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Barbara Bowman first publicly accused Bill Cosby of rape in 2004. But people didn't start believing her until now, when a male comedian called Cosby a rapist last month.

Bowman's story puts a personal face on the myriad reasons women are often hesitant to come forward with rape allegations. They often face disbelief, harrassment, or accusations of wrongdoing themselves. And a woman's chances of winning a conviction in a rape case are extremely low compared to other crimes.

In the most recent crime data released by the FBI, only 40 percent of documented rape cases ended in "clearance." Clearance indicates that officers were able to close a case, either via an arrest, or in some cases due to victim non-compliance - this latter method is called an "exceptional" clearance. This percent of rape cases cleared has declined sharply since 1995, while clearance rates for murder and aggravated assault have held steady.

But the reality is far more troubling than these numbers suggest.

Earlier this year, law professor Corey Yung released a lengthy paper providing evidence that police departments are systematically undercounting rape in large cities across the country. His numbers, which he calls "conservative," suggest that "an additional 796,213 to 1,145,309 forcible rapes of women have been reported to authorities, but police have hidden them from the public record, thereby feeding the myth of the 'great decline' in rape."

Yung looked at cities with highly disparate rates of murder and rape. Because murder rates are generally known to be quite accurate and correlated with rape, if a city's rape trends are considerably divergent from its murder trends, there's good reason to suspect that the rape numbers are off. And in many cases, rates of rape were considerably and unexpectedly lower than murder rates.

Even worse, the number of jurisdictions under-reporting rape cases has been increasing over the past 18 years, according to Yung's data.

Yung explains in the e-mail that "rape cases are viewed by many police as unlikely to yield a prosecution or conviction. ... Unfortunately, this creates a vicious cycle: police believe rape cases are unwinnable so they don’t investigate many cases [--] which then actually makes less rape cases result in a conviction which reinforces the belief that such cases are unwinnable."

This vicious cycle is at the heart of a just-released investigation of the New Orleans police department, which found that detectives only followed up on 14 percent of sex crime reports over a period of three years, leaving hundreds of allegations completely uninvestigated. "I think a lot of what happened in the NOPD could be found in police departments across the country," Yung said.

Even among the few cases that do lead to an arrest, only 4 in 10 end up with a felony conviction, according to data compiled by the Rape, Abuse and Incest National Network (RAINN). With the odds stacked to sharply against them, it's little wonder that many women are hesitant to even report rape to begin with.

There are signs that law enforcement is beginning to take rape allegations more seriously. Starting this year, the FBI finally updated its 80-year-old definition of rape, which had previously been defined as "carnal knowledge of a female forcibly and against her will."

As Slate's Amanda Hess points out, this definition excluded rapes of men, instances of non-vaginal penetration, or sexual assaults involving objects. "The new definition also drops the 'forcible' qualifier in favor of 'without the consent of the victim,'" Hess writes, "encouraging jurisdictions to report rapes perpetrated without a show of physical force."

This change could lead to better reporting of rape, and a better understanding of who commits it, and who the crime's victims are. But only if police departments make a good faith effort to use the new definition. "Because adherence to the new definition is optional," Yung says, "any changes in data from previous years will be hard to interpret without knowing which jurisdictions are using it." Hess reports that 10,000 out of 18,000 jurisdictions used it for their reports to the FBI this year.