4. Generalizing: Effects on Aggregation of Reinforcement and Maneuver

Reinforcement and Redeployment

A key assumption of the previous cases is that only the forces initially present in the main sectors conduct the battle. But what about reinforcement and redeployment? What if the sides commit their reserves? What if the defender redeploys forces from other sectors? What if the attacker also redeploys forces?[10]

One way to investigate such issues is to develop a simulation model. For current purposes, however, let us instead make some points more qualitatively by looking at the analytics. Repeating (20), we have again that

(27)  

Now let us account for reinforcement and redeployment as follows. Assume that:

• The defender commits his reserves to the main sectors at an even rate over a period T₁.
• The defender counter concentrates his entire force at an even rate over a period T₂(T₂>T₁) . That is, over a time T₂ he increases the concentration factor on main sectors at a constant rate until all his forces are on main sectors.
• The attacker follows the defender, maintaining a constant force ratio on non-main sectors. Thus, the attacker also commits his reserves to main sectors over a period T₁ and redeploys additional forces, eventually all of his forces, to the main sectors over a period T₂
• We express T₂ as a multiple of T₁.

Figure 5 shows the consequences of such assumptions graphically for an aggressive-attacker case. Although real-world changes would be more complex dynamically (e.g., attrition would affect force levels over time, reserves might be initially committed at a higher rate, and the defender might concentrate faster than indicated), this approximate treatment illustrates the basic features. In the example, both sides commit their reserves in time T₁ as shown, and the defender proceeds to counterconcentrate over time (the x axis only goes to 2 T₁, however, so some of the counterconcentration is incomplete).

Figure 5--Time Dependence of Reserve and Concentration Factors

Effects of Time Scale

As p_d(t), f_d(t) and f_a(t) change, so also does F*(t). If we use the time-dependent versions of these variables in (20) we can generate Figure 6.

Figure 6--Approximate Average Value of F* over the Course of Battle as a Function of Battle Duration Relative to Reserve-Commitment Times

The conclusion here is that if the battle is short relative T₁, then the break-even ratio is essentially the same as in the earlier section that ignored intra-battle reinforcement and maneuver (i.e., around 1.5 or so). However, if the battle is not so intense (lower attrition rates and longer duration), then the average value of the break-even ratio rises sharply, reflecting the fact that much of the battle will be fought under circumstances much less congenial to the attacker than intended. Indeed, if the battle lasts long enough, the sides will concentrate all their forces on the main sectors and the value of the original concentration will be greatly reduced--unless, of course, the attacker reconcentrates on a set of new main sectors (or the defender does similarly and goes on the attack).[11]

Effects of Aggregation Scale: Physical Scale and Command Structure

These observations are reasonable in the abstract, but how do they apply to real-world combat? Roughly speaking, the key point is that forces within isolated sectors with independent generals may be able to call in theater reserves quickly, but they will not be able to draw upon forces from other sectors. That is, in most theater conflicts, T₂ is large compared with T₁, probably much larger even than shown (e.g., T₂ could easily be 10 times greater than T₁ because of factors such as terrain, logistics, disagreements between sector commanders, coalition problems when different nations' forces are on different sectors, or confused intelligence). As a result, a break-even 3:1 ratio at the sector level translates into something more like half that at the theater level.

By contrast, if one were to try to do the same analysis with subsectors, one would conclude that intra-subsector maneuver would probably happen quickly relative to the duration of the sector's battle. Not necessarily, but plausibly. Thus, if the Lanchester equation and 3:1 rule applied at the subsector level (e.g., battalion-level battle), they would probably apply also at the sector level if the higher-level defensive command could reallocate forces within its control on a short time scale compared with the duration of the lower-level battle. An important subtlety here is that the relevant duration of lower- level battle includes the times associated with movement, reconnaissance, engagement and disengagement, and full-out battle. A given full-out battle may be remarkably short in modern warfare (e.g., ten minutes). If the defender is good at maneuver, however, and able to engage and disengage readily, he can drag out the duration of battle to improve his opportunity to "reequilibrate" forces. This ability to control tempo and the point of key battles by maneuver has even more leverage than that of prepared defenses, which helps to explain why field officers have long been much less enamored of static defenses than have analysts.

The conclusion here is that strategy variables (e.g., N_main/N)  and relative time scales determine the aggregation coefficients. These vary a lot from one level of combat to another.

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[10] These issues are critical in understanding the differences among defensive strategies and, as part of that, appreciating how much more demanding static forward defense strategies are in terms of the force levels needed for success. See, for example, Davis (1990) and Huber (1990). The former paper emphasizes the distinctions between static forward defenses with few reserves and strategies with larger fractions in operational reserve. The latter gives relatively more emphasis to redeployment among sectors, which Huber calls mobile defense. Huber and Helling (1995) summarize extensive recent work in Germany to estimate "stable theater-level force ratios" in a multipolar security environment.

[11] Note that T₁ should be considered to be a stochastic variable, which would mean that the effective coefficients of any theater-level model would be stochastic. There are many other examples of where stochastic considerations should be made explicit. For example, the probability distribution for sector-level combat is probably distinctly bimodal if the force ratio is 3:1. Thus, the situation at the "break-even force ratio" is not well described as "break- even" in the sense that the sides would stalemate. Instead, it is better described as implying a 50-50 chance of winning or losing. This is discussed, for example, in Huber (1990) and Huber and Helling (1995), based on detailed simulations by Hans Hoffmann and others at the University of the Bundeswehr.

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