The mayoral candidates threw around figures, debated ideas and avoided the topics they did not want to talk about.

The third debate Tuesday for Mayor Byron W. Brown and his challengers, Bernard A. Tolbert and Sergio R. Rodriguez, was the most sharply argued so far as the candidates criticized one another and defended themselves.

But did they get their facts right? The Buffalo News looked at some of their claims.

• Claim: Rodriguez called Buffalo the third-poorest city in America and the 11th-most dangerous.

• Fact: The city’s poverty rate remained stuck at about 31 percent in 2011, statistically unchanged from 2010, according to recently released census data. The city has the third-highest rate of childhood poverty, according to a report from the National Center for Children Living in Poverty, based on the 2011 census data. In cities of at least 100,000 people, Buffalo ranked 21st in the census data. Buffalo was the fifth-poorest among cities with a population of at least 250,000 – dropping two spots from third-poorest a few years earlier.

Statistics compiled by the FBI show Buffalo with the 11th-highest rate of violent crime among big cities, according to an analysis of 2012 figures.

• Claim: “We spent last year $11 million in overtime,” Rodriguez said. The city could instead hire 200 police officers at an annual salary of $55,000.

• Fact: Indeed, the city paid $11.2 million in police overtime last year, according to the City Comptroller’s Office. While that money would pay the $55,000 salaries for 200 officers, the cost of putting an officer on the street is closer to $100,000, and that does not include training.

• Claim: “The city has no poverty plan,” Tolbert said. A poverty task force “has done absolutely zero.”

• Fact: A poverty plan Brown unveiled in 2009 called for a task force with four work groups. It was widely panned.

In an Aug. 16 interview, Brown said that in looking at the response to the plan, he has decided that poverty should be worked on by many organizations in the community – not just the city.

The Brown administration did not respond when asked Wednesday about Tolbert’s claim that the task force never met or produced results.

• Claim: Tolbert said he did not condone sexual harassment or discrimination while he worked as a security official with the National Basketball Association. A woman who worked with him filed a lawsuit alleging that she was denied a promotion and raises based on gender. The NBA settled the lawsuit. “She did not accuse me of sexually harassing her,” Tolbert said. “That lawsuit was settled over my objections, I did not want to settle it. It was settled with no finding of wrongdoing on my part.”

• Fact: While Tolbert was NBA chief of security, he was named in a lawsuit, accused of making demeaning comments about women and passing over a female employee for promotion. The league settled the lawsuit confidentially, over what Tolbert says were his objections.

A lawyer for the plaintiff in the case confirmed Wednesday that there was no admission of guilt in the settlement.

• Claim: Tolbert said unemployment in Buffalo “is at an all-time high.”

Rodriguez and Tolbert repeatedly criticized Brown for the unemployment rate since Brown took office in 2006.

• Fact: The city’s unemployment rate was 6.3 percent in 2006, compared with 10.2 percent in July, according to data from the state Department of Labor.

The July rate, however, is not the highest ever recorded in the city. In 1993, the unemployment rate was 11 percent, and in 1992, it reached 12.1 percent.

The unemployment rate in the city was 10.9 percent in 2012, 10.5 percent in 2011 and 10.8 percent in 2010.

• Claim: Brown said the city has hired 230 new police officers, while Tolbert said the city has lost 260 officers through attrition, resulting in a net decrease for the force.

• Fact: The city budget for 2013-14 indicates that the total number of sworn personnel in the Police Department is 767, but 54 recruits now in training will soon bring that number to 821. The total number of sworn personnel recorded in the 2006-07 city budget – during Brown’s first year in office – was 778.

The Brown administration, citing figures from the City Budget Office, said 156 officers have retired since 2006, and the administration has hired 230 new officers, for an increase of 74 officers.

The budget figures may not reflect officers injured on duty, according to mayoral spokesman Michael J. DeGeorge.

• Claim: Brown said he supports the state’s new gun-control law, the Secure Ammunition and Firearms Enforcement Act. “I have been very clear on the fact that I support the SAFE Act,” he said.

• Fact: In January, Brown said he supported certain provisions of the new law but had concerns about others. He would not comment then on the law’s more controversial provisions, and that remained the case Tuesday.

During the debate, he would not answer – despite being asked three times – whether he supports a ban on assault weapons or limiting the amount of ammunition in a clip.

• Claim: Brown called the legal battle over a housing developer’s allegations of a “pay-to-play” policy at City Hall nonsense. “That lawsuit is absolute nonsense,” Brown said. “It is baseless, and we are fighting it in court, and we will prevail.”

• Fact: Cleveland housing developer NRP sued the city and accused Brown of conspiring to kill the firm’s $12 million housing project on the East Side. In July 2012, U.S. District Judge William M. Skretny allowed the lawsuit to continue but dismissed many of its claims, including breach of contract. The city asked Skretny to dismiss the lawsuit before a trial, but the judge said he found allegations of conspiracy “plausible.”