– Lt. Col. John Schwemmer is here for his sixth Iraq deployment. Maj. James Modlin is on his fourth. Sgt. Maj. Thomas Foos? "It's so many, I would rather not say. Sir." These soldiers are among 300 from the 5-73 Squadron of the 82nd Airborne Division of the U.S. Army, about half of them trainers, the rest support and force protection. Stationed at this old Iraqi military base 20 miles north of Baghdad, they are as close as it gets to American boots on the ground in Iraq.

Back now for the first time since the United States left in 2011, none of them thought they would be here again, let alone return to find the Iraqi army they had once trained in such disrepair.

Schwemmer was stunned at the state in which he found the Iraqi soldiers when he arrived.

"It's pretty incredible," he said. "I was kind of surprised. What training did they have after we left?"

Apparently, not much. The current, woeful state of the Iraqi military raises the question not so much of whether the Americans left too soon, but whether a new round of deployments for training will have any more effect than the last.

Iraq's army looked good on paper when the U.S. left, after one of the biggest training missions carried out under wartime conditions. But after that, senior Iraqi ­officers began buying their own commissions, paying for them out of the supply, food and payroll money of their troops. Corruption ran up and down the ranks; ­desertion was rife.

The army did little more than staff checkpoints. Then, last year, four divisions collapsed overnight in Mosul and elsewhere in northern Iraq under the determined assault of Islamic State in Iraq and the Levant fighters numbering in the hundreds or at most the low thousands, and the extremists' advance came as far as this base.

'They had it, they really did'

An army that once counted 280,000 active-duty personnel, one of the largest in the world, is now believed by some experts to have as few as four to seven fully active divisions — as little as 50,000 troops by some estimates — although the director of media operations for Iraq's Ministry of Defense, Qais al-Rubaiae, said that even by the most conservative estimates, the army now has at least 141,000 soldiers in 15 divisions.

Most of the U.S. soldiers were intimately involved in training Iraqi forces before, too. "When I left in 2009," Modlin said, "they had it, they really did. I don't know what happened after that."

"We used to say that every deployment was different," Modlin said. "But we quickly found out that this time was completely different from any other time. The Iraqis know that this time we're not going to do it for them, and they appreciate that."

The 300 U.S. soldiers here, with a smaller number of U.S. Marines at Al Asad air base in Anbar Province, are the only U.S. soldiers deployed outside Baghdad. But as the military sees it, they do not count as "boots on the ground" because their role is purely to train, advise and assist, as part of a 3,000-person deployment authorized in November by President Obama.

In fact, Master Sgt. Mike Lavigne, a military spokesman (one tour in Iraq, and three in Afghanistan), does not like that term at all.

"We do not have a single boot on the ground," he said. "Really, not one."

Even in a training role, however, this venerable Iraqi military base puts U.S. soldiers very close to what passes for a front line in the conflict with ISIL. From time to time, the extremists lob mortar rounds from their hiding places east of the base, just across the Tigris River.

There is little chance they will hit anything. The base is huge, and their aim is as bad as it was in Al-Qaida's day, when the Americans were last here — and also used it as a major training base. Nonetheless, no one goes around without body armor on.

Last Thursday, the American instructors were leading a live-fire exercise, teaching basic small-unit maneuvering while firing at pop-up targets. Squad-size groups of Iraqi soldiers charged through a scrub-brush field, so realistic fires popped up around them.

'Leave here trained'

"Small-unit maneuvering is pretty standard the world over," Command Sgt. Maj. Michael Ames said.

As basic as the training was, many of the trainees — even those in the army already more than a year — had never experienced it.

In all, 3,600 men from two Iraqi brigades are in the U.S. training program, and 4,600 more have graduated since the program began late last year.

With the Taji training site running at maximum capacity, as it is now, that means the program will reach at most about 30,000 Iraqi soldiers by the end of this year, probably far less. The Marines at Al Asad train smaller numbers of regular soldiers. "They're going to leave here trained," Schwemmer said. "But there's a big difference between trained and seasoned."