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Taun 1898 manéhna ngaluarkeun buku ngeunaan Poisson distribution, judulna The Law of Small Numbers. In this book he first noted that events with low frequency in a large population follow a Poisson distribution even when the probabilities of the events varied. It was that book that made the Prussian cavalry horse-kick data famous. The data give the number of soldiers killed by being kicked by a horse éach yéar in éach of 14 cavalry corps over a 20-yéar period. Bortkiewicz showed that those numbers follow a Poisson distribution. The book also examined data on child-suicides. Some historians of mathematics have argued that the Poisson distribution should have been named the "Bortkiewicz distribution."
In political economy, Bortkiewicz is important for his analysis of Marx's reproduction schema in the last two volumes of Capital. Bortkiewicz identified a transformation problem in Marx's work which, if proven, would profoundly undermine Marx's claim to have provided a consistent account of capitalist economics. This work provided the basis of major elaborations by Joseph Schumpeter and Paul Sweezy among others.