New York City's criminal justice system continues to have severe problems. Rikers Island prison, New York City's primary jail facility, has more staff and fewer inmates than in previous years—and yet it also has sky-high costs and increasing levels of violence, according to a forthcoming comptroller's report reviewed in an article in The New York Times.

The cost is higher than ever, and way out of proportion with comparable urban areas. The City of New York spent $1.1 billion to run its jails last year, a record sum, according to the report.

Housing a prisoner for a year in New York cost the city's Corrections Department $100,000 last fiscal year. That's a huge increase from a few years ago, and much higher than in other major metro jail systems. As the Times notes, the cost "is 42 percent higher than seven years ago and more than twice the amount spent per inmate by correction departments in other large cities like Chicago and Los Angeles."

Those cities have larger jail populations but significantly lower costs per person housed:

New York spends far more on its jails than other large American cities, even those with much larger inmate populations. Los Angeles, for instance, has an inmate population of nearly 19,000, about 7,000 more than New York. But taxpayers there spend only $44,965 a year per inmate, nearly half what New Yorkers spend, according to the report.

But the skyrocketing costs haven't resulted in a more peaceful prison system. In fact, the city's jails have become even uglier even as spending has ramped up. During the fiscal year that ended in June, the Times says, "there was a 124 percent increase in assaults on the staff by inmates at city jails, and triple the number of allegations of use of physical force by guards."

The violence at Rikers is horrific, and the city has tried to hide it from public view. A July report from The New York Times is chilling:

[The Times] found that over an 11-month period last year, 129 inmates suffered "serious injuries" — ones beyond the capacity of doctors at the jail's clinics to treat — in altercations with correction department staff members. The report cataloged in exacting detail the severity of injuries suffered by inmates: fractures, wounds requiring stitches, head injuries and the like.

The report was based on information that the city health department refused to make public.

Union representatives for prison guards have long argued that the solution is more guards. And it's true that the number of guards in the city's jail system has declined somewhat, from about 9,200 in 2007 to 8,922 this year.

But those guards are also tasked with guarding a declining prison population, and so the ratio of guards to prisoners has actually increased by 19 percent, according to the report. In other words, each guard now has fewer prisoners than ever to look after.

That hasn't helped. According to the Times, "a vast majority of the cost in New York, about 85 percent, goes to pay for personnel." Much of the excess spending can be attributed to overtime, which is apparently not being limited the way it's supposed to.

The improved staffing and lower inmate population have somehow produced a counterintuitive result, translating into a rise in overtime costs to $139 million in 2014 from $101 million in 2007, the report said. Correction Department regulations are supposed to limit the amount of overtime a guard can work to 57 hours a month. But Elizabeth Crowley, a City Council member who oversees corrections, said that some officers worked as much as 80 hours a month.

Scott Stringer, the comptroller who put together the report, was blunt when he spoke to the Times about the situation in the city's jails, saying: "We're spending more money on inmates and we're getting worse results."