The OP's article's information is interesting. Private citizens are more effective because they are there nearly 100% of the time. Note that there have been several mass shootings at military installations and police stations where there are virtually no private citizens involved and incidents where you have both responding.
However, the listing he provides is bogus. He provides a purely supeficial and decidedly unuseful in the sense of he isn't actually resolving the claims he is making.
He listed 23 killed at Luby's after a shootout with police by the gunman (suicide). He failed to note the terrible failures of at least 2 private citizens who charged the shooter and were gunned down long before the police were intervening.
He listed 16 killed by Whitman after being shot by police. He failed to note responded citizens shooting at Whitman or the fact that one of the people shooting Whitman as part of the responding entry team was not police.
He list 7 killed by Jeff Weise at Red Lake High School before suicide after being confronted by the police. He failed to note Weise was stabbed in the stomach with a pencil by Jeff May who was subsequently shot multiple times, but credited with saving the lives of several who escaped the room they were in because of his actions.
He listed 3 killed by Peter Odighizuwa at The Appalachian School in Grundy, Virginia who was stopped by 3 students. Undoubtedly, he considers these to be private citizens because he doesn't know what he is talking about. Two were off duty cops, both of whom retrieved guns from their vehicles, one grabbing a ballistic vest as well. The other was private and others pursued Odighizuwa.
I wil stop there because I think I have made my point. If you take the time to research the list in detail, you will find that many of the shootings ultimately resolved by cops first involved failures by attempts to be resolved by people inside. Yes, shootings resolved by private citizens will end in a lower number, but a large percentage of such shootings involve private citizens (or at Ft. Hood, other soldiers) attempting to stop the shooter and failing. So it could also be argued that incidents where private citizens attempts to stop the shooter and fail and have to rely on the cops result in a higher number of deaths and a high number of woundings and deaths by the failed private citizen responders. Okay, who wants to be cannon fodder? If you are successful, you will stop the shooter and save lots of lives. If not, you will most likely be injured or killed and if injured, likely punitively injured severely because you end up pissing off the shooter. Of course, the reality is that if you don't attempt to stop the shooter, he may still kill you, just not as soon, and if unchecked, he will continue to kill others. It is HIGH risk to intervene. It is still HIGH risk to just be present, however.
Also as noted, at least one of his incidents involved cops he thought were private citizens and he failed to note private citizens intervening with cops.
His use of the available data is decidedly a mess in terms of being able to draw the conclusions he has drawn. In short, he study is bogus and is NOT a very well done, very analytical view that separated much of the wheat from the chaff. He obviously was not familiar with the incidents he used in this article.
Somebody asked about more listing. I compiled this in response to folks who think that being unarmed means being defenseless. People actually make this sort of statement on gun forums, people who considered themselves "well prepared" and "head on a swivel" folks, but who are reduced to being defenseless because apparently you can't fight bad guys without guns. It is an attitude issue I was hoping to quell somewhat by pointing out all the times that tackling shooters stopped the shooters, but also noting that it is a very high risk endeavor. It works and it works often, but it also results in some people being wounded or killed directly because they did try to stop the shooter. Timing of such attacks (such as the apparent poor or unavailable timing at Luby's) seems critical to success of such an endeavor.
My lists of incidents do not include the distinction of cops/not cops per se and in fact lists numerous shooters stopped by cops who opted to tackle and not shoot (various reasons, but often because of timing or directions not prudent for shooting such as would have been the case for the Reagan assassination attempt or Oswald's assassination by Jack Ruby).
http://thefiringline.com/forums/showthread.php?t=436861&highlight=tackling
Davi Barker's article also failed to list one of my favorite mass shootings stopped by a private, unarmed citizen. That was of Sylvia Seegrist at a mall in Pennsylvania. It was Halloween and she walked around shooting people before a John Laufer, not realizing she was using real bullets, grabbed the gun, grabbed her, and held her for security/cops. Fortunately, he grabbed the gun before she pulled the trigger on him because he was clueless, but a hero none-the-less.
http://thefiringline.com/forums/showthread.php?t=436861&highlight=tackling