As I understood, most of the southern army headed south to go thru Turkey etc to get to the Suez cannal, go west, and then squish the allied armies in the North Africa, while Rommel attacked from the west to east. Hence putting a allies under a two front war in north africa.
By the time of Stalingrad, USA made, USA paid machines, guns, food, supplies AND EVEN STALIN'S LUNCH, was arriving in Stalingrad and againt all of Germany's fronts. At the same time, Germany armies were as far away from Berlin as ever so German's supplies were at an all time low. Fighting on three fronts, west in air vs USAF b17s and b24s (let alone the garrison army to protect from any d-day attempts, like the battle of Dieppe), south in africa then in Italy, and in the east vs Russia. To get to the point, all the Reich was surprised by the seemingly endless supplied opponents.
The other point is, that for the larger(?) portion of the Germany army that had gone south to squish with Rommel, now needed time to retreat or be cut off. By the time it came back, Paulus in Stalingrad was totally surrounded due to other axis armies being overran. Paulus had to stand or die to save the other retreating portion or there would have been no southern front at all.
It was USA supplies, their overwhelming impact, that won the battle of Stalingrad, and the fact that Hitler and his command didn't realize just how much was arriving on the opposing fronts. In a way, Paulus succeeded by 'saving' the southern portion enuf time to retreat.
One of the following battles of retreating German armies was in the crimea peninsula can be seen in the movie 'Cross of Iron' was pretty good, german side, entertaining. Sam Peckinpaw and James Coburn.
"I have a feeling that this whole thing is begining to slide" ~ Peckinpaw
"Here's to the cake!" ~ a german soldier
"Here's to the great German Wehrmact, even when its going down in defeat!" ~ another German soldier.
A good book on the subject; "the black march" by Peter Neuman, an SS soldier that was part of the army trying to save stalingrad, made it to the axis side of the front of stalingrad, but defeated. Read this for their state of mind and some horror stories.