, compared with this year, nearly half were related to severe weather, including snowstorms.

The railroad, however, remains vulnerable to even minor hiccups, especially during the rush hours, when many of its branches are already running at capacity, LIRR officials said.

“We work as fast as we can to clear the problem and get trains moving again but we’re also working on long-term infrastructure fixes that will add capacity and resiliency and reduce the impact of any single incident,” Nowakowski said.

Those long-term fixes include efforts such as the East Side Access link to bring the LIRR into Grand Central Terminal, a second track between Farmingdale and Ronkonkoma, and a proposed third track between Floral Park and Hicksville. “The solution to not having enough capacity is that we build more capacity,” Nowakowski said.

MTA Board member Mitchell Pally said railroad service has improved over the last year, but he understands why it may not seem so to some riders, especially in recent weeks.

“Obviously, some things the railroad can control and some things, like an idiot going on the tracks, you can’t control,” Pally said, referencing an incident on the morning of July 27 in which a drunken driver veered onto the tracks in Westbury, sparking a third-rail fire that affected the main line for hours.

“If you’re on the one train that is late, it doesn’t matter that the other 99 were on time. You think the railroad is doing a bad job,” Pally said.

Mitchell Moss, director of the Rudin Center for Transportation Policy and Management at New York University, said the railroad’s poor reputation among some commuters has as much to do with perception as it does performance. The growth of social media has contributed to that negative perception by giving exasperated riders an immediate forum for venting, Moss said.

“Go to Yelp. It’s much easier to tell people when you’ve had a bad meal than when you have a good meal,” Moss said. “The bad experience, the painful journey, the long delay, is always going to be more embedded in someone’s memory than the positive commute.”