The presented analysis is an attempt to create a reliable model that is useful for assessing the strengths of individual armies around the world, but based on objective, quantifiable, quantitative criteria. The model is, to paraphrase Albert Einstein, as simple as possible, but no simpler. Data was used which is not only not classified, such as tactical and technical parameters of weapons and the level of training of soldiers, but is also easily available for almost all countries on our planet.

We managed to obtain a very good match to the course and results of real armed conflicts that have taken place around the world over the past few years by making very few assumptions and using just three parameters – budget spending on the military, the level of corruption and the level of the given country’s GDP.

The methodology used, like any good scientific theory, also enables the formulation of hypotheses as to how possible conflicts could develop in the future and even where to estimate the risk of their emergence.

Ultima ratio – namely the wise man’s lens and eye

Armed conflicts around the world, and certainly media reports on conflicts, have intensified significantly over the past few years. War has also directly reached the Polish border for the first time since 1945, although fortunately it has not crossed it. This is a powerful stimulus, increasing interest in military issues. Numerous publications have appeared, often unfortunately of little substantive value – based on feelings, faith and superstitions, ‘analyses’ and ‘forecasts’, which proved to be completely wrong as early as on the next day.

Therefore, a rational, quantitative approach is needed, which is based on reliable, objective, quantifiable data – the wise man’s lens and eye. That is why it would be useful to build a model objectively showing the quality of the armed forces of the countries around the world, which is simple enough to be understandable and simultaneously useful to a large circle of analysts and commentators.

Just as the value of a football team becomes known by the results of the matches it plays, the value of every army can only be determined on an actual battlefield. However, unlike football matches, wars are fought relatively rarely and it is difficult to expect that we will ever have the opportunity to compare, for example, the Brazilian army with the Thai army in this way.

Without being able to measure this difference directly, we are doomed to use various types of indirect measures, which are visible in many different types of military rankings. They are most frequently designed with the use of a method of calculation – of the number of soldiers in active service and reserves, or the number of tanks, aircraft, guns, ships and other equipment. The values obtained are then multiplied by appropriate weight factors and added together to obtain a result. They are seemingly reliable, because they are numerical. But precisely, only seemingly. This is because there are two major traps here generating huge systematic errors. The first and less important one is the appropriate system of weighting. Are a hundred commandos worth more or less than one tank? And is the combat force of a strike aircraft equivalent to three, or rather five, self-propelled guns? The discussions on this can go on ad infinitum.

However, even if it were possible to establish appropriate weights, a much more serious obstacle is the ‘art is art’ approach. An aircraft is an aircraft, a soldier is a soldier, a tank is a tank, and a ship is a ship. Without any analysis of the quality of these aircraft, tanks and ships or assessment of the level of training and combat experience of the soldiers.

The results of the accumulation of these errors turn out to be downright humorous. In one – a popular firepower ranking conducted by the Global Firepower Index – which is often mentioned and treated very seriously by publicists – we see that the most powerful navies on Earth are Russian, Chinese, and… North Korean. In precisely that order.

The fact that Russia – the most powerful fleet in the world according to this classification – has just lost a naval war with Ukraine – a country that does not have a single battleship – does not make either the developers or the users of this ranking wonder at all.

Of course, it is easy to laugh and criticize. It is more difficult to offer constructive criticism, because taking into account military power, as well as the quantity and quality of the people and equipment in the comparisons, encounters almost insurmountable difficulties. Once again, a never-ending discussion can start on whether the most important factor of an aircraft is its range, the mass of the weapons attached to it, its maximum velocity, its ability to refuel in flight, or perhaps the ease of servicing it on the ground.

After all, the more we delve into the details, the more the scope of possible errors will increase instead of decrease. It appears that the development of a reliable, quantitative, objective indicator showing the quality of contemporary armies and enabling their comparison is simply methodologically impossible.

Fortunately, such a conclusion is premature. This is because rather than focusing on increasingly finer details, the opposite can be done.

Is an army worth as much as the money spent on it?

The armed forces are a special but, even so, part of the economy. A public service, a type of collective consumption. They can therefore be described using economic sciences. And in economics, all goods and services are worth what someone is willing to pay for them. From this point of view, an army is worth as much as the money spent on it.

