There is a useful math lesson buried near the end of Greg Jaffe and Karen DeYoung’s widely discussed story on an Afghan war game that the Obama administration is using to weigh the costs and risks of competing strategies.

One question being debated is whether more U.S. troops would improve the performance of the Afghan government by providing an important check on corruption and the drug trade, or would they stunt the growth of the Afghan government as U.S. troops and civilians take on more tasks that Afghans might better perform themselves. Another factor is cost. The Pentagon has budgeted about $65 billion to maintain a force of about 68,000 troops, meaning that each additional 1,000 U.S. soldiers in Afghanistan would cost about $1 billion a year.

I haven’t seen this figure before, and it is based upon a back-of-the-envelope calculation that might be undone by economies of scale. It is not obvious, for example, that the first 1,000 troops would cost the same as the last 1,000. Still, it is a reasonable estimate that is apparently being used inside of the Obama administration.

Accepting the number as basically accurate, the question then turns to “Is it worth it?” That can only be answered by weighing the opportunity costs.

If the Obama administration goes along with Gen. Stanley McChrystal’s request for more troops, and therefore chooses to spend additional money on this mission, the administration is saying, in effect, that an expanded troop presence will do more to prevent a repeat of 9/11 than if the money had been spent on countless other missions and programs ostensibly directed to the same purpose.

Count me a skeptic. There is considerable evidence that a large-scale and open-ended troop presence is counterproductive to fighting terrorism. Meanwhile, there have been a number of highly effective counterterrorism programs that cost far, far less than even $1 billion a year. The proponents of a huge troop increase in Afghanistan obviously disagree, and thus implicitly claim that $40 billion is money well spent (for reference, the entire Dept. of Homeland Security budget for FY 2010 will total $42.8 billion).

Let the advocates for a larger troop presence attempt to make that case. At least now we have a tangible measure for weighing competing options. Thanks to Jaffe and DeYoung for shedding some light on a previously under-reported statistic.