While I have no sources on how that number was arrived at (quite likely by testing the effects at the artillery firing range), I tend to think the value reflected the number of shells needed to be fired in order to either kill the crews or destroy the weapon itself.
For a Soviet commander who was tasked to break the enemy lines, it didn't matter if the AT gun or machine gun wasn't firing at his tanks or soldiers because it was destroyed or because the crew was killed.
If a tank is not blown up by mines or stopped by an antitank obstacle (ditch, dragon teeth) then the only other way with high probability of success is to stop it with AT weapons. If we exclude the Soviet tanks, then at Kursk that would have meant AT guns (attacks with Molotov cocktails and satchel charges looked good in the movies but couldn't do much in real combat).
An AT gun could fire on average 3 times before it was spotted by the attacking tanks. Once spotted, the Soviets were estimating it could fire another 3 to 5 times before being taken out (either by destroying the weapon or by killing the crew). So while there are instances when a single AT gun crew managed to kill or incapacitate a lot of tanks, the typical figure was one or two tanks killed per AT gun.
That in turn means that any section of trenches defended by a single AT gun could be overrun if a tank platoon (4 or 5 tanks) attacks it. The surviving tanks would then clear the machine gun nests and kill, suppress or bury alive the remaining infantry with their tracks, thus clearing the way for its own attacking infantry.
The same attacking tank platoon would have a near impossible task if the same sector of trenches is defended by one AT gun and as little as 2 tanks.
Material damage is about an order of magnitude harder to achieve than lethal.
The fact is infantry units were designed for defending, and were better at it than tanks. A force of WWII infantry is going to be better at defending than a comparable WWII armoured force.
By mentioning the D-day you have offered a very good example of why indirect fire alone was not enough and why breaching fortified positions was much easier/less costly if some high caliber direct fire could be employed against the defenders (by the way that is exactly why tanks were landed on D-day, before the beaches were secured).
Infantry can defend successfully against the tanks only in very special settings like in urban areas. In most of the cases, however, tanks can punch through trenches, even against infantry equipped with modern AT weapons (one example is the Ethiopia-Eritrea war).
The tanks at Kursk weren't defending. They were waiting to see where the breakthrough came, and rushed to counterattack. Ideally they could already be at that location and be infantry, but then the Germans would just attack elsewhere.
Infantry divisions were optimized for static defence. Armoured divisions were optimized for rapid assault.
Whatever examples you come across from different wars, you can pick a single battle, like Nijmegen or literally any random eastern front battle, and there will be loads of examples of tanks attacking being repelled, or succeeding. Usually the main factor is relative numbers of defenders and attackers. With infantry you can maximize that number and minimize their vulnerable.
Tanks aren't at all well armoured or heavy. Infantry are. Infantry are ridiculously hard to kill and have extremely deadly weapons compared to tanks, even today. A platoon of tanks was more vulnerable to artillery fire in WWII than a platoon of infantry. In German IX Corps in Italy in 1944 the single biggest killer of tanks was Allied artillery. In WWII the infantry's job was to defend because they did it better than any other kind of unit. In an armoured division against an infantry division, the armoured division isn't going to break through alone most of the time.
An anti-tank gun is also a small target, much smaller than a tank. That's why they were used.
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Infantry is as versatile as the humans are, and its limitations are due to the limitations of our biology (and technology). To compensate for the natural limitations, infantry is provided with equipment which enhances a human being's ability to defend and attack. This does not mean infantry is optimized for one role or another. Due to infantry's most potent weapon (the brain), every army throughout the history tried to maximize the effect a human moving on two legs can have on a battlefield.
It so happens that from the end of WW1 til today, thanks to the development of tanks, tanks are a better assault force than infantry.
However, just like we have seen repeatedly in the past, technology is in the process of helping infantry to bridge the gap. While it is quite difficult to make infantry able to withstand the hit of a tank round, it becomes easier for infantry to destroy tanks. The process is similar to the Middle Ages answer to fully armored knights. The infantryman didn't become more resistant to the charge. He simply improved his ability to kill knights (by using pikes, crossbows, longbows, arquebuses).
The tanks themselves were developed as a means to make possible direct fire on the largest infantry killers: machine gun nests and artillery. The solution was to make them "invulnerable" to bullets and projectiles.