Such an approach has many advantages. Defence budgets themselves are mostly public information and accessible. It is also easy to compare them. There is no need to find out how many fourth-generation tanks a fifth-generation fighter is worth, because this conversion factor is expressed in their price. Naturally, some of the costs can be hidden in other parts of the budget using various methods of creative accounting, which is probably the case in such countries as Russia and China. Even so, the error related to this will be smaller than in the case of the laborious counting of tanks, guns and soldiers.

Of course, an objection can be raised here that the real military market is far from the ideal free market in economic models. Fans of the armies of backward, primitive and corrupt countries, such as Russia or China, often claim, for instance, that a rifle used by a Russian soldier is better biez anałogow w mirie, [English: without anything similar in the world] than the rifles used by soldiers of civilized countries, and certainly no worse. However, if Russia could produce weapons – or anything else – of a comparable quality, but much cheaper than on the world market, everyone would, after all, be rushing to buy these goods precisely in Russia. And, according to the theory of comparative advantage, Russia would do nothing else but mass-produce weapons for the whole, or almost the whole, world. Meanwhile, nothing like that is happening.

Russia’s share of global arms trade is relatively small. And is constantly declining. This is because. if Russian equipment really were to be half the price of similar equipment produced in France and does not displace it from the market, it is precisely because it is also no better than half as good as the French equipment.

Of course, we also have to take into account the fact that there is considerable inertia in the case of military spending. There is a long investment process in this sector. Even if we were to spend a lot of money on the military in a given year, the effects of this spending will only be visible in later years. The equipment has to be ordered – because no manufacturer in the world has ready-made guns in a depot that can be loaded and shipped immediately – and then manufactured, delivered, implemented and integrated. Soldiers also need to be recruited and trained. Appropriate supplies of ammunition and spare parts have to be accumulated. All this takes time. But, when the equipment is delivered, it can be used for many, many years before it becomes technically or morally obsolescent or worn out during training and manoeuvres, and needs to be replaced with newer models.

The army’s real combat value is therefore proportional not to one-off, but to cumulative, long-term spending. That is why we have used a twelve-year period to analyse the military potential of the world’s armies.

Chart 1 presents total military spending of individual countries in 2012–2023. It contains the thirty countries with the highest military spending. The SIPRI institute from Stockholm posts the necessary data on its website.

Chart 1. Military spending 2012–2023 in billions of dollars

Wykres 1. Wydatki militarne 2012–2023 w miliardach dolarów

Source: own analysis based on data from the SIPRI Institute in Stockholm.

The schedule presented in Chart 1 is of a power-law nature, which is shown with the appropriate fit curve. There are few countries – specifically two – that spend huge amounts of money on weapons, and many countries that spend much less. The existence of such a distribution is somewhat of a surprise, because it suggests that the ‘Matthew effect’, which is known from economics, is taking place here. This is named after the biblical quotation from Matthew 25:29 ‘For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them.’ It looks as if the amount of military spending increases in proportion to the spending already incurred. The more a country spends on weapons, the stronger becomes the tendency to spend even more on them.

The United States incurs the highest military spending – not only in the years 2012–2023. It spent more on weapons than the next 14 countries after the U.S. combined.

China ranks far behind the U.S. in terms of such spending.

Russia, which until recently considered its army to be the second in the world until the real war that broke out in Ukraine brutally and compromisingly for Moscow corrected this presumption, is in third place.

However, the further countries in the ranking are comparable to Russia in terms of military budgets.

Therefore, it might seem as if this is the order and the mutual proportions of the armed forces of individual countries around the world. However, although the model we have just presented is very simple, it is too simple. This is because money alone is not everything. It still needs to be spent effectively, namely converted into real combat power.

The power of the military largely depends on the effectiveness of defence spending

Although the army is part of the economy, this is a special branch of that economy. This is because it is entirely within the public sector and is managed by the state. The condition of the army is therefore a simple reflection of the condition of the whole country. State spending is never as effective and economic as private spending. And the worse the state is managed, the greater is the difference. An honest, efficient and competent government will certainly spend money more effectively than a corrupt and inept one.

