The New York Times has been running OpCharts for the last few years marking the changes in critical metrics regarding the war in Iraq. For the last several there has been a decided pattern emerging from the numbers that indicate that the biggest changes have NOT involved changes in strength of US troops.
The data shows that the combined strength of US and Coalition troops was:
November 2004 = 162K
November 2006 = 158K
November 2008 = 154K
There does not appear to be much of a change in deployment, despite spikes that temporarily had US troops at 180K. Unless the argument is that the added US troops are significantly better than the British and Polish and Rest of the World troops that have been withdrawn there must be another reason for the reduction in violence.
Irag Security Forces
November 2004 = 114K
November 2006 = 323K
November 2008 = 559K
So we have been adding military age Iraqis to the government payroll steadily for several years now. Even if they are not particularly effective combat troops they represent huge numbers of Iraqis at an age where they would be potentially causing other problems for the government and US Forces. But it doesn't stop there as the Times also gives us numbers for the "Sons of Iraq", the Sunni based militias of which approximately 50,000 of the 100,000 strong force are also on the government payroll. So while the US and Coalition forces have remained relatively stable over the past four years, the number of Iraqis carrying guns has skyrocketed to well over 600,000.
There are many other reasons why the level of violence in Iraq has been reduced. Clearly the continuing cease fire between the government and the Mahdi Army of Sadr has made large difference. There could be a drain off of Qaeda resources to Afghanistan. All the killing could have exhausted the elements fighting the US and Iraqi government forces. But the salient fact is the run-up of the number of people being paid by the Iraqi government to keep the "peace". Only a continuation of the type of arrogance that led to 4000 + American deaths would focus the credit of the reduction in Iraq violence on the continuing presence of US troops. This conclusion is important as our new government plans for the (hopefully) quick withdrawal of US troops in 2009.