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Evaluating the "43 times" fallacy

by David K. Felbeck
Michigan Coalition for Responsible Gun Owners
August 10, 2000

Those who oppose the use of firearms for self-defense have for fourteen years quoted a study by Arthur Kellermann and Donald Reay published in the June 12, 1986 issue of New England Journal of Medicine (v. 314, n. 24, p. 1557-60) which concluded that a firearm in the home is "43 times more likely" to be used to kill a member of the household than to kill a criminal intruder. This "statistic" is used regularly by anti self-protection groups which surely know better, and was even published recently without question in a letter to the Ann Arbor News. Representative Liz Brater cited this "43 times" number in a House committee hearing just a year ago. Thus the original study and its conclusion deserve careful analysis. If nothing else, the repeated use of this "statistic" demonstrates how a grossly inaccurate statement can become a "truth" with sufficient repetition by the compliant and non-critical media.

The "43 times" claim was based upon a small-scale study of firearms deaths in King County, Washington (Seattle and Bellevue) covering the period 1978-83. The authors state, 

"Mortality studies such as ours do not include cases in which burglars or intruders are wounded or frightened away by the use or display of a firearm. Cases in which would-be intruders may have purposely avoided a house known to be armed are also not identified…A complete determination of firearm risks versus benefits would require that these figures be known." 

Having said this, these authors proceed anyway to exclude those same instances where a potential criminal was not killed but was thwarted.

How many successful self-defense events do not result in death of the criminal? An analysis by Gary Kleck and Marc Gertz (Journal of Criminal Law and Criminology, v. 86 n.1 [Fall 1995]) of successful defensive uses of firearms against criminal attack concluded that the criminal is killed in only one case in approximately every one thousand attacks. If this same ratio is applied to defensive uses in the home, then Kellermann's "43 times" is off by a factor of a thousand and should be at least as small as 0.043, not 43. Any evaluation of the effectiveness of firearms as defense against criminal assault should incorporate every event where a crime is either thwarted or mitigated; thus Kellermann's conclusion omits 999 non-lethal favorable outcomes from criminal attack and counts only the one event in which the criminal is killed. With woeful disregard for this vital point, recognized by these authors but then ignored, they conclude, 

"The advisability of keeping firearms in the home for protection must be questioned." 

In making this statement the authors have demonstrated an inexcusable non-scientific bias against the effectiveness of firearms ownership for self defense. This is junk science at its worst.

This vital flaw in Kellermann and Reay's paper was demonstrated clearly just six months later, on Dec. 4, 1986 by David Stolinsky and G. Tim Hagen in the same journal (v. 315 n. 23, p. 1483-84), yet these letters have been ignored for fourteen years in favor of the grossly exaggerated figure of the original article. The continual use of the "43 times" figure by groups opposed to the defensive use of firearms suggests the appalling weakness of their argument.

But there's more. Included in the "43 times" of Kellermann are 37 suicides, some 86 percent of the alleged total, which have nothing to do with either crime or defensive uses of firearms. Even Kellermann and Reay say clearly 

"…[that] the precise nature of the relation between gun availability and suicide is unclear." 

Yet they proceed anyway to include suicides, which comprise the vast majority of the deaths in this study, in their calculations. Omitting suicides further reduces the "43 times" number from 0.043 to 0.006. 

"Reverse causation" is a significant factor that does not lend itself to quantitative evaluation, although it surely accounts for a substantial number of additional homicides in the home. A person, such as a drug dealer, who is in fear for his life, will be more likely to have a firearm in his home than will an ordinary person. Put another way, if a person fears death he might arm himself and at the same time be at greater risk of being murdered. Thus Kellermann's correlation is strongly skewed away from normal defensive uses of firearms. His conclusion is thus no more valid than a finding that because fat people are more likely to have diet foods in their refrigerators we can conclude that diet foods "cause" obesity, or that because so many people die in hospitals we should conclude that hospitals "cause" premature death. Reverse causation thus further lowers the 0.006 value, but by an unknown amount.

In conclusion, if we use Kellermann's data adjusted for reality, a firearm kept in a home is at least 167 times more likely to deter criminal attack than to harm a person in the home. This number is some 7000 times more positive than the "43 times" negative figure so often quoted. Should groups and individuals that knowingly perpetuate a figure that is at least 7000 times too large be given any credence at all?

With two million defensive uses of firearms each year, both inside and outside the home, the value of protection against criminal assault provided by firearms vastly exceeds any dangers that they might present.

David K. Felbeck
Ann Arbor, Michigan
Director, Michigan Coalition for Responsible Gun Owners