In reality, money from the budget never translates 100% into an increase in the combat power of the military. Some part of it is always stolen or simply wasted along the way. How big a part?

Transparency International prepares a Corruption Perception Index (CPI) for countries around the world on a scale of 0 to 100, where 100 means a complete lack of corruption and 0 means total corruption.

In 2023, the most corrupt country in the world was Somalia with 11 points, while the most law-abiding country was Denmark with 90 points. For our purposes, we will assume that the level of corruption in the military sector is the same as that of the whole of the national economy. This assumption does not have to be completely accurate because, due to the high degree of secrecy and weaker public control, corruption in the military could be even higher than the average, but this distortion applies to all armies, so they differences cancel each other out.

To obtain the real strength of the military, the budget spending incurred in a given year needs to be multiplied by the current CPI expressed as a percentage and only then can all these products be added together.

The ranking of the military strength of individual countries created by this algorithm is presented in Chart 2.

Chart 2. Military spending 2012–2023 in billions of dollars adjusted by the level of corruption

Wykres 2. Wydatki militarne 2012–2023 w miliardach dolarów skorygowane o poziom korupcji

Source: own study based on data from the SIPRI Institute in Stockholm and the Corruption Perception Index (CPI)

As can be seen, the ranking of the first thirty countries differs slightly from the case of the budgets alone. The U.S. army is still the first army in the world. Because the U.S. is decidedly less corrupt than China, not to mention Russia, America’s global military dominance is even more overwhelming than arises from the analysis of financing alone.

The ratio of strength between the U.S. and China increases from 3.5 to over 6, while the American advantage over Russia, which is financially 10, is actually 25 in real strength.

Russia’s ‘second army in the world’ drops from third place to ninth, behind Saudi Arabia and even India. Interestingly, on this list of the thirty strongest armies in the world, Poland was also ranked twentieth, having spent a total of 156 billion dollars on the army over the last twelve years, of which, after taking into account the corruption factor, over 90 billion actually translated into the level of the Polish armed forces. The Polish army is – which few people would have intuitively expected – 50% stronger than the Turkish army, whose budget in this period was only slightly less than Poland’s, but a far greater amount of it ended up in the private pockets of politicians and generals.

Theory vs. practice

The ultimate test of any theory is an experiment, namely checking the extent to which the theoretical predictions reflect reality. In our case – the course and outcome of real wars.

Let us analyse three major armed conflicts in recent years.

In the first case, Azerbaijan defeated Armenia in the Nagorno-Karabakh War. This comes as no surprise, because according to the model that was developed, the Azerbaijani army is two and a half times stronger than the Armenian army.

The second case is the Iranian missile attack on Israel. An attack that ended in a miserable failure and the complete defeat of the aggressor. Once again, no wonder, because the Israeli military has an eight-fold advantage over the Iranian military.

These two conflicts fit our model perfectly. Unfortunately, this is not so in the third case, the most interesting of all for us, namely Russia’s aggression against Ukraine. Let’s take a closer look at it.

Chart 3 shows Russia’s and Ukraine’s annual, corruption-adjusted military spending in 2012–2023 in detail, together with the ratio of these two values illustrated with dashed lines.

Chart 3. Russia’s and Ukraine’s effective military spending in millions of dollars

Wykres 3. Efektywne wydatki militarne Rosji i Ukrainy w milionach dolarów

Source: own study

Before the first invasion, in 2014, Russia was more than twenty times stronger than Ukraine. It therefore comes as no surprise that Ukraine was unable to put up any serious military resistance at that time. However, the case was somewhat different in 2022. During this time, Ukraine had not only increased its military spending, but also reduced corruption, ceasing to be the most corrupt country in Europe. As a result, the Russian advantage declined to ten in 2022.

When the war broke out, Ukraine again increased the financing of its army and, in 2023, reduced the difference between it and the Russian army to only one and a half. Additionally, the assumption that corruption in the military is approximately equal to corruption in the whole country does not hold true in the case of Ukraine. This is because Ukraine is spending money from Western donors, countries that are decidedly better organized than Ukraine, with a lower level of corruption, and which more effectively ensure that the funds provided are used properly. Therefore, in this exceptional case, the level of corruption in the military is lower than the Ukrainian average, so effectively the Ukrainian armed forces may already be at the same level as the Russian ones, or maybe even a little higher.

