These are basic differential equations for 6-7th graders, surely you will know how to use them? Here, Alpha and Beta represent each belligerents efficiency/killing parameter, A and B the initial force strengths, declining over time dt. You may have to add R(t), for replacements/reinforcements and a variable for mechanical failure and environmental attrition (abandonment, accidents, stuck in mud and bogs). Bonder-Farrel differential, pH/pK, or a probability matrix are usually better suited for tank models though.
In the second half of 1943 the German armament industry produced a monthly average of 908 tanks and
assault guns (some of which were, of course, intended for other fronts) (according to Frieser, and accepted this datum here)
The more you lose, the more you have to replace. If Soviet losses increased, they also increased the output accordingly, which is also heavily influenced by labour, crew replacement/training and raw material situations.
Even if you are down to almost zero tanks, the war is not over. Tanks are overall just a small asset of the entire armed forces (this can however result in delays).
Thus although the tank kill ratios at Kursk through combat alone are indeed heavily skewed in the Germans' favour, this factor alone is not the thing that wins and loses wars.
I do not think that anyone was able to convince him.
The actual exchange rate tank vs tank is irrelevant. I am inclined to believe there may be a very high exchange ratio in favor of German tanks simply because of the enourmeous density of anti tank guns and artillery employed by the soviets in all engaged sectors will cause a high ratio of German losses beeing not caused by soviet Tanks. But the focus is misleading. The soviets didn’t plan to fight tanks with tanks, they intended to utilize strong defense, mines, anti tank gun belts covered by artillery to absorb the German armored thrust. Tanks were used to prevent maneuver if breakthrough had to be sealed. Kursks can teach a lot about how to embrace different tactical doctrines depending on the realities of the tactical situation. Rather than using tank vs tank descriptive statistics as a proxy for battlefield effeciancy one should look into the combined arms aspects more deeply.
The exchange rate is an expression for the disparity in quality which manifests in the attrition coefficient, a general rate of substitution. The exchange rate is favourable on all levels and if we ignore the microscopic layer for a moment (and I do not disagree with any indepth analysis and note that the one does not exclude the other), it is exactly what it is.
Armed forces are defeated by either annihilation, capture or occupation of the military and administrative complex. This is hard for people to understand. All armies, no matter what doctrine and bureaucratic apparatus, are bound to these laws
, without exception.
To keep on the pressure, the Soviets relied on a constant output, while drawing on an effective replacement and training system for personnel (the same applies to the Wehrmacht, Wehrkreise). Again: This is equal for all belligerents. Faction A dies faster than B, but has a higher replacement rate, thus it is able to keep on the advance. Should you half the Soviet frontline strength and diminish the quarterly replacement rate, then its over. If the war would have continued at such a pace beyond 1945, that is, should the German Army continue to "kite" the Red Army (loss of territory, adequate replacement), then further offensives would have been stalled. Soviet daily casualties and those per Division do not lower, i.e. the Soviets pay a higher price in order to advance quickly. Advance rates are heavily influenced by these factors as well, the weaker the Axis forces on the EF, the faster the Soviets advance.
The exchange rate is exactly what enabled the Wehrmacht to survive for more than 4 years on the Eastern Front. If we remove the exchange rate and hypothetically assume that the quality parameters were the same, then the Wehrmacht is annihilated in a few months and not in 4 years.
If people cannot understand this basic concept and intellectual side of war, then this is just plain ignorance.
On the macroscopic layer, you have two buckets full of water, with different sized holes at the bottom, resulting in leakage. Greater development levels, greater per capita investment, better manufacturing quality and training institutions, leadership, officer corps and NCOs, changing any of these elements would result in narrowing the gap between both combatants (e.g. a better projectile design, giving them GPMGs or Assault Rifles, or outfitting the infantry with an adequate number of half tracks etc.). What happens on the battlefield, is expressed in losses, that is the sum of the losses from the tactical level to the operational level. The Soviet doctrine can be summarized by sacrificing more men and they could afford it.