As Overton worked earlier this year on his own exercise in accounting, I asked Nic Marsh, a researcher at the Peace Research Institute Oslo, to take a crack at the same tally, but using other sources he tracks, most notably export data from the European Union and American military inspector-general reports. Marsh’s back-of-the-envelope total for the two wars also exceeded the Pentagon’s by a large margin. By examining declared arms transfers from Europe, he found official reported totals of more than 465,000 firearms provided by the Pentagon to Afghanistan since 2001. Marsh said the exports included weapons from Albania, Britain, Bulgaria, Canada, Croatia, Czech Republic, Germany, Hungary, Italy, Montenegro, Pakistan, Poland, Romania, Russia, Serbia, Slovakia, Slovenia and the United States. He also found at least another 628,000 firearms exported to Iraq from 2003 to 2014, from a similar list of nations, plus Bosnia, Estonia, France, Latvia and Turkey. His Iraq count does not include almost 300,000 more firearms that he suspects were moved there for the Pentagon but for which the records are not quite clear. “The number is much larger” than 628,000, he said, “but we are not certain the exact number exported from Bosnia.”

The weapons sent from Europe to Iraq, and the crates of ammunition necessary to keep them fed, filled cargo planes — though Marsh said the available data also does not say how many were directly paid for by the United States, as opposed to those bought by Iraqi ministries with American-donated funds or those donated by countries unloading old stock. This is an important observation, because the latter two categories – state-to-state gifts via American handlers or otherwise and firearms purchased directly by Afghanistan or Iraq — might not be in Overton’s final count. This is one of many reasons to suspect that the 1.45 million tally might understate the real quantity of weapons disbursements during a long run of years when the Pentagon played the role in Afghanistan and Iraq of small-arms provider. “It could be twice as much, as far as we know,” Overton said last Friday, not entirely in jest.

Overton’s analysis also does not account for many weapons issued by the American military to local forces by other means, including the reissue of captured weapons, which was a common and largely undocumented practice.

Adding to the suspicion that the number is even larger, Overton is certain that his tally missed shipments, because the data that the Defense Department made available was incomplete or laden with contradictions that were not readily reconciled. For example, the contracts it released were for more than $6.5 million or $7 million, depending on the year. Overton suspects that this hides many smaller purchases. And the contract data often labeled purchases vaguely, sometimes making it difficult to determine exactly what was bought, much less for whom. The Pentagon’s data, in short, did not declare much of what the Pentagon actually bought.

One point is inarguable: Many of these weapons did not remain long in government possession after arriving in their respective countries. In one of many examples, a 2007 Government Accountability Office report found that 110,000 Kalashnikov assault rifles and 80,000 pistols bought by the United States for Iraq’s security forces could not be accounted for — more than one firearm for every member of the entire American military force in Iraq at any time during the war. Those documented lapses of accountability were before entire Iraqi divisions simply vanished from the battlefield, as four of them did after the Islamic State seized Mosul and Tikrit in 2014, according to a 2015 Army budget request to buy more firearms for the Iraqi forces to replace what was lost.

These spectacular losses were on top of the more gradual drain that many veterans of the wars watched firsthand — including such scams as Afghan National Army recruits showing up for training and disappearing after rifles were issued. They were leaving, soldiers suspected, to sell their weapons. On the outposts where American troops and Afghan and Iraqi units worked together, the local units were often a fraction of their reported strength and dwindled as ever more national police officers or soldiers disappeared or deserted, vanishing with their firearms. The American arming of Syrian rebels, by both the Central Intelligence Agency and the Defense Department, has also been troubled by questions of accountability and outright theft in a war where the battlefield is thick with jihadists aligned with Al Qaeda or fighting under the banner of the Islamic State.

By this year, various internet arms traders, including many on Facebook, were hawking a seemingly unending assortment of weapons of obvious American origin, including the M4 offered by Hussein Mahyawi, whose Facebook profile spoke of his background in interior design. In April, after being approached by The New York Times and reviewing data from Armament Research Services, a private arms-investigation consultancy, Facebook closed many pages in the Middle East that were serving as busy arms bazaars, including pages in Syria and Iraq on which firearms with Pentagon origins accounted for a large fraction of the visible trade. Hussein Mahyawi’s profiled vanished. But many new arms-trading Facebook pages have since cropped up, including, according to their own descriptions, virtual markets operating from Baghdad and Karbala. The trade goes on.