High Energy Physics (HEP) has a decades long tradition of statistical data analysis and of using large computing infrastructures. CERN's current flagship project LHC has collected over 100 PB of data, which is analysed in a wold-wide distributed computing grid by millions of jobs daily. Being a community with several thousand scientists, HEP also has a tradition of developing its own analysis toolset. In this contribution we will briefly outline the core physics analysis tasks and then focus on applying data analysis methods also to understand and optimise the large and distributed computing systems in the CERN computer centre and the world-wide LHC computing grid. We will describe the approach and tools picked for the analysis of metrics about job performance, disk and network I/O and the geographical distribution and access to physics data. We will present the technical and non-technical challenges in optimising a distributed infrastructure for large scale science projects and will summarise the first results obtained.