Krevetka raised a very important problem.

Here we have to stop and explain that there is no magic whatsoever in counting combat effectiveness of any weapon system because all of those calculations--some of them are extremely complex and tedious--are based on the foundation of weighted averages and its more general form--mathematical expectation. I wrote about it a few years back. So, what is the criterion of the combat effectiveness? It is obviously--a number of targets--in our case for air defense complexes--which are shot down. But not all targets are created equal, nor are air defense complexes. You cannot compare S1 Pantsir to S-500--two totally different systems. Plus, you have to account for conditions of intercept. This is where we have to give a simplest (utterly simplified) example.

Weighted average looks like this:

*x*

*1, x2*, and

*x*

*3*. For the sake of simplification we will use very simple numbers and simplest possible scenario. Let's say first Tor shot down 14 out of 15 missiles of Olkha class, thus providing empirically confirmed probability of intercept for Olkha class as:

*x**1=14/15= 0.933*

Now we go for the second Tor which shot down 40 out of 42 drones:

*x**2=40/42= 0.952*

The third one*, *say, shoots down all HIMARS rockets it faced thus providing the probability of:

*x**3=1* * *

And here is a conundrum: we can easily do simple average of these probabilities and state that those three Tors provided the average probability of shoot-down of aerial targets as:

*X=(0.933+0.952+1)/3= 0.962*

Very good. But this is not how professionals calculate it, they calculate it based on constant flow of statistical data which is WEIGHTED. As I already stated--not all targets are created equal. E.g. for the third Tor, HIMARS is a standard target and* *if that Tor* *operated in a favorable ECM environment, had early warning* *and radio waves propagation was good, its empirical probability could be "degraded" accounting for almost perfect and easy conditions which themselves are calculated as math expectations and that is the whole other story altogether--weighted coefficients *w**i*. So, we introduce (remember--**it is a spherical horse in vacuum type of example for the simplicity and demonstration only**) the weight *w**3* which is: *w**3*=0.98. Then, depending on conditions and types of targets, we may introduce *w**2*=0.992 and *w**1*=0.99 and now we can calculate this weighted average:

*X = (0.933 x 0.99 + 0.952 x 0.992 + 1 x 0.98)/(0.99+0.992+0.98)=*

* =2.848054/2.962= 0.962. *

So, in our case a simple average turned out to be the same as weighted one, but this is because weights assigned have been very close to 1 and it was done for demonstration purpose only, in real life, of course, those number will differ. But on this simplest example we can say that this battery of three Tor-M2 systems has a probability of intercepting three types of listed targets with probability of *0.962*. I deliberately used probability as an example--** it is ONLY an example of calculations**--in reality they will calculate numbers of targets shot down, but that will require a serious elaboration. This, however, allows one to

**the operation of**

*forecast***(probability of intercepts say of a mixed salvo) depending on the conditions of the battle against aerial targets. In this case, the number of shot-down enemy targets will be calculated as math expectation. There is no magic--only one non-stop stream of information which is processed by modern combat management systems and proper adjustments are made. Hope this helps.**

__a battery__
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