That should not necessarily mean an expansive American military presence, Mr. Inbar added. Indeed, there is little appetite in the region for a return to the more interventionist policies of President George W. Bush. But if Mr. Bush was judged to be too assertive, many here consider Mr. Obama too restrained, and hope to see some middle ground.

To be sure, America’s approach to the Middle East has rarely followed a consistent set of goals or course of action, as Patrick Tyler wrote in his book “A World of Trouble,” a history of 10 presidents and the region. Each president managed the Middle East from different perspectives. Richard M. Nixon saw it as part of his chess match with Moscow. Jimmy Carter and Bill Clinton pursued diplomatic breakthroughs between Israel and its enemies. Mr. Bush and his father focused on Saddam Hussein’s Iraq.

Mr. Obama certainly inherited a messy situation in the region with the war in Iraq. But by the time he took office, Mr. Bush’s troop surge and Gen. David H. Petraeus’s strategy change had helped turn the war around to the point that Mr. Bush felt free to negotiate a three-year withdrawal plan with Baghdad that Mr. Obama then followed.

The next president will not find such a clear-cut playbook waiting. Like Mr. Bush before him, Mr. Obama is on track in his final months in office to leave his successor an improved military situation on the ground as American-backed Iraqi, Kurdish and Syrian rebel forces retake territory from the Islamic State.

But even if the terrorist group is battered on the battlefield, the Middle East remains torn by so many other conflicts that it requires a scorecard to keep track. The Arab Spring revolutions of 2011 failed to deliver democracy except perhaps in Tunisia; instead they upended the traditional structures and touched off a civil war in Syria that has killed or wounded hundreds of thousands of people, displaced millions and continues to consume much of the region.

Mr. Obama has defended his resistance to being dragged deeper into the Syrian war beyond the limited engagements against the Islamic State, arguing that it would only enmesh America in yet another bloody quagmire. But even if the next president imposes a no-fly zone, as Hillary Clinton has promised, or aligns more closely with Russia, as Donald J. Trump has suggested, the political crosscurrents will remain treacherous.