People around the world who watch the Super Bowl on television Sunday will surely see plenty of beauty shots of San Francisco, but football fans who visit and venture beyond the city’s spruced-up core will find some views that aren’t so beautiful.

Scores of tents line Division Street under the freeway, just one of many camps across the city. Human feces and needles litter sidewalks. Deranged people scream and threaten pedestrians in broad daylight. One man believed to be homeless allegedly slashed a California Highway Patrol officer in the throat near an encampment last week.

Visitors may wonder why one of the wealthiest cities in the world can’t cough up enough money to alleviate homelessness, but, in fact, San Francisco spends tremendous amounts of money on the problem. The city is allocating a record $241 million this fiscal year on homeless services, $84 million more than when Mayor Ed Lee took office in January 2011.

But the city struggles to track exactly how all that money is being spent and whether it’s producing results. Eight city departments oversee at least 400 contracts to 76 private organizations, most of them nonprofits, that deal with homelessness.

No single system tracks street people as they bounce among that galaxy of agencies looking for help.

That’s a major systemic weakness that’s been noted before: Fourteen years ago — a lifetime in politics — the city controller called for a single information network to ensure better tracking of homeless people as they seek services and better tracking of money spent to help them. There’s still no network and still no plan for one.

That’s a mistake, said Dr. Josh Bamberger, a UCSF professor who for many years has helped craft homeless policy in San Francisco and for President Obama.

He said few things are more crucial to tackling homelessness than having a system that tracks people through every aspect of service and that such a system has helped New Orleans, Minneapolis, Salt Lake City, Phoenix and the state of Virginia make great progress.

“You have to treat the sickest homeless people first, because they use the most resources, and the only way to do that is to know exactly who and where they are and what has worked or hasn’t in each case,” Bamberger said. “Once those people are housed, you can concentrate on the rest of the population and snowball to ending homelessness.”

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Last month, Supervisor Aaron Peskin called 911 because a homeless man, naked from the waist down and his legs smeared in feces, was standing on the Filbert Steps on Telegraph Hill, screaming obscenities and blocking the path of passersby.

Currently, there’s no way for the police officer who responded or a doctor at San Francisco General Hospital to easily learn much about the man’s service profile, such as stints in rehab, which city-funded nonprofits might have tried to help him, if he receives food and shelter, or if he gets government benefits.

“There’s no question it has gotten exponentially worse,” Peskin said of homelessness in San Francisco. “How the city spends a quarter of a billion a year, I have not figured out. It’s not working.”

Maria Cristini would not argue with that assessment.

The executive coach and mother has lived on Potrero Hill for 25 years and has been stunned and saddened to see the huge tent encampment spring up on Division Street. Block after block is filled with tents, and it’s obvious the homeless have dug in.

Peskin calls it Division National Forest — swap the concrete for trees, and it might pass for a standard campground. The city recently counted 140 tents filling sidewalks, along with lawn chairs, old carpets, clotheslines and even wooden structures.

Cristini’s son visited recently from college and said, “Mom, this is a shantytown.” He isn’t wrong.

In the blocks around the Division camp are streets and alleys dotted with still more tents or lined with homeless people living in RVs. Some homeless campers set up tents in parking spaces, tucked between cars.

“If I did that with my belongings, I’d get a ticket,” Cristini said. “I have extra things — should I put out a little shed in a parking lot and call it a day?”

City officials, including Sam Dodge, the mayor’s point man on homelessness, say violence and drug addiction have been growing concerns about the campers on Division, and many campers also worry.

On a recent night, in a two-hour period, one man was beaten and robbed, three fights broke out, and two men smoking methamphetamine stormed up and down the traffic median, screaming at each other and traffic for more than an hour. At least 250 people cycle in and out of the camp.

Cristini said she feels torn between frustration at the takeover of the neighborhood and sadness for the people who live in the tents.

“These people are definitely not being taken care of,” she said. “Are we not providing for them?”

She has asked these questions in numerous e-mails to Lee and supervisors, but has received no response. Asked whether she thinks her taxpayer money is being spent well when it comes to homelessness, she said, “Obviously not! I just see the results, right?”

Although it might not seem like it to Cristini, the city is spending more than ever to tackle homelessness.

The $241 million is about equivalent to the annual budget for the Public Works Department, which cleans all the city’s streets, repairs its sidewalks, cleans up illegal dumping, maintains its trees, removes graffiti and more. That much money would pay for San Francisco’s entire library system for two years.

In truth, the figure is even higher. It doesn’t include emergency services from police or the Fire Department when they respond to homeless people in crisis, because spending by those departments isn’t broken out that way.

The number is likely to grow this year. Lee is pushing a June ballot measure that would dedicate $20 million to modernize homeless shelters and build more sites like the Navigation Center in the Mission District, which temporarily houses entire camps of homeless people and tries to steer them into services.

Supervisor Mark Farrell — a venture capitalist who is among the more moderate members of the board — is considering a November ballot measure to bring in even more revenue for homeless services.