This is how the stagnation that is currently seen on this front can be simply explained. However, this is only happening now, after Ukraine has received allied help. This was not the case in February 2022, and Russia had an advantage, albeit smaller than in 2014, but it was still huge.  The Russian corps should therefore have completely wiped out the Ukrainian defence and quickly settled the outcome of the war. Perhaps not in three days, as Moscow’s propaganda was announcing, but certainly in a few weeks. This did not happen, so it is clear that the adopted model is missing some important parameter that should be supplemented.

Operational capability, namely the ability to intervene militarily outside its borders

Every army in the world has fallen into one of two categories since time immemorial. Either it was a mass army, which was intended to defend the territory, in large numbers, but consisting of poorly armed and poorly trained people attached to the area they were supposed to defend, which was incapable of manoeuvring outside this area, or they were elite troops – professional, excellently trained and armed, able to intervene and transfer their strength even very far from their bases.

Mieszko I and Bolesław the Brave already had a professional team of expert swordsmen, who they could send to very distant battlefields, e.g. to Italy to help Emperor Otto. However, if necessary, they called up a general movement of the people in a given territory which happened to be the target of an invasion.

In addition to the movement of the people, later Polish monarchs had their own units of court knights, who were constantly combat-ready. Finally, in the 16th and 17th centuries, in addition to the still functioning movement of the people, the Polish–Lithuanian Commonwealth had well-trained but small professional regular armies.

Therefore, you can have either a large army, which is capable of defending a given territory, but not doing much else, or, for the same money, a professional army, which is small in number, but capable of long-range projection of strength. All armies in the world fall into one of these two categories to this day.

The parameter that determines the affiliation is operational capability. We will define this as the total spending on the military, adjusted, of course, for the corruption parameter, namely the strength of our army, divided by the number of soldiers in active service, as presented in Chart 4.

Chart 4. Operational capability – military spending per soldier in service 2012–2023 in thousands of dollars

Wykres 4. Operacyjność – wydatki militarne na jednego żołnierza w służbie 2012–2023 w tysiącach dolarów

Source: own study

Chart 4 shows that the diversity of the armed forces in terms of operational capabilities is much smaller than in terms of strength.

Once again, the United States takes first place. It has an army that is not only the most powerful, but also of the highest quality in the world. More than U.S. $7 million per U.S. soldier was spent over 12 years, and over $5 million of this actually translated into combat efficiency. He is literally worth his weight in gold. A life-size statue of him made of solid silver would be a quarter of his value. These golden soldiers are capable of operating effectively anywhere on the globe, and possibly even beyond.

After the U.S. come the armies of developed, civilized, law-abiding and wealthy countries. U.S. allies. We will not find any Chinese or Russian troops here. They both have large numbers, but are immobile.

In terms of operational capability, the Chinese army ranks 32nd in the world, while the Russian army is in 48th place.

Although Russia is still the largest country on Earth, it must also defend the largest territory, while pursuing an aggressive, imperial and antagonistic policy outside its borders, without any major allies or even peaceful neighbours, only enemies and uncertain vassals. Therefore, all this must be guarded militarily.

While the attacked Ukraine, which is also not impressive in terms of its operational capability, can defend itself with all its potential, Russia can only assign part of its potential for aggression. Therefore, Moscow’s successes, even at the start of the invasion, despite having a tenfold advantage in strength, remained limited, because Russia was unable to effectively redirect this strength to Ukraine.

Comparing Russia with another of its potential victims, it can be seen that one Estonian soldier is worth more than three Russian soldiers, but, unfortunately, Russia has well over a hundred times more of these soldiers.

Operational capability is therefore a measure of the ability to intervene militarily outside a country’s borders, obviously, on condition that it has something to intervene with, namely it has the appropriate strength.

Such countries such as the U.S., Australia, Great Britain and Canada, which have high places in both of these rankings, are capable of doing this. Meanwhile, Russia certainly does not, as it has proved empirically.

