By reading the language in Isis' claims on attacks, one can see which of them were heavily directed, as in Paris and Brussels, and which were simply inspired by the group's ideology. There is a clear difference between claims made after attacks that Isis leaders knew about beforehand, and attacks they didn't.
In the case of Paris, for instance, highly detailed press releases were distributed right after the carnage, complete with videos and pictures. On the other hand, Amaq, Isis' media arm, claims responsibility for "inspired" attacks only once it gets credible information of a link, either from a source of its own or from the news media. Isis does not always have its own inside source.
"What has evolved is that they are doing much the same thing that we do as analysts, which is watch these attacks and try and figure out if it is Isis-inspired," said JM Berger, a fellow with George Washington University's Programme on Extremism and the co-author of Isis: The State of Terror.
After a man blew himself up in Ansbach, Germany on Monday, it took Amaq 24 hours to claim that Isis inspired the attack. After a 17-year-old axe-wielding Afghan went on a rampage on a train, also in Germany, it took nine hours to issue such a claim. After Mohamed Lahouaiej Bouhlel mowed down dozens in Nice with a truck, it took a full day and a half.
"For these inspired attacks, it's important to know that [the media people in Syria] don't even know of these guys. They have nothing to do with them. They aren't in contact with them directly," said Amarnath Amarasingam, a fellow studying extremism at Dalhousie University in Canada and the co-director of a study of Western fighters for Isis, based at the University of Waterloo in Ontario, Canada.
The lag time in claiming an attack reflects a need to establish a credible link between the attacker and Isis. Many have lampooned Isis as an organisation keen to claim each and every terrorist attack around the world, but analysts say it has a vested interest in being accurate.
"They're careful about it. They couch their terms a bit," said Berger. "If they can accurately insert themselves into the narrative around an attack, they win, essentially."
In other cases, though, it has proved effective for Isis to claim attacks in which the link is far sketchier. For instance, in the San Bernardino attack last December, the media widely reported that the couple who carried out the attack had posted an oath of allegiance to Isis on Facebook. Amaq then proclaimed them "soldiers of the caliphate". But the FBI never confirmed that the Facebook post was ever written, and Director James Comey said at the time, "I've seen some reporting on that, and that's a garble". San Bernardino nonetheless gave Isis the chance to claim its first "inspired" attack on American soil.
If they can accurately insert themselves into the narrative around an attack, they win, essentially.
Beyond credibility issues, the hesitance to immediately claim the attacks like the most recent ones in Germany and France may also reflect embarrassment the group felt after associating with particular lone-wolf attackers.
In the weeks following their attacks, news reports indicated that the attacker in Nice, Mohamed Bouhlel, and Omar Mateen, who killed 49 people at an Orlando, Florida, nightclub in June, may have had sexual relationships with other men. Mateen and Bouhlel were each embraced by Isis before that became public, and homosexuality is punished through gruesome death penalties in the "caliphate".
In cases like those, attackers unvetted by Isis may still be at worst a double-edged sword for the organisation. After all, despite bad publicity, Isis can still claim that it inspired those attacks. And the greater the perceived threat from the group becomes, the more it may stir calls for larger-scale retaliation or anti-Muslim policies, leading to the radicalisation of others.
Yesterday's killing of an octogenarian priest in France yielded a relatively quick claim. Between "directed" and "inspired" attacks, it seems that this one lies somewhere in the middle of the spectrum. News reports quickly uncovered one of the attackers' attempts last year to travel to Syria. Amaq's statement called the men "executors" and "soldiers of the Islamic State," but more or less acknowledged that Isis had not directed the attack. Instead, as in other "inspired" attacks, Amaq said the men had responded to a call for attacks to be carried out in countries participating in the coalition fighting Isis in Iraq and Syria.
But it attributed its claim to an "insider source," whom Amarasingam said was likely to be someone the attacker was in touch with during his failed "hijra" to Syria last year. The part-directed, part-inspired nature of the attack poses a dilemma for law enforcement in the West: Does preventing people from travelling to Syria increase the likelihood of an attack at home?
"That's been part of Isis' propaganda," said Amarasingam. "You either pack your bags or sharpen your knives. And if you're unable to travel here and join the caliphate, either because you can't afford it or law enforcement is watching you, you do have another recourse, which is to defend us wherever you are."