How effective are cheap drones actually?

How effective are cheap drones actually?

These days we are seeing a lot of good news messages regarding the use of cheap, commercial drones in the Ukrainian conflict. It suffices to type ‘cheap drone Ukraine’ in the Google search bar to get dozens of hits all claiming the efficiency of cheap drones in the Ukrainian conflict and how these drones are changing the face of modern warfare. Many of these messages remain fairly superficial regarding their 'objective' grounds on which they have come to such a conclusion, but some try to take it a step further. A rather ‘objective’ approach to try to quantity the efficiency of these cheap drones against legacy weapon systems, can be found on the Euromaidan Press website.

In this approach, the cost per system is taken into account, next to the cost per shell and the probability of kill for a given enemy weapon system (an armoured vehicle or a tank), backing the aforementioned claims up with ‘objective’ numbers. But are they really…?

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Although the seemingly mathematical and methodical approach, the shown numbers do come with several serious inconsistencies.

Firstly, the analysis is actually based on the probability of hit, not on the probability of kill. It is clear that whereas an improvised, 40mm, recycled shaped charge jettisoned from a small drone may actually destroy a main battle tank, it will not exactly have the same effect as the impact of a much larger caliber shaped charge from a Javelin, let alone a direct hit from a 155mm artillery round. And an impact of that small recycled shaped charge on for instance the fender of a vehicle, will not give the same result as that aforementioned 155mm high-explosive artillery round hitting that same fender... So whereas the analysis is simplified into having the probability of hit correspond directly to the probability of kill, the correct analysis should actually determine the probability of kill as the product of the probability of hit times the probability of kill if hit:

Assuming then that the probability of hit corresponds directly to the probability of kill, basically comes down to making the hypothesis that every hit is a kill, or mathematically:

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?And hence:

Admittedly, there is no easy way to determine the probability of kill if hit, so many analysts, even professional ones, often have to make very basic assumptions on its actual value. So for the time being we will just continue with this very basic assumption of always having a kill whenever we hit the target.

The second issue with the analysis is that the calculated required number of shots to destroy a single target (see the small print in the second column from the right) is unfortunately plainly wrong. The author of the study has made a very common statistical error in that he assumed that the probability of kill Pkill of n weapon employments/shots is given by the sum of the probabilities of the individual shots:

Unfortunately, statistics do not work that way (they never work easily, do they?). The probability of kill of n shots is, to start with, not simply a sum of probabilities of individual shots. The latter would mean that every six times you throw a dice, you should always have thrown exactly one six! And we all know that sometimes we are lucky and throw a six immediately, whereas on certain occasions, the six seems to have vanished from the faces of the dice… So the probability of kill requiring n shots is actually given by the cumulated probabilities of not having any kill with n shots and taking the complement of this number in reference to 1 (or 100% as we are more accustomed to in the world of probabilities). So the probability of having a kill after having to try n times (so performing n shots or weapon employments) is actually given by:

?Which for

Simplifies into:

With this, it is already worth revisiting the results shown in the table above. However, there is an additional issue, namely that the left-hand side of the last equation presented above can never become 100%, unless in the notional case that Phit is 100% where we always hit with the first shot. Remember our dice? We know that on average one out six throws should give us a six, but sometimes it takes a lot more throws to actually get that six (and sometimes you only need a single throw!). This means that this last equation can only be applied to this case if we fix the probability we want to have to kill a specific target. For the remainder of this work, this probability was selected to be 95%, but any other high value could have been preferred (e.g. 90% or 99%). Fixing this value then permits to calculate the average number of shots that are actually needed on each target to assure that 95% kill probability. Applying this, and for all other parameters taking the same values of the original study, one gets the following results (by the way, the author made a mistake to calculate CEP values into probabilities as well for the artillery calculations, so this was corrected as well):

So what have we gained? The above figure still gives a clear advantage to the cheap FPV drone and the heavy drone, but their advantage in cost ratio has been reduced by a factor three. For the expensive high-precision systems, the corrected approach did not change a lot, as for probabilities of hit nearing one, both the old, wrong calculation as the new, correct one give very similar results. The corrected approach to take into account the CEP values for regular artillery projectiles on the other hand, clearly illustrates why regular artillery is not a good anti-armour system (this is why we introduced Improved Conventional Munition – ICM, also known as cluster munition, at a certain moment in time). However, it should not be forgotten that against concentrated troops, artillery shells are by far the most efficient! But hey, aren’t the drones in the end still not cheaper (by far) than the other systems? So what is the big fuzz?

For that we need to add a new parameter, namely effective range. Whereas cheap drones currently have a limited range of less than 500 meters (!) before being lost due to the intensive electronic warfare (EW) capabilities deployed by Russia, the high-tech military systems are basically unaffected. So by taking effective range of all these systems in account, one can now also calculate a cost ratio per kilometer of range, or likely even more important, per square kilometer covered. By normalizing by the cost of the FPV drone, the following results are obtained:

It is immediately clear that the very low effective range of the FPV drones severely hampers their efficiency, both for engaging in depth as for covering an area (although one should take the actual operational areas and distances whereas here a first estimate was simply based on maximum effective range of the different systems). Although the Javelin is a very expensive system, it outperforms the cheap drones easily when the covered area by a single system is taken into account (the analysis also did not consider the fact that the Javelin also has high hit probability on moving targets, something not uncommon for armoured vehicles…). The locally produced alternative, the Stygna ATGM does even a better job than Javelin, thanks to its long range and low cost. This however did not take into account the likely higher probability of kill for the more advanced Javelin which, in a more detailed analysis, might give it the advantage again. Even ‘dumb’ conventional artillery outperforms cheap drones by more than an order of magnitude! High-precision military-grade systems with long range capabilities like Switchblade 600 and Excalibur by far exceed the capabilities of the other systems (the range of the Excalibur was selected to be its minimum stated value, newer versions have considerably higher effective ranges which would make Excalibur by far the preferred solution).

So what is the final message here?

Lesson 1: statistics are not easy. If you do not know exactly what you are doing, you can get easily biased results. However, and even if this analysis started with the correction of an analysis made by another author, this by no means takes away the appreciation for the effort of the latter. It is important to validate not only qualitatively, but also quantitatively, these recent claims on the ‘extreme cost-effectiveness of commercial drones’.

Lesson 2: there is more than meets the eye. Commercial drones are not the new super-weapons and might not even be that efficient at all, contrary to what is claimed everywhere else. A large part of the drone frenzy is likely caused by survivor bias (a term that anyone with an interest in operational research and military statistics should look up, but we are deviating from the subject here) where we only see the successful drone attacks, but not the hundreds of drones consumed on a daily basis that never reach their intended targets.

Lesson 3: high-precision systems like Switchblade or Excalibur may seem overly expensive at first sight, but are actually extremely cost-effective. It is however important to have the necessary industrial capacity to rapidly and effectively supply a sufficient number of munitions in case a large-scale, high-intensity conflict erupts.

Although even this analysis is likely to be too simplified to be of actual value in current or future operational research projects, it does show the importance of trying to quantify as much as possible. It is only in exploring the available data of past and current conflicts, that we will be able to improve our odds in the future.