In the first major action between the Germans and Americans, at the battle of Kasserine Pass http://en.wikipedia.org/wiki/Battle_of_the_Kasserine_Pass, the Germans inflicted casualties against (mostly) the inexperienced Americans at the rate of about 5 to 1. Fortunately, the Americans were able to improve substantially on this ratio in the days and weeks ahead.
The early American experience was by no means atypical; the Poles suffered physical casualties of between 3 and 4 to 1 in 1939, with this rising to about 15 to 1 counting prisoners. http://en.wikipedia.org/wiki/Invasion_of_Poland_(1939) Allied to German casualty rates in France 1940 were similarly lopsided.
In the first few months of the 1941 campaign, the Soviets suffered casualties at six or seven times the German rate.
With the notable exception of Kasserine Pass, where American artillery held the day, the massive German kill ratios (in Poland in 1939, in France in 1940, and in the Soviet Union in 1941, the massive German kill ratios were accompanied by massive territorial gains.
This ratio fell steadily in 1942, with the Soviet to German casualty ratio of roughly 2 to 1, in line with their respectively populations, at the "turning point" campaign of Stalingrad. Diminishing kill ratios accompanied "diminishing returns" for the Germans in 1942.
In a war between 80 million (ethnic) Germans on one side, 130 million Americans, 170 million Soviets, and 50 million Britishers on the other, the Germans would have won if they could inflict casualties at the rate of 5 to 1 (or "better") on the Allies throughout the war, the latter' superiority in manpower and material notwithstanding. The Soviets, British, and Americans won because they were able to bring their loss ratios below their overall numerical preponderance.
Have any historical accounts tied Germany's early successes to the their massive early "kill ratios," and their subsequent lack of success to the fact that their "kill ratios" fell below their overall numerical disadvantage?