SAN JOSE — This year’s mayor’s race has been dominated by public safety on a level unseen in San Jose’s modern history, with one side pushing promising trends and the other side portending scary times ahead for the country’s 10th-largest city.

Election brochures that have been appearing in mailboxes and other campaigning illustrate those opposing contentions: Crime rates are either heading downward, according to Sam Liccardo’s supporters, or there are crowbar-wielding masked thieves lurking at nearly every residential corner, if you believe Dave Cortese and his supporters.

So what’s really happening?

A 10-year look at crime data shows property crimes in San Jose rose sharply between 2008 and 2012 before starting to dip in 2013. Statewide, there were corresponding but less dramatic ups and downs, while national trends show a consistent decline over those same years. But San Jose’s violent crime rate has stayed well below state and national averages and in 2013 was the lowest of any large U.S. city, according to figures from the San Jose Police Department, state attorney general and FBI.

With property crimes, the city is leveling off from a recent peak in 2012, when its rate of 2,930.2 incidents per 100,000 residents marked the first time in at least a decade San Jose exceeded the state and national rates. There has been some relief by way of successive 10 percent decreases in 2013 and the first six months of 2014. In 2013, San Jose’s property crime rate ranked sixth-lowest among the 35 U.S. cities with at least 500,000 residents, a list that includes New York City, Los Angeles, San Francisco and San Diego. But it remains far higher than many longtime residents are used to.

Violent crime in San Jose saw a similar rise and fall along with the rest of the country, though the violent-crime rate of 326.6 incidents per 100,000 residents has remained persistently below big-city peers. The city’s violent-crime rate is now at its second-lowest level of the past decade, even with a 4 percent rise in the first six months of 2014.

In this political year, what the voters are really seeing is candidates who slice and dice those statistics to support their campaign, according to Greg Woods, a lecturer in the criminal justice studies department at San Francisco State University whose expertise includes criminal justice research methods.

Supporters of Councilman Liccardo, a close ally of outgoing Mayor Chuck Reed, are focusing on the recent drop in crime. Meanwhile, Supervisor Cortese, the candidate backed by the police union, is emphasizing the overall increase in property crime over the past few years.

“That’s why we should view this data critically. In a vacuum, statistics don’t do anything — it’s in how you use those numbers,” Woods said. “It’s playing with fear. It’s not about two plus two equaling four, it’s about emotions.”

A particularly vivid example came when Reed recently put out a news release boasting a 70 percent drop in violent gang crimes through the first nine months of this year. Upon closer scrutiny, it became clear the percentage was so high because the first month of the year had the worst numbers and the ninth month had the best; the numbers in the intervening months did not substantiate the trend Reed cited. A more reliable comparison, which Reed said he was warned against doing because of data limitations, shows the drop to be closer to 15 percent.

Woods noted that property crimes have outpaced violent crimes in the public consciousness because of the economic profile of San Jose, where homeownership is relatively common.

“When you have high percentages of the population that own things, high property crime is going to be more meaningful to them,” Woods said.

San Jose is not alone in seeing fluctuations, particularly the elevated property crime rate that parallels a similar upward trend in California, although the city’s increase prior to 2013 was somewhat more pronounced. Law-enforcement and civic leaders throughout the state have attributed the rise at least in part to “realignment” policies instituted by the Legislature and governor in 2011 that allowed early release for offenders convicted of certain nonviolent crimes — often property crimes — in response to court orders to relieve prison overcrowding.

Many cities in the state have also cut police staffing amid budget tightening and contentious pension reform efforts. That is probably most evident in San Jose, which in six years has gone from 1,400 officers to just over 1,000. The police union and its allies contend the result has been lagging police response times, deflating residents to the point where they are reporting nonviolent crimes less frequently. Arrests have also dropped by half in the same time frame.

Woods said it leads to a paradox that becomes difficult to quantify. When people feel unsafe, what’s changing: the level of crime or our awareness of it?

“Usually it’s pretty simple: The more police you have in the community, the less crime there is in the community,” Woods said. “Are we only perceiving more crime because there are more cops on the street, or seeing less of it because we have fewer cops on the street?”

Perception may be the most important factor in the political debate over crime. For several years in the 2000s, San Jose was second lowest, after New York City, in property crimes per capita among large U.S. cities. At the time, San Jose was routinely lauded as the safest large city in the country. Property crime has generally risen since then, and residents have noticed.

“If one of the reasons people live here is that it’s a safe city, and crimes against people go up, it might not be the worst city, but considering where it was, there are expectations,” said Larry Gerston, a longtime San Jose State political science professor and analyst. “Unfortunately, when you gain a reputation for something, it’s a lot easier to lose it.”

Contact Robert Salonga at 408-920-5002. Follow him at Twitter.com/robertsalonga.