China is unable to conquer Taiwan for exactly the same reason. The difference in strength is similar to the difference between Russia and Ukraine in February 2022, but the operational capability of China’s troops is not much better than Russia’s, while the topographic challenges – the need to conduct a sea landing – are much greater. Of course, just because China does not have the capability to conduct such an invasion does not mean it will not try to do so. Russia was also incapable of conquering Ukraine, but it tried anyway.

Military effort – namely what percentage of GDP spent on defence shows who is preparing for war

In our considerations so far, we have treated the military as part of a given country’s economy. However, this is a special part. What a given economy produces, an amount referred to as gross domestic product, is roughly split into investment and consumption.  The military is neither one nor the other. This is purely a cost. A loss. Like the destruction after an earthquake.

Money spent on the military is money lost for the economy. Arms production is the production of scrap. Literally. Military equipment either lies in warehouses, is used up during training and manoeuvres, or is destroyed in war. Unlike an excavator, truck or rake, it will not be used for anything else and will not generate any added value.

Therefore, states that are not planning to wage any war in the foreseeable future try to spend as little as possible on the military. The matter is different in the case of those that are either seriously concerned about being attacked or are planning to attack someone themselves; they are arming themselves as much as they can, accepting the inevitable damage to the economy.

In our assessment of military potential, we have been operating in absolute values – money – millions and billions of dollars. This enables a comparison to be made between the world’s armies. However, the scale of a given country’s effort in arming itself cannot be presented in this way.

A million dollars spent on rifles is exactly the same combat strength, but it is a completely different expense for the U.S. and a completely different one for Sierra Leone. Therefore, in order to assess not the army’s combat capabilities, but the degree of a given country’s military effort, we will use the third indicator – in addition to strength and operational capability – which we will call effort. To calculate it, military spending should be related to a given country’s total production, also referred to as Gross Domestic Product, GDP.

The level of GDP can be used to assess the extent to which a given country’s government is preparing for war.

For example, in the 1930s, military spending of countries not planning wars were at a level of several percent of their GDP; in Poland it was 5%. However, military spending of the Third Reich and the USSR was well over 20% of GDP.

Roughly speaking, it can be estimated that spending of more than 5% of GDP on weapons already causes visible problems in the remainder of the economy, while a level of more than 10% of GDP means an economic disaster in the long term. Unless a war breaks out and all the costs are borne by the enemy, if not materially, then at least morally, verbally and through propaganda.

Since Hitler and Stalin decided to significantly cross this dangerous barrier in the 1930s, this meant that they had already decided to go to war and any agreements with them no longer made any sense. Unfortunately, few decision-makers were aware of this dependence at that time and many tried in vain to ‘save the peace’ until the last moment.

The list of countries by average military effort in 2012–2023 is presented in Chart 5. Since we are currently assessing unreal military strength but the political intentions behind it, we have not applied the corruption adjustment.

Chart 5. Military spending as a percentage of GDP – average 2012–2023

Wykres 5. Wydatki militarne jako odsetek PKB – średnia 2012–2023

Source: own study

The U.S. is not in this ranking – either in first place or even in the top ten. The United States is vastly superior to all others in the world in terms of its military potential. In fact, it is as powerful as the whole of the rest of the world’s armies combined, while their golden soldiers are able to intervene anywhere. However, as the U.S. is also the most affluent country in the world, it has no major problems in maintaining this strength, while American military spending is at a quite reasonable level of 3.6% of U.S. GDP.

Even though Russia is spending proportionally more on armaments than the U.S., the United States is a superpower, while Russia only wants to be considered as one.

Although Ukraine is arming itself even more, as already mentioned, it covers these expenses largely with allied aid and therefore they are not such a burden on its budget.

There are countries in the world that are not only more militarized than the U.S., but there are also those which exceed the limit of decency, namely 5% of GDP. Countries that are either already fighting a war or have recently fought wars (Russia, Ukraine, Azerbaijan, Armenia, Israel) or are under a very serious risk of war are generally positioned at the top of the ranking.

Two countries at the top of this ranking, Algeria and Saudi Arabia, are a mystery.  While Algeria – although it is not known who it is arming itself against – is a poor country and even 5.8% of its GDP is not enough to build a noticeable military force (in this respect, Algeria is in 29th place in the world and is half as strong as Poland), Saudi Arabia has become a global military power. It has built a truly serious military force, the fifth in the world, at the cost of an effort that was dangerous to its future and long-term prosperity. Its operational capability is quite significant, outperforming its only potential regional opponent that is capable of facing it, namely Israel.

