Bill Cosby arrives at the court house in Elkins Park, Pa., to face charges of aggravated indecent assault in December. (Kena Betancur/AFP/Getty Images)

A Pennsylvania judge will consider Tuesday whether to dismiss charges against Bill Cosby related to an alleged sexual assault in 2004. The case is unusual not only because the defendant is a 78-year-old celebrity. Very few accusations of sexual assault ever make it into a courtroom.

Researchers estimate that at least hundreds of thousands of crimes of this type are committed every year. A fraction of them result in charges and even fewer cases are heard by a jury. Ultimately, only a handful of people who commit sexual assault are ever convicted.

The low rate of convictions results from a series of challenges at every stage of the legal process.

Many rapes go unreported — though just how many is difficult to determine. Reliable figures on the prevalence of sexual violence are hard to come by. Even reported rapes are difficult to quantify. As with other crimes, there is no national database with comprehensive information on the results of investigations into incidents reported to police.

"All in all, the data around the second most serious crime is terrible," said Carol Tracy, executive director of the Women's Law Project in Philadelphia.

In total, the Justice Department estimates that 150,000 people were victims of rape and sexual assault in 2014. About half of those crimes are rapes and attempted rapes and a quarter are other kinds of sexual assault. The Justice Department also includes "verbal threats" of sexual assault in the category, which constitute most of the remaining quarter. About a third of all the incidents were reported to police.

Prosecutors say Cosby drugged the victim in the case, Andrea Constand, then fondled her and penetrated her digitally. He is charged with aggravated indecent assault. Cosby's lawyers have called the charge "unjustified" and say they expect him to be exonerated.

The Justice Department's data has been criticized, though, and other studies have yielded much larger figures.

The department conducts an annual survey, interviewing a sample of the population in person and asking whether they have been victims of crime. A panel of statisticians and criminologists convened by the department concluded in 2013 that the questions the survey used were ambiguous and that some respondents might not feel comfortable speaking honestly about rape with interviewers.

Another federal survey was conducted by the Centers for Disease Control and Prevention, using a gradual approach to the questions to attempt to build rapport in interviews conducted by phone. The agency estimated that in 2010, about 1.2 million women had experienced rape or attempted rape during the previous 12 months — about 16 times as many as in the Justice Department survey. About 6.6 million women and 6 million men were victims of other kinds of sexual violence.

That survey also found that 92 percent of victims of rape know the assailant in some way. Despite the fact that law enforcement would have little trouble identifying the perpetrator in almost all of these crimes, the FBI reported just 21,000 arrests on charges of rape last year.

One arrest can account for several crimes, as some rapists have multiple victims over the course of a year. Still, there is clearly a large gap between crimes and apprehensions.

Some of that gap results from the low rate at which victims report sexual assaults. Some victims prefer not to tell police about what happened or aren't able to describe it clearly, because the trauma interferes with memory. Other victims doubt their ability to tell their stories in a believable and convincing way.

Still others try to put rape behind them by not talking about it or even thinking about it.

"There are certain things that, as part of the human condition, we do in order to be able to continue to survive in a quote-unquote 'normal' way," said Viktoria Kristiansson, a former New Jersey prosecutor. "For some people, it is easier to just shut that off altogether and never even allow the brain to get to the point where there is an acknowledgment that a crime occurred."

Intentionally or not, law enforcement officials can also discourage victims from seeking justice. A typical law enforcement investigation involves asking parties connected with a crime to tell their stories repeatedly and looking for inconsistencies in an effort to determine whether they are credible — a process that could be disheartening for the victim of a rape.

For these reasons, many victims will avoid conversations with law enforcement, and others recant their accusations in the course of the investigation, even if accusations are true.

As Wonkblog has reported, researchers who have obtained detailed files on rape investigations from police departments around the world have generally concluded that no more than 10 percent and possibly as few as 2 percent of reports are false.

Even when a case does result in arrest and police turn over the paperwork to the district attorney, prosecutors often decline to take the matter any further. Because defendants can claim that intercourse was consensual, rape cases are often more difficult to prove before a jury.

"Prosecutors — as we've seen in the Cosby case — are very reluctant to prosecute rape cases unless they have a slam-dunk case with witnesses and additional violence," Tracy said. Dozens of women have said that Cosby drugged and raped them.

Physical injury and the use of a weapon, which are clear evidence that the victim did not consent, increased the chances that prosecutors would pursue charges. Yet that evidence is rarely present. A review of prosecutorial decisions in sexual-assault cases in Miami, Philadelphia and Kansas City, Mo., published in 2002 found that the victim was injured in just 26 percent of cases, and the alleged perpetrator used a gun or a knife in just 16 percent of cases.

Racial prejudice, on the part of prosecutors themselves or the juries they expect to face, might also affect the chances of an arraignment. In cases in which the victim was white, the defendant was more than twice as likely to be charged as in cases in which the victim was black.

In all, the review found, prosecutors pressed charges in just 55 percent of cases that resulted in arrest.

"I do think prosecutors should be filing charges in more of these cases, and not just the cases where they're convinced that they’re going to win," said Cassia Spohn, one of the authors of the review and a criminologist at Arizona State University.

Once prosecutors make the decision to pursue a rape case in court, half of defendants plead guilty to a felony, according to a study that the Justice Department conducted using data from courts in the country's 75 largest counties — in May 2009. Some of them plead guilty to a lesser felony than rape.

Another 10 percent plead guilty to various misdemeanors, and a quarter are dismissed at some point after the prosecutor files charges.

If the case against Cosby proceeds and he pleads not guilty as expected, his case would be decided at trial — a rare occurrence. Just about 11 percent of cases filed by prosecutors reach a verdict at trial, according to the Justice Department study. Seven percent are convicted of a felony, 1 percent of a misdemeanor and 3 percent are acquitted.

To conclude, at least 21,000 people were arrested on suspicion of rape in 2014. Of those, prosecutors likely charged a little more than half, and of those defendants who were prosecuted, a little more than half were probably convicted of rape or another felony. These figures suggest that while as many 1.2 million people could be victims of rape or attempted rape in a given year, there might have been as few as 7,000 felony convictions.

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