“If we want to be serious about tackling the issue, it’s going to mean spending a ton more,” he said.

When Lee took office in 2011, the city spent $157 million a year on homelessness out of a total budget of

$6.8 billion. The current budget is pushing $8.6 billion. That means homeless spending has grown 54 percent since Lee took office and is consuming a bigger chunk of the budget than it used to.

Of the $84 million increase, 40 percent came from inflationary pressure, according to Kate Howard, director of the mayor’s budget office. Rent, labor and contract costs have all risen.

But 60 percent has come from new spending. During Lee’s tenure, 1,600 units of supportive housing have been built. He boosted funds for eviction-prevention programs, doubled the size of the Homeless Outreach Team, opened the Navigation Center, and expanded the Homeward Bound program, which provides one-way bus tickets home.

Almost half of the $241 million — $112 million — is spent on supportive housing for the formerly homeless. Nationally, permanent supportive housing that includes social workers and other care is considered the best way to end homelessness. It’s also less expensive than caring for people on the streets — $17,353 a year per person, compared with $87,480 a year for each of the 278 homeless “high users” of the city’s public medical system, Howard said.

But, as the city builds more supportive housing, it must continue to pay the cost for all those new residents. Few of the formerly homeless are ever able to find jobs, afford market-rate apartments and shrug off city support.

The last in-depth accounting of city spending on homelessness was conducted by Harvey Rose, the Board of Supervisors budget analyst, for the 2012-13 fiscal year.

Supervisor London Breed has asked Rose to update his report, a big undertaking considering the many departments and city-funded nonprofits that work on homelessness. There’s no way to tell from the thick annual budget book how the city is spending its homeless money in any detail.

“I want something comprehensive,” Breed said. “We’re talking about millions of dollars, and who’s getting what and what they’re spending it on. We’re looking at the effectiveness of their programs and who they’re serving. Have they delivered?”

She said seeing the city’s huge homeless problem, while not having an easy way to understand what the city is doing about it, is frustrating.

“I don’t think any elected leader is doing a good job on homelessness, including me,” she said. “We have to be just as aggressive about helping homeless individuals as we are about trying to get the Warriors here and the Super Bowl and all these things that bring economic growth. ... It just makes me crazy.”

Perhaps even more frustrating is that the situation on the ground continues to worsen despite major progress by the city.

Since January 2004, the city has moved 21,742 people off the streets. Of those, 9,286 people left with a bus ticket from Homeward Bound, at an average cost of $185 per person. The rest were housed through a variety of city programs.

“We’ve housed thousands of people and changed the trajectory of their lives forever,” said Dodge, the mayor’s homeless adviser. “We’ve been able to stay at least afloat by making these investments in supportive housing.”

Lee pledged in December to concentrate intensely on homelessness during his second term — to finally bring all the players together in one department and to move 8,000 more people off the streets. A national search is under way for someone to lead the new department. The goal is to have it up and running by Aug. 1.

The directors of the two city departments that would be most affected, Public Health and Human Services — with combined budgets of about $2.5 billion — are enthusiastic about the plan because they think it will lead to better coordination.

The health department has a Coordinated Case Management System, which tracks homeless people through health services as they are helped by Homeless Outreach Team street counselors. The Human Services Agency has its own Homeless Management Information System, which follows people through housing and welfare programs.

But they aren’t combined, and they don’t comprehensively include information from those 400 contracts throughout the city that nibble at the same problem.

“As it is now in the city, sometimes we replicate services,” said Barbara Garcia, director of the Department of Public Health. “What if we had just one assessment for every person who comes in, and they didn’t have to do that 10 times?”

Trent Rhorer, director of the Human Services Agency, has advocated for a single computerized tracking system for years, and several city studies dating back more than a decade have supported that point of view.

Lloyd Pendleton, who oversaw Utah’s homeless programs and virtually ended chronic homelessness in Salt Lake City, said it’s essential to have a single tracking system.

“We have one that tracks people all over the state, and it became key to our success,” he said. “You waste less time.”

In the meantime, there are plenty of problems that should be easier to figure out, but aren’t. Take the Division Street encampment.

Last month, Supervisor Scott Wiener wrote a letter to Rhorer, Dodge, Garcia and three other department heads asking why the city’s ban on tents in public spaces isn’t being enforced.

“I’ve never seen the tent situation get so extreme,” he said, adding there are camps in the Castro, and one was even spotted with a propane tank inside. “It’s dangerous, it’s not healthy, and it’s not humane.”

Jennifer Friedenbach, director of the Coalition on Homelessness, called Wiener’s call to enforce the ban on camping “cruel” in the middle of winter.

In his letter, Wiener asked how many tents are on the streets, how many people live in them, how many shelter beds are vacant every night, and what the plan is to get tent dwellers indoors.

He has yet to get any answers.

Heather Knight and Kevin Fagan are San Francisco Chronicle staff writers. E-mail: hknight@sfchronicle.com, kfagan@sfchronicle.com Twitter: @hknightsf, @KevinChron