Although the paper could have provided a more quantative introduction, like with the doomsday part, however the math on these kinds of things have been done and

Although the paper could have provided a more quantative introduction, like with the doomsday part, however the math on these kinds of things have been done and done again over and over in so many papers, approaching from geological (looking at the rock layers and looking for the frequency of layers that indicate poor living conditions like embedded soot, certain rock types that suggest high energy impact, etc.), archeological (looking at the number of species from fossils in rock layers and looking for large decreases), and physical (solar system asteroid simulations, mathematical study, etc.). In the end it's been done and the scientific community are well aware of the evidence. They don't need to re-invent the wheel be summarising/repeating this research...