When the media covered the Petraeus-Crocker hearings, they missed one really big story: With about 160,000 combat troops, Gen. Petraeus managed to stem the rising tide of violence in Iraq. That is a statistic worth noting because, according to the "experts," it couldn't be done.

Long before and after the invasion, the experts, including an authoritative study by RAND, an official government think tank, flatly concluded that U.S. troubles in Iraq could be traced to a lack of "boots" on the ground. The conventional wisdom was that an occupation without at least 300,000 troops was a forlorn hope. The country couldn't be pacified by anything less.

RAND even produced equations, charts and statistics to make their case. Anyone who swore that many hundreds of thousands of troops had to be used to subdue Iraq was declared a prophet. This particular criticism of American policy has been repeated so often that many accept it as a historical fact. Yet the testimony delivered to Congress reminds that Petraeus tackled the problem with about half the "magic" number needed for victory and produced real results, under conditions far worse than those U.S. forces encountered after toppling Saddam.

That requires some explaining.

The weekend before the historic hearings on the Hill, I was at my 30-year reunion with the West Point class of 1977, back among the fortress-like academic buildings where ramrod professors in crisp green uniforms lorded over impressionable young cadets, dispensing wisdom on the ways of war. One military maxim often imparted was "that God was on the side with the biggest battalions," a reminder that quantity has a quality all its own. Perhaps it was that kind of thinking that inspired the boots-on-the-ground crowd in their unshakable belief that flooding Iraq with troops was not only the answer -- but the only answer.

But while military Ps (professors) acknowledged that it is always nice to have more forces than the enemy, they also taught cadets that there was no rulebook or fixed set of guidelines that guaranteed victory. They would have dismissed the notion that mathematical formulas could spit out what was required to win.

West Point officers had another saying, quoting Napoleon: "The mental to the physical is as three is to one," a reminder that there is more to winning wars than wielding big numbers. Napoleon, of course, loved big armies, but he also on many occasions fought -- and won -- while outnumbered.

Numbers alone don't tell the whole story. What often matters just as much, if not more, is how troops are trained, equipped, led and employed. The genius for war, the ability to fight smart, is an incalculable combat edge.

It's worth conjecturing how events in Iraq might have turned out:

• If the coalition powers had entered the post-conflict phase with forces organized, equipped, trained and properly led to conduct occupation duties.
  
• If there had been true unity of effort between the combat forces and civilian agencies working at post-war reconstruction and reconciliation.
  
• If all the military and non-military assets being employed in the fight shared common doctrine and executed a common campaign plan.

In short, it's interesting to muse what might have been -- if America had a military in 2003 capable of doing the things that the Army in Iraq can do in 2007, with skills learned in on-the-job training and honed by leaders in the field.

America's troubles in Iraq began not because it didn't have the numbers, but because America began the occupation lacking the mix of civilian and military capabilities, political and combat leaders on the ground, and integrated planning and execution necessary to fight and win a peace against determined, resourceful adversaries.

The irony today is that, counting the Iraqi (though many Iraqi units are still not ready to stand on their own) and coalition forces together, the military available is approaching the magic 300,000 supposedly required to pacify the nation.

It would be a tragedy, having finally taken steps toward dealing with spiraling violence in Iraq, if America abandoned the opportunity to help build a country that can govern and defend itself. It would be equally tragic to forget ever again that winning the peace is part of winning the war, and the United States must build and sustain the capacity to do both well -- or risk relearning the bitter lesson of Iraq on some future battlefield.

James Jay Carafano is Assistant Director in the Kathryn and Shelby Cullom Davis Institute for International Studies and Senior Research Fellow in the Douglas and Sarah Allison Center for Foreign Policy Studies.