President Barack Obama declared the latest beheading by the Islamic State group — this one of American aid worker and former Army Ranger Peter Kassig — an act of “pure evil.” But as ugly as the act was, it was also an action taken with a strategic end in mind. The question we should be asking is: To what end? Why has the Islamic State group pursued a strategy of beheading Westerners, and specifically Americans?

One potential answer is that it wants to create fear. At the international level, the Islamic State group might gain from instilling fear and caution in the minds of Western leaders to discourage them from getting engaged in its fight for control of Iraq and Syria. In this light, the beheadings could be seen as a warning of how badly things will go for the U.S. and its allies if they send ground troops to confront the group.

At the regional level, by beheading Westerners, the Islamic State group is showing other groups that it has the strength and resolve to thwart the Great Satan and to carry out its plans, enhancing both its status and recruiting capability. By extension, terrorism’s fundamental purpose is to control through fear, something that the citizens of Iraq and Syria know all too well. Though its vicious tactics have not garnered much love, the strategy of violence has probably enabled the Islamic State group to exert greater control over its occupied territory than it would otherwise have been able to do.

All of that is certainly plausible, but it is also possible that the beheadings reveal a more complicated strategy of baiting the United States into overreaction. What if the Islamic State group wants the United States to get more involved? What if it wants the United States to send more ground troops?

This may sound bizarre on the surface, but it makes sense if we assume that the Islamic State group understands the likely consequences of its strategy. And of all people, its leaders should recall what happened the last time a group started killing Americans. Al-Qaida’s leadership fully expected the U.S. to react to 9/11, even if it did not realize that it would lead to full-scale war in Iraq and Afghanistan. Given that the Islamic State group now has the benefit of hindsight, it seems reasonable to assume that its current strategies account for this knowledge. It would be strange, in fact, to assume that the Islamic State group did not think that its strategy would provoke a strong U.S. response.

Making this even more plausible is the fact that baiting governments into overreaction has been a core element of terrorist strategies throughout history. The goal, typically, is to build support among the people when the adversary’s brutality is revealed through the overreaction. To that end, the Islamic State group already benefits from visible signs of U.S. overreaction in the form of widely feared and loathed drone strikes, not to mention attacks carried out on civilians by groups supported by the United States. In all of this the Islamic State group holds the upper hand when it comes to framing and explaining events to local populations given the lack of trust in the U.S. not to mention the Islamic State group’s savvy use of media and communications.

Further, if we look at the timing of this latest act of cruelty, it is clear that the beheading comes as the United States is considering whether to send more troops to Iraq. It may be giving the Islamic State group too much credit to assume that it follows U.S. foreign policy closely enough to time beheadings in order to influence debate, but given events like the 2004 Madrid bombing (right before a national election), assuming it doesn’t is dangerous.

To circle back to the main question: Might the Islamic State group want the U.S. to overreact and get more engaged in the Middle East? Yes, but how engaged? Al-Qaida’s experience makes it clear that there is a level of pain at which the U.S. political system will go into high gear looking for targets. Is that what the Islamic State group wants? That seems unlikely — as much drama as 9/11 produced, in the end it did not bring al-Qaida closer to its goals. If the Islamic State group pushes too hard, it could wind up with the United States reoccupying Iraq and perhaps the southern part of Syria. That seems like a risky path, even if the U.S. occupation of Iraq was in part what created the conditions that now allow the Islamic State group to create its own coalition.

What seems more likely is that the Islamic State group wants to keep the U.S. fully engaged in order to keep the specter of U.S. involvement hanging over the fight, to sustain the fear that the U.S. might come back in, and to keep people in a constant state of aggravation at the United States for the drone strikes and for interfering with the internal affairs of Iraq and Syria. In short, provoking the U.S. into engaging with the Islamic State group helps the Islamic State group prove that the United States is exactly the interventionist occupier that bin Laden originally claimed it was in the wake of the first Gulf War.

As Obama and his foreign policy team consider expanding the U.S effort, they must consider both how effective it will be and how U.S. policies will feed in to the Islamic State group narrative about what’s happening on the ground. As ugly and evil as they are, beheadings are not the only ugly and evil things happening in the Middle East today; U.S. drone strikes and its attempts to influence events from outside are also widely seen as evil by many in the region. Expanding the U.S. effort risks giving the Islamic State group increased credibility with every U.S.-caused casualty. If expanding the effort moves the U.S. closer to its goals, the risk might be worth it, but to date Obama has not provided any compelling argument that more air strikes or adding a few thousand more military advisers will do much to change the situation on the ground.

For many reasons, both instrumental and political, Obama feels pressure to do all he can reasonably do to deal with the Islamic State group, and beheadings do nothing but amplify that pressure. But the last thing Obama needs to do is allow the Islamic State group’s tactics to drag the U.S. down a path that promises more death and destruction without promising a light at the end of the tunnel.