Inspired by Kraut's shooting range post, and having a ton of free time during the lockdown, I ran my own test of tank gun accuracy.
Panther A as the shooter, Regular crew, +2 commander. Sherman M4A1 target, stationary, almost but not quite exactly facing directly towards the Panther. 625 meters. Sherman buttoned and immobile since I just wanted it to serve as the target, not shoot it out with the Panther. Panther hatch open to improve spotting. I ran the test 100 times.
This test was to determine how many shots it took the Panther to get a turret or hull hit. I counted wheel hits and "weapon" hits where the round hit the target's external machine gun mount as misses. There were only 3 or 4 of those in 100 tests.
Results were interesting. At 625 meters, against a stationary target, I would have thought the Panther's gun would put somewhere around 75 % of first-round shots on target, but not so.
First round hit: 57 %
Second round hit: 35 %
Third round hit: 7%
Fourth round hit: 1%
Even more interesting was the enormous variety of times required for the Panther to spot the Sherman. Honestly, I wish I had recorded the spotting times because it would be equally useful info. In some tests the Sherman was spotted and correctly identified in 2 seconds; in most cases I would guess between 8 and 20 seconds. In a handful of cases the Panther didn't spot the Sherman during the entire 60 seconds, despite the Sherman firing as many as 5 rounds and scoring hits on the Panther. In the most extreme case it took 1:38 for the generic "Tank?" icon to appear, 1:45 to identify it as a Sherman, and 2:05 to get a round on target.
And in one test, the Sherman got the notorious gun mantle deflection hit down into the Panther's crew compartment and wounded the Panther's driver.