The Battle of Kursk consisted of two phases: Operation Citadel (the German attack) and the Soviet counteroffensive after the attack had failed. Amazingly, the Germans achieved a 3:1 exchange ratio during Operation Citadel (when attacking prepared Soviet defenses), and 4:1 exchange ratio for the battle as a whole. However, the Soviet Union had much deeper manpower reserves than Germany. With the British and Americans invading Italy, and preparing to invade France, an exchange ratio like that probably brought the Allied victory closer.
The Soviet force at Kursk consisted of 1.9 million men, compared to 800,000 men for Germany. Germany had seriously depleted other parts of its eastern front to achieve its force concentration at Kursk. The Soviets had concentrated their forces as well–they had been warned by German traitors to expect an attack–but they had not needed to deplete other areas of their front to the same extent Germany had. The Soviets used their months of preparation time to make the Kursk salient one of the most heavily defended areas in human history.
In a best-case scenario for Germany, the Kursk salient would have been completely encircled and destroyed. To create this best-case scenario, four things would have been necessary. 1) The Germans would have needed to identify and destroy the traitors responsible for handing over valuable information to the communists before the decision to attack Kursk had been made. 2) The Germans would have needed to attack quickly, before the Soviets’ defensive preparations had been complete. 3) The Germans would have needed to keep attacking, even if the U.S. launched an offensive in Italy. 4) The Germans needed a lot of luck.
In the actual attack, Germany experienced 54,000 casualties. Suppose, for the sake of argument, that Germany had been able to encircle and destroy the Kursk salient at the cost of 150,000 Germans. Roughly 2,000,000 million Soviets for 150,000 Germans would have been a 13:1 exchange ratio: far better than the 3:1 - 4:1 ratio it actually experienced. A 13:1 ratio is probably the absolute best Germany could have hoped for on the Soviet front, and truly represents a “best case” scenario. (There were other times when Germany had achieved a 13:1 ratio on its eastern front. But those were times when von Mannstein had been in charge. At Kursk, both Mannstein and Guderian were overruled; and Hitler sided with the majority of German generals.)
Had Germany achieved that 13:1 exchange ratio at Kursk, it might well have been able to win some follow-up victories as well. But the Soviets would have continued to add 500,000 men a month to their army during 1943 and into ‘44. The Germans could not possibly hope to come anywhere close to the Soviets’ recruitment rate! There were limits even to the Soviets’ manpower reserves, but they could afford to lose several 2 million man forces before reaching those limits. The best a German victory at Kursk could have achieved would have been moderate-scale follow-up victories in '43, followed by a relatively stable German-Soviet front in '44.
However, the German force in Italy was greatly outnumbered by its Anglo-American counterpart. While the Germans were skillful in using terrain and superior generalship to slow the Allied advance with relatively few men, the Germans were slowly losing ground. The German military’s strategy in Italy was to buy time. But time to do what?
The D-Day invasion was launched in '44, about a year after Kursk. The Allies won at D-Day for a variety of reasons, including their air supremacy, the truly massive bombardment efforts of their battleships, the sheer scale of their invasion effort, and the fact they’d deceived the Germans into thinking the invasion would hit Calais, and the fact that so much German military strength was tied down on its eastern front. A victory at Kursk could (potentially!) have allowed Germany to mitigate that last factor. However, sending some additional strength west would not have been overly helpful, unless that strength had been coupled with the realization that Normandy needed to be defended as effectively as Calais. Also, that strength would have been shipped away from the Soviet front, at a time when the Soviets would have recovered from their (hypothetical) defeat at Kursk; and would have been at least as strong on that front as their German counterparts.
The Anglo-American army was strong enough that, if it was not stopped on the beaches of Normandy, it would quickly overwhelm all of France. It’s a stretch to imagine that the Germans might have achieved a 13:1 exchange ratio at Kursk. It’s also a big stretch to imagine that this Kursk victory might have translated into a victory at Normandy. But had both those things happened, Germany would have received the gift of time–on both its eastern and western fronts. Only on its southern front–in Italy–would there have been significant Allied progress. Possession of most of Italy was non-critical to Germany’s war effort.
Had Germany achieved stability on its eastern and western fronts in '43 and '44, it could have used the resulting reprieve to do two things: 1) increase its industrial capacity, and 2) increase its technology. Between '42 and '44, Germany tripled its military output. That alone would not have been enough to win Germany the war: in '44, Soviet military output was roughly equal to Germany’s, while the U.S.'s was double that of Germany. But if Germany could combine that increased military output with significantly more advanced weapons than those the Allies were using, the effect would have been much stronger. The wonder weapons Germany needed–and was in the process of deploying–including the jet, the Wasserfall, the air-to-air and air-to-surface missile, the smart bomb, the assault rifle, the long ranged Panzerfaust anti-tank weapon, the E-Series tanks, and the Type XXI U-boats. Had Germany been able to achieve wide scale deployment of all of these weapons by the end of 1945, 1946 could have been a very good year for Germany. (1945 would have seen wide scale deployment of some of these weapons, thereby buying Germany an extra year.) It would have been critical to deploy large numbers of jets, Wasserfall, and air-to-air missiles in 1945, so as to prevent the United States from dropping an atomic bomb on Berlin. (Which it otherwise would have done.)
To make a long story short: even if the Germans had won at Kursk, a number of other things would have had to go right for Germany to have had a chance.