The probability of using this machine in a real battle should therefore be considered very high. We just do not know where this will happen and against whom.

The black hole of arms

The indicator called effort shows the direction of a given country’s military policy over a long, twelve-year horizon. However, such a policy can change, even very rapidly, as has already been seen in the case of Ukraine and its weapons. Therefore, in addition to the average effort over the last twelve years, momentary effort is also interesting.

The 2023 military effort does, in fact, differ from the twelve-year average.

Chart 6. Military spending as a percentage of GDP in 2023

Wykres. 6. Wydatki militarne jako odsetek PKB w 2023 r.

Source: own study

The extent to which Ukraine depends on foreign aid can be seen immediately. Even totalitarian countries, such as the Third Reich or the USSR, have not managed to achieve military spending of 37% of GDP to this day, as they would have collapsed immediately had they done so.

Ukraine is defending itself, but it was not looking for war itself. As recently as in 2021, Ukraine’s military effort was at a level of 3.4% of GDP. The impression may have been that Russia’s effort in 2023 was much smaller than Ukraine’s, but this is purely illusory. Russia’s actual spending on the war is probably higher than the official 6% of GDP. It is primarily not covered by foreign donors and has to be borne by the primitive, backward and corrupt Russian economy.

In response to Russia’s aggression against Ukraine, not only did Ukraine start to arm itself, but so did the country that would logically be one of Russia’s next targets if Ukraine were to fall. Poland’s high position in the ranking of military effort in 2023 is hardly surprising, but this is no reason to be satisfied.

The military is an economic black hole. If the government spends billions on highways, citizens and goods will travel along them and GDP will increase as a result. If it spends money on hospitals, citizens will be healthier, they will work longer and more effectively, generating GDP. But if the government buys a thousand tanks, they will just sit there and rust. Of course, unless a war breaks out. The increase in Poland’s military strength is therefore only justified by the threat from Russia, which is a kind of extremely expensive insurance policy to cover such a case. Once this threat passes, it will be possible for Poland’s military spending to be reduced to a minimum reasonable level. One that will be sufficient to create a small but professional armed force, capable of supporting the country’s allies in possible conflicts around the world. The force might even remain at its current level. However, corruption must be reduced, because Poland is still lagging behind the world’s leading countries in this respect, and size of the military should be reduced, which will increase operational efficiency. With less corruption and the continued growth of the Polish economy, the effort could then be reduced to a healthy level of 2% of GDP.

The end result

Every army in the world can be described by just two parameters – strength, namely the cumulative product of military spending and the corruption factor, and operational efficiency, namely this spending divided by the size of the military. If a third parameter, namely effort, is added to this, we will obtain a complete description of not only the army itself, but also the whole of the given country’s military policy.

The list of global armed forces based on these three parameters proves to be a perfect fit for actual armed conflicts around the world, reproducing their course and outcome.

Despite the currently prevailing sentiment, it should be stated that the current period of the beating of the war drums is an atypical statistical fluctuation, an unlikely deviation from the long-term trend. Armed conflicts have been gradually declining since the start of the industrial revolution, namely since the early 19th century, at least among the most developed countries. This is indicated by both the theoretical models derived from game theory and actual observations collected by Steven Pinker in his works ‘Twilight of Violence’ and ‘The New Enlightenment’.

This is because while, in the pre-industrial period, war, naturally only a war that was won, could bring many benefits to the victors that far outweighed the losses incurred, the industrial revolution gradually reversed these proportions. The costs of war gradually increased and profits decreased. Wars are currently only started by extremely primitive, backward and corrupt countries and, even in such a case, regardless of their course and outcome, their balance is always negative. After all, it is difficult to specify any tangible benefits that Russia could achieve from conquering Ukraine, which would outweigh the costs and losses related to that conquest. The balance became even more negative when it became clear that Russia cannot conquer Ukraine.

The future belongs to peace. War will end up in the garbage can of history, alongside slavery and human sacrifices to the gods.