I have a small theoretical model, nothing special - it might still be of interest, though.

Businesses know the term "leverage"; it's really simple. The more you work with borrowed capital, the more extreme becomes the profit for the equity capital owners. The drawback; the magnifying effect works also on the risks; the losses are also magnified.

The military has a similar mechanism at work. That's what the model is about. (Actually, the analogy isn't even close to perfect, but I didn't come up with a better one.)

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Imagine a large force attacking a smaller force of 100 personnel.
Those 100 personnel are 40% "fighters" and 60% "helpers".
The "helpers" don't fight; to keep it simple is usually a good idea in theory models.

The superior force encircles, then attacks and has a loss ratio of 2:1 (2 attacker casualties per defender casualty).

The fight takes out all 40 "fighters" and 80 attackers (again; keep it simple to make details visible).

A "good" battle for the defender? Not really. The 60 "helpers" are still in the pocket and can be taken prisooners by the attacker without further casualties.

The end result is thus 80 attacker losses vs. 100 defender losses. That's an offensive success despite the unfavourable 2:1 loss ratio in the actual fighting. The reason is of course that the targeted unit broke and wasn't able to make good its escape (due to being in a pocket).

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That most simple example was quite unrealistic, of course. Let's add one additional variable; the "fighters" don't fight to the last men. Their morale breaks at 40% fighter casualties. This is still terribly inaccurate, but again - KISS. Defending divisions historically broke at about 10-40% losses (just a rule of thumb). Some formations and armies prevail better in crisis than others.

Let's also change the loss ratio in combat to 1.5 because defenders are quite disadvantaged in a pocket battle. They are short on suplies and might need to launch counterattacks to hold ground - and counterattacks are attacks, therefore not gifted with the tactical advantage of the defender. This loss ratio is in reality very unpredictable, of course.
Modern army forces might also end up having less than 40% "fighters", so let's use 30% as an example.

30% "fighters", the combat loss ratio of 1.5:1 disadvantages the attacker and the "fighters" fail after 40% of them became casualties.

40% of 30 = 12. 12*1.5 = 18. The attacker would have 18 casualties till the defending "fighter"'s will breaks and all remaining defenders surrender.

The end result in this calculation is thus 18 to 100 losses. Some of the 18 may be wounded personnel who recover, so 15 to 100 is more reasonable.
That's a quite drastic overall loss ratio for opponents of even quality.

It did merely take an encirclement (pocket) and local attacker superiority in numbers. It's no wonder that encirclements have such a drastic reputation in military literature and history.

I had the impression that the literature emphasises the "cut off supply" aspect of pockets more than the "grab the support troops for free" aspect. This model suggests that the latter may be important as well.
Support personnel is of course not entirely devoid of combat power. The model is simplified and exaggerates the combat power difference to an all-or-nothing, but that's how many theoretical models work until someone bothers to enlarge the model and someone else bothers to spend years on researching the value of all variables.

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The model shows more, of course. It confirms several long-known facts:

(1) Avoid / break out of pockets ASAP. This hasn't been so self-evident in the time of effective fortresses (till the late 18th century). The Red Army's costly defence in 1941 should have settled the case (it was nevertheless re-opened in '44/'45).

(2) Unit cohesion is very important. Unit cohesion is represented in the model by the "defenders surrender at xy% fighter casualties" variable. The better the cohesion, the lower the variable. A higher unit cohesion reduces the leverage (reduces the difference between overall attacker and defender losses).

(3) A higher percentage of combat troops produces a more robust force. This one is complicated. We could enlarge the model and let a higher share of support personnel improve the combat loss ratio.
This in combination with some combat power for the defenders could produce situations with too few support personnel. Combat power for defenders is messy for the formula, though. It wouldn't be possible to set the moment of surrender that easily. Everything would become more fuzzy, and that hurts the explanatory potential of a model.

(4) Exchange ratio in battle. This is most obvious. More enemy casualties per own casualty is better. That's trivial.

(5) Combat value of "helpers". Again, more is better. "Everyone a rifleman" and such. Trivial as well. That didn't keep me from writing about it in '08, though. Ouch.

Sven Ortmann

edit: shortened

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