TL:DR Most studies find figures ten times lower than this one.
The "80 times more often" figure comes from a single study: "Kleck and Gertz:Armed resistance to crime: The prevalence and nature of self defense with a gun. Journal of Criminal Law and Criminology 1995 (Fall); 86:150–187", in which the authors estimated that there were 2.5 million occasions per year in which a gun was used in self-defense.
Here is a brief summary of the methodology:
Kleck and Gertz’s claim of 2.5 million defensive gun uses per year is derived from a telephone survey of 5,000 American adults conducted in 1992. Fifty-six respondents to this survey reported that they had used a gun in self-defense during the past year. Kleck and Gertz multiply the proportion of respondents in their survey who report a defensive gun use (X /5,000 = Y percent) by the number of adults in the U.S. (around 200 million) and the number of defensive gun uses equals 2.5 million per year.
Although published in a reputable journal, the figure has been widely criticised by other researchers on many grounds: statistical, methodological, and by comparison with other known figures.
Here is a typical criticism::
The primary problem is that, even if the Kleck and Gertz’s estimates were accurate, defensive gun use is a relatively rare occurrence in that only 1% of respondents reported a defensive gun use during the previous 12 months. As David Hemenway of Harvard University has pointed out, inaccurate reporting of these events by a relatively small number of respondents could lead to population projections that are orders of magnitude different from the true incidence.14 For example, if one-half of one percent of the survey respondents incorrectly reported that they had used a gun to defend themselves against a criminal attack during the past year, the estimated number of defensive gun uses would be twice as high the true number.
Other researchers find that attempts to cross-reference these figures with other better-established ones lead to contradictions:
[According to Kleck and Gletz] Guns were reportedly used by defenders for self-defense in approximately 845,000 burglaries. We know that there were 6 million burglaries in the year of the survey and in only 22% of these cases was someone certainly at home.Since only 42% of American households own guns, and since the victims in 2/3 of the occupied dwellings were asleep, the 2.5 million figure requires us to believe that burglary victims use their guns in self-defence more than 100% of the time.
Other researchers conducted a similar survey (obtining compatible figures) and then checked on the credibility of the reports:
Our closer examination of the [Defensive Gun Use] reports in the [out survey] suggests that almost half of the incidents appear to contain some internal inconsistency, or other-
wise do not make sense. We are persuaded that surveys of this sort generate estimates that grossly exaggerate the true number of DGUs
This overview cites the National Crime Victimization Survey which places the number of defensive gun uses at 100,000, and other estimates come it at about 250,000 - ten times less than the figure quoted.
In short: while there is much disagreement over the true figure, the "80 times" figures is very much at the top end of the range of estimates. Most estimates are ten times lower.