It was then realized that tanks can be used for something more than just opening the way for the infantry. Once the tanks have breached the defense in even a narrow sector, they can wreak havoc on the enemy supply depots, command posts, artillery batteries, etc. That results in depriving of support and coordination the rest of the enemy soldiers, even though their trenches might be still intact.
But in order for the tank to be able to do that type of strategic damage, it first needs to be able to break through the infantry defenses. Therefore the tank never strays far from its primary role: that of a path-opener.
Doing damage behind the enemy line can be achieved even with WW1 cavalry or modern humvees. But first the defense needs to be breached by some type of unit less vulnerable to enemy fire. That role is the role of the tanks since the end of WW1.
Before the tank was introduced, that role was assigned to the stormtrooper infantry. We could call them "infantry optimized for attacking trenches" but the "optimization" consisted mainly in new tactics and some weapons highly effective at close range. Which once more supports the point that infantry is highly versatile and can be "optimized" for whatever role it is needed.
Countering the tanks could be done by using mines, tank obstacles (those were simply slowing down the tanks, exposing them for a longer time to artillery fire), infantry AT weapons (magnetic mines, satchel charges, AT rifles, bazookas, etc), AT guns, general-purpose artillery or other tanks. Out of all those means, tanks (or the junior variant - tank destroyers) are the most versatile tool in a commander's toolkit.
Yes, WW2 statistics show that from the end of 1943 onward the general-purpose artillery became the most effective weapon against the German tanks. But that happened only because several factors contributed to it:
1) The United Nations' artillery outnumbered and "outcalibered" the Axis' one;
2) The United Nations' air force dominated the skies, allowing the coordination of the fire of their already numerous and powerful artillery.
Before that, tanks or tank destroyers were a much better tool for destroying the tanks because they were armored better than the AT guns and because they could move (so they were both moving targets and could be shifted from one sector to another, according to how the situation developed).
Remember the previous post, about a tank platoon concentrated on a sector defended by a single AT gun?
Tanks need to attack in "packs", because some of them will be knocked off by the defender. So before attacking, they need to come together somewhere out of the sight of the defender. Then they have to rely on speed to reach their target before the high caliber artillery can destroy them with indirect fire.
If the skies belong to the enemy and if there are enough high caliber guns, then the tanks can either be destroyed while concentrating or they can be destroyed when moving in close order towards their target.
If the enemy cannot see the tanks formations from the air, artillery barrages are much less effective.
At Kursk the Soviets didn't have yet the air superiority so they needed to rely on their own tanks to prevent the Germans from breaching their otherwise highly fortified lines.
I'm fairly sure that Soviet armoured doctrine evolved due to issues of C3, as well as the blitzkrieg aspect, just as the Russians always had a healthy respect for the effect of massed artillery.
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Overall, Hitler's non-retreat order really helped Soviet Deep Operation doctrine, as its breakthrough phase seems only suited for immediate breakthrough of line - in other words, if the actual frontline was far behind then the breakthrough phase would be painfully slow. That be said, elastic defense + fire brigade would be best defense against Deep Operation doctrine.
I'm going to explain what Blatta was talking about, since I think most people completely missed it.
The smallest unit in a military force is always a tent/bunk group. A handful to about a dozen (depending on how big your tents are) who sleep, mess, march, and fight together. We call this a squad or team or crew if its small enough.
A Roman Decuria was called a Contubernium of 10 men. 8 combatants (legionary) and 2 noncombatants (probably a blacksmith and a carpenter), and a pack mule (to carry the tent and crap). That's why a century is "only" 80 men. The tent is the building block of esprit de corps. These are your brothers in arms. They were under the oversight of a squad sergeant called a Decanus.
The next largest unit is the Century, a Platoon of 100 men and equipment, ideally including a dissembled ballista and siege engineers, a handful of officers (the lieutenant is called the Centurion, his platoon sergeant is called the Option and he has a second special sergeant called a tesserarius who oversaw the night watch. There were other supernumeraries like standards and musicians. The century is a tactical building block.
The next largest unit is the Maniple. These did not go away they just stopped being a tactical unit. Roman maniples are administrative units. There were 3 maniple types: Hastati, Principes, and Triarii (Pilus). These units again, did not go away. There were two centuries in each maniple, a prior (senior) and posterior (junior) century based on the seniority of the Centurion in charge of them. Hastati were the greenest legionnaires, principes were experienced legionaries, and Pili were the senior soldiers. Again these units were purely administrative, so the differences are negligible. The "Prior" Centurions are Captain-Lieutenants and the "Posterior" Centurions are Lieutenants in effect.
