  In 2019, Anderson et al. proposed the concept of rankability, which refers to
a dataset's inherent ability to be meaningfully ranked. In this article, we
give an expository review of the linear ordering problem (LOP) and then use it
to analyze the rankability of data. Specifically, the degree of linearity is
used to quantify what percentage of the data aligns with an optimal ranking. In
a sports context, this is analogous to the number of games that a ranking can
correctly predict in hindsight. In fact, under the appropriate objective
function, we show that the optimal rankings computed via the LOP maximize the
hindsight accuracy of a ranking. Moreover, we develop a binary program to
compute the maximal Kendall tau ranking distance between two optimal rankings,
which can be used to measure the diversity among optimal rankings without
having to enumerate all optima. Finally, we provide several examples from the
world of sports and college rankings to illustrate these concepts and
demonstrate our results.
