Tuesday, June 26, 2018

Why Mathematical Models Break Down. And Why Our Life Depends On That-3

Continuation, first two parts are HERE and HERE.

When speaking about some kind of financial "adjuster" in this particular formula we, of course, may say that there should be a way of bypassing the tedious task of finding such an adjuster and go with nominal military expenditures figures while paying attention to what is inside the bracket—that is what theoretically should account for military potential thus providing the number for this proverbial bang for a buck. But this method has its own serious drawback. No matter how we play with numbers any kind of quantifiable comparison will not convey a crucial factor of geopolitical posture and doctrines which are derived from this.

Surely, there is always a way to "compare". Consider, for example, this famous dyadic technological relation of forces. 

Don't be intimidated with those Sigma notations—they merely stand for sums of products of the year of introduction of technology (types of aircraft, tanks, ships, subs etc.) and of the number of those types. Let's give an example: we start with a very simplified example of the United States Air Force and Tank forces—we take numbers from open sources and "trim" them to avoid a tedious calculation for a huge range of years and types—remember, we do it merely for demonstration. So, we go HERE and choose the number of combat aircraft in the USAF "inventory". Let's limit ourselves to strictly fighter and attack aircraft. This will give us roughly:

235 F-15 Eagles, 220 F-15E Strike Eagles, 570 F-16 Fighting Falcons, 195 F-22 Raptors and 287 of good ol' A-10s Thunderbolts. So, now to demonstrate what it gives us in terms of first ratio inside the bracket we assume, in order to avoid this tedious calculations for each batch of the same type of aircraft, that:

1. Out of 235 F-15 Eagles 35 was manufactured in 1980, 100 was manufactured in 1990 and the last 100 was manufactured in 2005. So, that gives us first term for the type (F-15) of aircraft: 

              =69,300 + 199,000 + 200,500 = 468,800.

Now we can divide this number by total number of F-15 Eagles and we get:


This number is our "weighted" (sort of) technological (which translates into combat) "value" of F-15s.

2. Now we do similar operation with F-15s Strike Eagles and for simplicity of experiment we say that 110 of them were manufactured, say, in 2000 and another 110 in 2005. Thus our Sigma for F-15Es will be: 

             110*2000 + 110*2005= 220,000+220,550=440,550

Now we divide by the number of F-15Es and get:


By now you should get a simple idea behind these calculations, so I will omit further calculations for each type of aircraft and will merely state the numbers based on UNIFORM or averaged year of manufacturing for the rest of aircraft. Of course, this is not the case in real life, but:

3. For F-16s we choose uniform (or average) year of manufacturing, say, 2004, this gives us 570*2004/570=2004.

4. For A-10s we get the year of 1989, so their value is 1989;

5. For F-22 Raptor we get the (average) year of manufacturing of 2005, so their value is 2005.

Now what is left for us is to add all this together to get the value of the USAF combat aircraft:   

      1,994.9 + 2002.5 + 2004 + 1989 + 2005=9,995.4

This is roughly what the value of USAF is in our example.

Absolutely the same method is used for US Army's tanks, if we to assume the number of about 6,000 of all types of M-1s being "in inventory", how many of actually combat ready tanks is out there remains really a secret—this number will be much smaller than "inventory" or "storage" but since we are at it, we may as well count ALL of them, including in storage and that number is about 6,000 American Main battle Tanks which is all iterations of M-1 Abrams. As the formula goes, once technological value of tanks is calculated, you add them to the value of aircraft and then divide this sum by 2 (or multiply by 0.5) we supposedly should get the T, that is technological value, which could be compared with the T of other nation and this is supposedly give us Dyadic Technological Advantage Delta T. For Russian AF and tank forces the information is readily available, so feel free to play with those numbers. 

 Obviously, any T in this formula is nothing more than weighted time of introduction of military technology into service and this DOES NOT represent a real technological advantage, or otherwise, since ignores completely a mode of employment of forces. Yes, the year of introduction matters but what about upgrades and modernization? As an example, an upgrade of Russia's venerable SU-27 fighter to SU-27SM produced a very capable 21st century combat aircraft capable of turning and burning with the best of them and here we are talking about airframes some of which are 20+ years old. Same goes for upgrades of F-16s which will get AESA radar among other things, thus making this old timer not only still one of the sexiest aircraft out there but make it deadlier.

Moreover, when calculating any technological advantages one must consider not just comparisons of the likes—aircraft to aircraft, tank to tank or ship to ship. It doesn't work like this and never did. Vietnam War—a bulk of massive USAF losses (around 10,000 aircraft) were due to AAA and SAMs. Since then, USAF never encountered Air Defense of such a capability it encountered in Vietnam. One then is forced to ask an inevitable question: what could be possible, however improbable, performance of USAF against air defense assets of Russia? I do not even want to go there because this could be one of the thresholds which will force the United States to escalate to nuclear option. One, again, must consider how opposing forces deploy and fight. 

So, no matter how we play with numbers and popular formulas, so far—they do not really represent a reliable picture of capability. Indeed, what is better to have and who comes out on top in the scenario of 4 F-22s against 6 Su-35s, how about 6 F-22s against 4 Su-35s and two S-400s? Are these legitimate questions to ponder? Of course they are. In the open ocean any, even modern state-of-the-art, SSK will become inevitably much more vulnerable against modern SSN, while in its own littoral and under the cover of own ASW patrol aviation, those SSKs become deadly hunters against any nuclear powered sub. 

So, how we are to approach those comparisons? Obviously, some people go for the jugular and create all kinds of Firepower Rankings. They name whole 55 factors which influence their "calculations" and that is fine and dandy but does it reflect properly the only ability which matters in this world—to fight and WIN the war. Does it answer the question of WHAT war? It doesn't, because Russia, as an example, is not intent nor is planning for fighting the war in Europe, unless attacked first, let alone she is not intent nor is preparing for fighting a war inside the United States. The United States, however, is intent on fighting war both around and, in some mad scenarios, inside Russia. That brings us to inevitable conclusion that ANY comparison of military power outside the (respective) doctrinal frameworks is useless and is nothing more than mental acrobatics which, sadly, sometimes has a very serious and grim consequences for those who base their decisions primarily on those rankings and numerical "values".   

To Be Continued....  

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