Al-Baghdadi has been No. 1 on a U.S. kill list of about two dozen senior ISIL leaders drawn up after the group's stunning conquests in Iraq and Syria last year. He thus joined a long line of terrorist leaders in that spot, going back to Osama bin Laden.

In 2001, then-President George W. Bush said the al-Qaeda leader was wanted "dead or alive," and the hunt has been on for leading terrorists ever since. There have been many successes: Abu Musab al-Zarqawi, the fearsome commander of al-Qaeda in Iraq; his successor Abu Ayyub al-Masri; Bin Laden himself, of course; along with many of the "core al-Qaeda" hiding out in Pakistan. Secretary of State John Kerry announced in January that we have "eliminated" 50% of ISIL's "top command."

With a success rate like that, we should pretty much have won the war on terror by now.

Except that in many ways, things have gotten worse. For example, since the ISIL leader was put out of action, reportedly with severe spinal injuries, back in March, his group has conquered or assaulted large swathes of western Syria, the Iraqi city of Ramadi and Iraq's major oil refinery at Baiji. It has also gained fresh adherents in Yemen, Libya and even Texas. In the same way, al-Qaeda in Iraq, ISIL's forerunner that fought U.S. forces, reached its greatest effectiveness after Zarqawi was killed.

How could this be? How could the loss of capable and charismatic leaders not degrade their group? The answer may lie in a little-known study carried out in Iraq in 2007 by a small semisecret unit, the Combat Operations Intelligence Center. Targeting "high value individuals" was the principal U.S. strategy in Iraq, and the COIC analysts were interested to see whether it worked. They took the list of 200 "IED cell leaders" eliminated between June and October 2007 and looked at the results.

They were dramatic, in the worst way. Removing the leaders did not lead to a decline of violence in the area where they had operated. Instead, attacks on U.S. and coalition forces went up, sharply. After three days, they were up by an average of 40%. Five days later, they were still running 20% above "normal" (defined as the average for the pre-strike 30 days). After 10 days, they had fallen back to the pre-strike level, and the situation was as bad as before.

The reason for this unexpected result, so the analysts concluded, was that the dead leader was almost always replaced immediately. The new man would be eager to "show his bones," by making a big impression as well as to avenge his predecessor (often a relative) as well as learning from the mistakes that had gotten him killed.

In fact, this startling result should not have come as too much of a surprise. In the 1990s, the Drug Enforcement Administration had adopted the "kingpin strategy" — targeting the kingpins heading up the infamous Colombian cocaine cartels. On paper, and in the headlines, it was a great success. Pablo Escobar, leader of the infamous Medellin cartel, was hunted down and killed in December 1993. Twenty months later, the chiefs of the equally powerful Cali cartel were captured and jailed. Other triumphs followed, all of which should have at least put a crimp on the drug trade.

It had the opposite effect. Cocaine supplies to the U.S. actually increased, as evidenced by lower prices — thanks to the kingpin strategy. Removal of the cartel leaders had opened the way for new competitors, who pushed for market share and competed with increased supplies and lower prices.

Back in Iraq in 2007, the intelligence analysts briefed their findings to the high command with the concluding comment, "Our principal strategy … is counterproductive and needs to be re-evaluated."

Maybe it's time we took those words to heart.

Andrew Cockburn is the author of the newly published Kill Chain: The Rise of the High Tech Assassins. He is the Washington editor of Harper's Magazine.