Germany was one of the three major scientific powers in Europe in the 19th and 20th centuries (along with the United Kingdom and France), and with them made up the most powerful scientific countries in the world until the mid-20th century (when the three European powers, damaged by war and brain-drain, were eclipsed by the new superpowers of the United States and the Soviet Union).

Each of these countries has its own story about its rise to scientific prominence, but the German one is about a new "model" of science that welded scientific research institutions, the strong (Prussian-style) state, and massive industrial combines that subsidized and sponsored research work. This is in stark contrast with some of the other scientific powers of the era, in which science was treated as something mostly done by (non-state) universities, where research was funded largely by philanthropy, and where many scientists considered industrial research "tainting" to the scientific enterprise. The "German model" was immensely successful in certain areas of scientific research, not unsurprisingly often ones connected directly with industrial applications (it is no coincidence that they excelled at thermodynamics and physics and chemistry), and it appears to have been a real "rising tides lifts all boats" situation even with non-applied sciences (their work in mathematics and theoretical physics was excellent as well). The Germans inaugurated the modern research university as an institution (which is to say, to see the purpose of universities as research output, funded by educational tuitions — as opposed to putting education as the primary role of the university, as it still was in many other places).

So to answer your question — it is definitely not random, it is definitely systemic. As an aside, one of the things the US did in the interwar period, and especially during and after World War II, was import the "German model" to its own shores, both by creating new universities (like Johns Hopkins, which was explicitly based on German approaches) and by converting the internal reward systems at existing ones (James Conant, President of Harvard, did this in the 1930s; during World War II he would become a major figure in organizing the American defense science effort).

Again, this is not the only way to do things (the French and British have their own somewhat different trajectories), and the Germans by much of this period were not entirely unique in this, but they started this system in a big way and managed to be very successful with it (which also probably contributed to its continued success as a nation in this regard — for much of the 19th and the first quarter or so of the 20th century, if you were a scientist not in the UK, France, or Germany, you had to do your graduate study in those countries if you really wanted a world-class education). This is not to say that there were not great accomplishments by scientists outside of these nations either, of course, but you don't see anything like the systemic accumulation of prizes and discoveries that you see in these ones during that time. (Prizes, of course, are not always the best barometer, since they are chosen by national committees, previous winners, etc., and so can have their own systemic biases built-in.)

One last little point I always make when I teach courses on the history of science and technology: there is absolutely nothing random or arbitrary about which nations end up being very prominent in scientific work or technological development. Every nation has its own random assortment of people, including a few geniuses and savants. What differs between them are the conditions of science and scientists (and whether said geniuses and savants — much less the regular "slightly above average intelligence" people who end up doing the bulk of the work in such fields as well — end up in favorable conditions or not). We can absolutely look at a country's scientific history and say, "oh, here's why they were good on the whole at this, and here's why these people ended up being able to make contributions there." We can also look at these histories and see where they could have probably done better — excluding +50% of the population (women, poor, minorities, etc.) for much of this history means you are missing out on a lot of potentially productive scientists! We tend to imagine that scientific success is the produce of "genius" and so on, but historians of science view it more as systems of organized research and the institutions that support them. The reason we tell the stories of science as a litany of "geniuses" is largely pedagogical and cultural, not a reflection of the actual history (on this, see Kuhn's classic The Structure of Scientific Revolutions, which makes this point very well). I always tell my students that there is nothing fated about a nation's scientific success. You end up with the science (and technology) that your society is set up to develop. Change those conditions and you change what you get out of them.

One very nice book on these different national "styles" in science is Helge Kragh's Quantum generations, which is mostly focused on developments in modern physics, but does a very good job of contextualizing scientific output in general among different "primary" scientific powers (Germany, UK, France) as well as the "secondary" scientific powers (US, Japan, Russia) prior to World War II (when everything changes, which he also covers well).