"If you can be seen, you can be hit. If you can be hit, you can be killed."
That was the mantra repeatedly drilled into our heads when I was a young Second Lieutenant of Infantry.
Those are the 4 steps of John Boyd's decision making process. In combat you have to Observe what is going on, Orient yourself based on what you see of your enemies' acts in terms of what you understand of his doctrine, and make an attempt to understand what he is trying to do. Then you Decide what you do to counter, and you Act. If you can go through the 4 steps faster than your enemy, you have a big advantage. If your enemy goes through the 4 steps slower, then his fires are inaccurate, his maneuver is uncoordinated. Your advantage increases with each time you cycle through the OODA loop. Eventually your enemy will lose his will to resist, and attempt to escape.
The Sherman tank had superior ability to Observe. The Sherman gunner had a gunner's periscope that gave him better ability to pick up a target, rather than the very small optics of German tanks. The US tanks also were faster to act, having the ability to train their tank cannon while moving over fairly rough ground. The M-4 main gun stabilizer was, over fairly rough ground while moving at 15 miles per hour, had about a 70% probability of hit from 300 to 1200 meters. That meant they could hit repeatedly with the coax machine gun, and had a good chance of hitting with the main gun. The turret traverse was fast, 15 seconds to traverse 360 degrees, and for a 30 degree traverse, about a second and a half. In short, the unit equipped with Shermans in a mobile battle could be the first to see, the first to hit, and its advantages would continue the longer a battle lasted.
By contrast, A Panther had to identify the target, command the vehicle to come to a halt. The driver would have to shift to neutral, and then race the engine to permit the Panther's hydraulic traverse to use high rate. The Panther gunner had to pick up the directed target through the sight, and then make small corrections with hand wheels. The Panther had a very good gun (so good it was copied by the French and mounted by the Israelis to the Sherman after the war). and began many battles from an ambush position. There was a high price paid by US tankers when they were ambushed by Panthers. But as the battle continued, the US advantages increased as the battle continued. German fire became less effective. German maneuver became increasingly disjointed from the units mission.From ambush position, it was often difficult to see the Panther, as they used low flash powder.
The Sherman had lighter frontal armor, and its crews tried to engage M-4 front to Panther flank. LtC Abrams of the 4th Armored division was sent to the 12th Armored division to coach them in how to use the Sherman to win. M-4 has a weaker gun, thinner armor, but greater reliability, narrower width, and shorter height than Panther. Its fast traverse and ability to train the gun while moving gave the M-4 crews a great advantage when attacking from flanks. So get to the enemy flanks, sneak up on them. Play cowboys and Indians. Use covered and concealed routes.
And so, when US tankers took his coaching to heart, they were able to win. Not without losses, and not without risk. but in battle after battle the US was able to take ground defended by Panther, and because of the proliferation of M-4s (14 armored divisions plus separate tank battalions that made up the equivalent of another 25 armored divisions) take ground where there were no Panthers.
German armored units were only 5% of German combat units. The M-4 with its 75mm gun had a great HE round with good effectiveness against those 95% of German combat units. Against the 5% of German armor units, the US was able to concentrate more units. That itself was a great advantage.
The Lanchester equations are differential equations which describe combat effectiveness based on relative strengths. The relative strengths provide an advantage to the larger force, how much advantage is expressed as an exponent in the equations. When armed with spears, the exponent is 1. (A 5 to 1 numerical advantage gives to a 5 to 1 combat advantage). when armed with repeating weapons, the exponent is 2 (a 5 to 1 advantage in numbers gives a 25 to 1 advantage in combat power). The ability of the M-4 to conduct long road marches and still be able to fight at the end was of great advantage.
A German officer, captured by the 2nd Armored Division asked "how many 2nd Armored Divisions do you have?" His intelligence appreciation put the 2nd Armored Division 70 miles north of the Ardennes. It was not possible for an armored unit to break contact, drive 70 miles in winter, and fight at the end of such a road march. Well it wasn't possible for the German armored divisions. That is exactly what the 2nd Armored division had done. Nor was that rare. The 10th Armored Division at Bastogne, and the the 7th Armored Division at St. Vith had made similar road marches.
What happened during the Ardennes Offensive? The German main effort was to be made by the 6th Pz Army. They were to lead with an artillery barrage, and exploit with an infantry infiltration. Then the Armored striking force was to dash through the holes thus created. The artillery barrage was of little effect. The infantry infiltration did not succeed. The armored units were able to punch through a weak point, but had little backup. without the infantry followup, without the German artillery able to move forward, and above all without German air cover, the US engineers were able to blow bridge after bridge in front and on the flanks of the German attack. US truck companies were able to move fuel depots away from the identified attacks.
The main battlegroup of the 1st SS Panzer Division was Kampfgroup Peiper. He got the job because as a battalion commander he had taken two Russian towns, and murdered all the inhabitants prior to burning the towns. His mission was the bridges over the Meuse. He never came close. He lead his 5,800 men against the US, and only 770 were able to walk back without their vehicles. Over 500 were captured and interrogated as POWs on his actions, and their testimony was instrumental in his war crime trial. Peiper's unit murdered over 350 Belgian civilians, and about 135 US soldiers.
Further south, the 5th Panzer Army was also able to penetrate, and captured two regiments of the sadly green 106th Infantry Division. The 5th Pz Army was unable to accomplish their mission and that of the 6th Pz Army too. Their losses were too heavy, their progress too slow. The 2nd US Armored division was able to move from the north, the 4th Armored division from the south.
And so the Ardennes battles were decisive. Germany lost 6 months of their increasingly anemic armor production. They would never attack again.