(TNS) -- It’s the daily lament of the public transit rider: When will the bus show up?

The NextBus system is supposed to answer that for Muni riders. It displays anticipated arrival times through electronic signs in bus shelters, with a phone service for people who call 511, on a website and on a smartphone app, harvesting information from GPS devices in Muni’s fleet. Now a study by a San Francisco startup says it’s accurate about 70 percent of the time, with the worst performance during commute hours.

The researchers have their own plan to improve accuracy: They created a crowdsourced iOS app called Swyft. Some 40,000 Bay Area residents, about three-quarters of them in San Francisco, now use the app to report when their Muni bus, BART train or AC Transit bus is delayed, overcrowded or otherwise experiencing problems. That lets the app deliver real-time information to its users in conjunction with the NextBus predictions.

“The union of those two provides better context for riders” to figure out when their bus really will arrive, said Jonathan Simkin, co-founder and CEO of Swyft, which has raised a little over $500,000. “We built Swyft to optimize how you get around town.” Swyft has been tested since January in the Bay Area. An Android version is coming soon.

An app for iOS and Android called Moovit also uses crowdsourcing combined with transit information to predict bus or train arrivals. Moovit, released in 2012, now has 35 million users in more than 800 cities in 60 countries, giving it a bigger user base than Google Maps, it said. The company couldn’t say how many users it has in San Francisco. The Israeli company has more than $81 million in venture backing.

When users ride public transit with the Moovit app open, it anonymously tracks their speed and location, and integrates that with schedules to predict when a bus will arrive. It also lets users report problems such as how crowded or clean a vehicle is, for instance.

On Thursday, Moovit is adding a Live Directions feature to give riders step-by-step directions throughout their trip. For instance, it alerts riders when their stop is close and it’s time to get off.

Simkin said he and his Swyft co-founders, who live in San Francisco, had long wondered how accurate the NextBus predictions were. To find out, they collected all its predictions for the whole city of San Francisco in August, amassing several hundred million data points.

The researchers winnowed that down to predictions within a 30-minute window before estimated arrival time, and then compared them to actual arrivals, which it figured out by looking at the final prediction a few seconds before a bus showed up.

“We had a generous definition for accuracy,” Simkin said. They decided to consider a NextBus prediction accurate if the bus came during a window between 30 seconds before the estimated arrival up until four minutes afterward. (The smaller window for early arrivals is because they could make a rider miss the bus altogether.)

“As riders, we intuitively knew there are times when it’s frustrating because the bus doesn’t arrive when it says it will,” Simkin said. “But we had no idea what the actual accuracy was — until now.”

The 70 percent accuracy rate for predictions is slightly better than Muni’s published 60 percent on-time rate compared with its schedules. NextBus was least accurate during commute hours, when traffic is most congested.

Susan Shaheen, co-director of the UC Berkeley Transportation Sustainability Research Center, was not involved in the study but is familiar with it.

“Obviously it shows there is room for improvement,” she said. “But I would cast it in a positive light: 70 percent accuracy on arrival times is a vast improvement from where we were 15 years ago” before Muni adopted NextBus.

“This shows there are opportunities through public-private partnerships for data sharing that could offer systematic improvement in increasing urban transit,” Shaheen said.

©2015 the San Francisco Chronicle Distributed by Tribune Content Agency, LLC.