An outline of an alien stands high during the annual Alien Festival in February in Capilla del Monte, Cordoba, Argentina, the site of an alleged UFO sighting 30 years ago. (AP Photo/Natacha Pisarenko)

Last December a woman in Florida was awakened by the sound of an intruder in the house. She grabbed her gun, confronted the intruder and fired one fatal shot, according to police.

This is the type of scenario many Americans envision when buying their first or second or third firearm. Forty-eight percent of gun owners say they own a firearm primarily for protection, according to the Pew Research center, a share that's up 22 percentage points since the late 1990s. Gun rights groups like the National Rifle Association compile reports of incidents like the Indianapolis home invasion to point out the social benefits of good guys with guns who protect themselves and their communities from would-be wrongdoers.

But the latest research on the prevalence of firearm use in self-defense finds that these incidents are much less common that many gun rights advocates believe. Eor every person who uses a gun in self-defense, the research finds, nearly six people use a gun to commit a crime.

Those figures come from a Harvard University analysis of data from the federal National Crime Victimization Survey. David Hemenway, director of the Harvard Injury Control Research Center, examined five years of data from the survey covering the period between 2007 and 2011, with responses from nearly 160,000 individuals.

Hemenway found that not only are self-defense gun uses rare -- people defended themselves with a gun in roughly 0.9 percent of crimes committed over this period -- but in many cases they don't lead to better outcomes for crime victims.

"The likelihood of injury when there was a self-defense gun use (10.9%) was basically identical to the likelihood of injury when the victim took no action at all (11.0%)," Hemenway and co-author Sara J. Solnik found.

Looking at what happened after people took action to prevent a crime, Hemenway and Solnik found that people were far better off either running away, or calling the cops if possible, rather than attempting to stop a crime with a gun. "Running away and calling the police were associated with a reduced likelihood of injury after taking action; self-defense gun use was not," they write.

The use of guns were, however, were linked to better outcomes in certain circumstances. In cases of robbery and burglary, victims who didn't try to stop the crime lost property nearly 85 percent of the time. Victims who attacked the intruders or threatened them with a gun had a better outcome, losing property 39 percent of the time. But those are slightly worse odds than for victims who fought back with other weapons -- this latter group lost property 35 percent of the time.

Of course, there's a huge problem with this analysis, as with all attempts to quantify and describe self-defense gun uses: These cases are so rare that it's difficult to gather a meaningful body of data about them. And conclusions based on analyses like these are subject to a high amount of error.

Among the 160,000 people surveyed in this dataset, for instance, there were only 127 instances where someone used a gun in self-defense. This kind of rarity leads to wild variation in estimates of how many times people use guns in self-defense in a given year.

One of the most famous estimates of the annual prevalence of self-defense use, made in the mid-1990s by criminologists Gary Kleck and Marc Gertz, claimed between 2.2 and 2.5 million defensive gun uses annually. This estimate was based on a national survey of 5,000 people, of which 66 reported using a gun in self-defense in the past year.

But subsequent research has found that this high number is simply mathematically impossible. As crime prevention researcher Philip Cook has pointed out, "The Kleck-Gertz survey suggests that the number of DGU [defensive gun use] respondents who reported shooting their assailant was over 200,000, over twice the number of those killed or treated [for gunshots] in emergency departments." In other words, in order for the estimate of 2.5 million defensive gun uses to be correct, we would have to assume that self-defense accounts for literally every single gunshot victim in the United States, as well as a massive number of invisible gunshot victims completely unknown to medical or legal authorities. That simply isn't plausible.

In an email, Cook notes that getting reliable survey data on rare occurrences can be tricky. "Whenever you’re surveying about a rare event like DGUs, estimates may well be inflated by the small fraction of respondents who are drunk or deluded or simply having fun," he said. He points out that the percentage of people reporting a defensive gun use in Kleck's survey is similar to the percentage of Americans who say they've been abducted by aliens.

A more reasonable estimate, based on the National Crime Victimization Survey, would peg the annual number of self-defense gun uses to be around 100,000 per year. Researchers generally view these estimates as more reliable because the NCVS includes a much larger sample size and it surveys the same households multiple times, which ensures that people are recalling events more accurately.

To be sure, 100,000 is still a very large number. But there's another problem, too, and that's that there's a lot of murkiness around what "self-defense" really means. "Self-defense is an ambiguous term and whether one is a defender or a perpetrator may depend on perspective," Hemenway and Solnik write in their latest research.

In a 2000 study,Hemenway and colleagues asked criminal court judges to read 35 accounts of gun owners who said they used their guns in self-defense in a national survey. In the judges' opinions, over half of these gun uses were probably illegal.

For instance, in one of the cases a 58-year-old man said that he was watching TV when a friend interrupted him. The man, who was carrying a gun at the time, told the friend that he was going to shoot him, and the friend ran outside. In the eyes of the man with the gun, this was an act of self-defense against a "verbal assault" by his friend.

In another, a man responded to an alarm at his business. When he arrived, he shot at two men standing outside the business without knowing whether or not they had set off the alarm.

In both cases above, men who said they were acting in self-defense were actually committing crimes of aggression using a gun. The simplistic narrative of "good guys" versus "bad guys" is often inadequate to describe the complicated interactions between people and their firearms.

The home invasion shooting in Florida is another case in point. The "intruder" was actually the woman's 27-year-old daughter.