ISIS has lost around a quarter of the territory it once held in Iraq and Syria. Important commanders have died in airstrikes; an estimated 20,000 of its fighters have been killed. The group has run out of high-profile hostages to extract ransom for or publicly assassinate for propaganda purposes.

The ISIS brand needed a facelift: Attacks in Paris, Beirut, and against a Russian airliner over the last three weeks — all of which ISIS has claimed credit for — have given them that. At a time when ISIS is facing setbacks on the battlefield, its success in striking targets beyond territory it has seized in Iraq and Syria has given its loyalists something to cheer about.

The terrible success of these attacks, analysts say, puts Western powers in a lose-lose scenario: Beating ISIS in its self-declared caliphate in Iraq and Syria will likely motivate more international terrorism, as the group, clinging to power and relevancy, seeks to strike back abroad.

Worse yet, a complete collapse of its so-called caliphate could free up tens of thousands of ISIS militants — currently busy defending that territory — to focus on terrorism.

This grim scenario was drawn by analysts as Western leaders continue to grapple over how best to respond to the ISIS threat. Until recently, its grisly reach appeared limited to Iraq and Syria, and to parts of North Africa, the Middle East, Afghanistan and Asia where it has elicited oaths of loyalty from previously-established extremist organizations.

But any notion that ISIS’s tactics would be limited to areas where they already hold sway was shattered as the organization took credit for the Oct. 31 bombing of a Russian airliner over Egypt that killed 224; last week’s twin suicide bombing in Beirut they killed 43; and finally, Friday’s attack on Paris that left 129 dead.

The attacks came more than 13 months since U.S.-led bombing against ISIS expanded from Iraq into Syria, an effort that President Barack Obama has defended despite calls for a more aggressive military engagement.

“From the start, our goal has been first to contain, and we have contained them,” Obama said in an interview with ABC News mere hours before the attack on Paris. “They have not gained ground in Iraq. And in Syria it — they’ll come in, they’ll leave. But you don’t see this systemic march by ISIL across the terrain.”

It’s the very success of that containment policy that is motivating the terrorist attacks, says analyst Clint Watts, a fellow at the Philadelphia-based Foreign Policy Research Institute.

“Part of what has sustained ISIS in Syria and Iraq is battlefield success — they pursue battlefield successes and broadcast it on social media,” he said. “They’re no longer having those. And they’re actually losing ground for the first time since they took Mosul in June 2014. So whenever you can’t find the success you need to keep your fan network going, you start to look for other options.”

And it worked, noted analyst J.M. Berger, a fellow at the Brookings Institution and the author of the book, “ISIS: The State of Terror.” ISIS has lost territory near the cities of Kirkuk and Ramadi and the Baiji district in Iraq, and parts of northern Syria. Last Thursday, global media was reporting that ISIS was losing Sinjar province in Iraq, which it held since August 2014. By Saturday, Berger noted, “the big story was ISIS is rampaging out of control all over the world.”

ISIS has always had the capacity to terrorize the heartlands of its enemies, but has not deployed it until recently because they had other means of provocation, Berger said.

“For a while they had hostages they were able to provoke the West with, and they didn’t have to go anywhere to do it,” said Berger.

Now that they no longer have a supply of Western hostages to exploit — only one is known to still be held — they have moved into provocations abroad.

This is hardly a new tactic for extremist organizations: For instance, Somalia’s Al-Shabaab, an Al Qaeda affiliate that controlled large portions of Somalia, including Mogadishu until 2011, has ramped up attacks in neighboring Kenya as it has lost territory in Somalia over the last five years.

“This is classic playbook,” Watts said. “Enrage the enemy, get them coming at this on all planes, and now you can rally the Muslim world against the West. This is exactly what unravels a containment strategy, is you have a terrorist attack, and everyone gets upset, and then they are primed to take action, which is exactly what ISIS wants.”

There is considerable debate about ISIS’s motivations for the international attacks it is now claiming credit for. It may be a desire for revenge against the West. It may be a calculation that the more nations become embroiled in a response to the Syrian civil war, the more difficult it will be for the international community to coordinate a response. It may be a desire to jumpstart an apocalyptical battle with the West that religious texts favored by ISIS have predicted.

Regardless, ISIS has been explicit in stating such attacks help drive people to their cause, as counterterrorism analyst Harleen Gambhir of the Institute of Study of War described in The Washington Post recently. Islamic State publications earlier this year said that terrorist attacks will elicit a harsh anti-Muslim response from Western “crusaders,” which will in turn alienate and radicalize otherwise moderate Muslims, Gambhir wrote.

“The group calculates that a small number of attackers can profoundly shift the way that European society views its 44 million Muslim members, and as a result, the way European Muslims view themselves. Through this provocation, it seeks to set conditions for an apocalyptic war with the West,” said Gambhir.

The U.S. has thus far favored a more moderate response to the attacks. Its containment policy, Watts explained, is designed to wall ISIS into increasingly restricted territory and letting it fail due to its own mismanagement, economic problems, and internal discord, rather than because of the actions of a foreign oppressor.

“ISIS gets a lot of its money by taking the wealth of the places it captures, and we’ve held them back from any major conquests in the last months, so right now they’re squeezing blood from a stone, economically speaking,” said Berger. “That’s not something they can do indefinitely, so if they reach a tipping point, we could see ISIS collapse in a very short amount of time. The problem is we don’t really know how long that will take to happen, and a lot of bad things can happen between now and then.”

But the more “bad things” happen, the less palatable a slow pace of advance against ISIS will seem to Western leaders. Already, France has begun aggressive military actions in response to last week’s attack, calling them an “act of war” by ISIS.

“The question is will the West have the patience to let the containment policy work,” said Watts. “The whole idea of terrorism is to get the targets to overreact — and you see it already here, with the backlash at refugees, people calling for more airstrikes, hitting targets that we’re not really sure what they are, just to show symbolically that we’re doing something.”

But losing patience and using pure military might to decimate ISIS’s hold on its territory might do nothing to stem its international terrorist ambitions, said Berger.

“One issue is they already have a lot of people deployed abroad. And a second issue is if you went in with force and took their territory away from them, you’re freeing up tens of thousands of fighters who are currently involved in policing the Islamic State, securing its borders, running checkpoints — all those guys are free to do terrorism then, if they don’t get killed in the attack,” Berger said.  “In terms of a happy ending any time soon, I find it hard to imagine.”

Regardless of approach — containment or stepped-up military aggression — the West is likely to suffer more attacks, because there are so many potentially dangerous people in Europe now, according to Watts.

“Where (Western leaders) have fallen down is that they’ve let this problem fester for four years,” he said. “They let the borders in Turkey flow, they let their own citizens flow in and out of Turkey, they let them fight with (Al Qaeda affiliate) Al Nusra and ISIS, they’ve let them come back into the country, they haven’t done programs to counter violent extremism at home, they haven’t done other programs to try to rehabilitate their communities — so what’s happened in Paris is completely unsurprising to anybody who’s been watching the foreign fighter flows over the last five years.”