Okay then we get to the primary tactical unit, the cohort, composed of the six centuries I mentioned earlier. This was led by the Pilus Prior, the Major-Captain-Lieutenant of the Battalion. 480 fighting men are under his command, he has 6 ballistas and an onager in his personal siege train with their own siege engineers, there's a sizeable baggage of about 120 non combatants and at least 60 mules. There are 2 captain-lieutenants and 3 lieutenants under his command and a host of NCOs. He commands a fighting force which is fairly potent on it's own as a combat force. This is in modern terms a legitimate battalion. These Battalions would in the Auxiliaries vary significantly in construction, but still follow the set pattern for the most part. Similarly we have different types of battalions in more modern forces. This formation has a Cohort flag bearer and musicians as well for coordination. They fight as a single maneuver element but can be divided into 2 to 6 smaller parts.
Then we get to the administrative unit called a legion. This is the building block of strategic operations. You've got 9 identical cohorts, ranked by Pilus Prior seniority from the second to the tenth. However the first cohort is totally different. You have your 480 combatants and 120 noncombatants and mules, but then you have 300 additional support, essentially 30 per cohort, but all attached to the first cohort because it's seniority and senior officer are (I think) tasked with protecting them in the march order (legions marched in in a massive column stretching about 13 miles long, which is why I think the fighting elite of the legion got stuck with the cooks and bakers as well as scouts, spies, and so forth. I imagine the 120 men of the Legion cavalry, would also be attached at this level although they'd range in 4 turmae of 30 horse under 3 Decurions, led by the most senior. These would in the marching column naturally take forward and rear point as well as range on the sides of the column, their job is to notice enemy forces and hoof it back to the main column so the legion can figure out what to do, they're just scouts, 30 man cavalry units are of no value in an open battle except to hunt fleeing men when circumstantially prudent. Auxiliary cavalry at the strategic level would serve in a similar role but for groups of legions. Anyhow, the Major, Primus Pilus (First and Senior) Centurion is basically supposed to run the first cohort with all it's myriad duties, but he gets to be the man of honor, the first man of the first platoon of the legion.
The Legion was basically commanded by the Praefectus Castrorum, an even older, meaner son a of a ***** ex Primus Pilus. This guy is a Lieutenant Colonel or Colonel. He's basically supposed to run the camp, that is to say the entire legion (outside of battle.) As you can see, the Centurions have a lot of duties, which is why they have optiones and tesserarii to delegate duties to. I would imagine that the Optiones generally run the individual century. After all the Prefect has 4800 infantry plus officers, 120 cavalry plus officers, something like 1,500 non combatants, and 7,000+ baggage animals, with 60 ballistae and 10 onagers to oversee, so he needs to trust his officers can do their jobs so he doesn't have to babysit things, otherwise everything grinds to a halt. Evocati would also be present, essentially Warrant Officers with 20+ years with the Legion, on their second (lifer) enlistment. They didn't have an official commission as centurions, but they weren't part of the regular enlisted body like the Decani and Optiones. In theory the Praefectus Castorum and Primus Pilus can run the legion autonomously like a well oiled machine. However they're joined by six political officers (commissars) with good personal military records called Tribunes, which rotate authority so that there are two active on any given day. These guys are all ranked as Equestians or Senators, so of the 8, 4 would be in charge at any time. They're maybe competent, but like I said, they're still flashy political appointees so I'm sure the enlisted man hates their guts.
Then you've got a bunch of General Staff officers who are basically there to command in battle. In practice the Legatus is a Brigadier General, not a Colonel. Yes, he runs a Regiment, that is to say a Legion, but he is also the Legatus of any auxiliary units brigaded to his regiment. Regardless he's a Senator, possibly even Provincial Governor. In major military operations a Dux (Captain General) will be called to command a handful of legions and their auxiliaries. In really important situations the (an?) Emperor would be in person serving as Commander in Chief of the Armed Forces Loyal to him.
So like Blattus was saying this isn't about manpower or formation, it's about tactical and strategic organization and need. Nothing has changed since the dawn of warfare. We still have similar units conceptually in ancient, medieval, and modern organizations. Although admittedly while ancient armies and modern armies tend to synchronize in units and roles easily, medieval forces are slightly different and probably deserve another rant.
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