Ordered data is ubiquitous. Recommendation systems attempt to leverage information regarding one’s preferences to suggest new content (e.g. music, movies) or products (e.g. books). Ranked-choice voting is used for local, provincial/state, and national level elections across the globe. Even Cornell uses ranked-choice for its elections! In sports, orderings frequently determine tournament structures and season schedules, and in games or general forms of competition, ordered data is a natural way to express outcomes. While the expanding areas of application shows no signs of slowing down, it also reflects two main difficulties: 1) disunity of the theories that underpin available models and 2) computational issues that arise when dealing with permutations of k objects, which scales factorially. Both of these difficulties contribute to the ad-hoc flavor of available methods as well as the relatively small body of work focused on inference. Using the most complete dataset on surfing competitions, we take a four step approach to present the material: First, we define ordered data as a set of objects endowed with a strict order relation (ie. a permutation) and discuss the various ways to represent ordered data mathematically and as a data structure. Second, we construct the main methods/models from the ground up and implement them using the surf competition data. Third, we present a simplified and portable probability model on permutations and demonstrate its effectiveness by identifying empirical distribution(s). Lastly, we present some of the hurdles encountered throughout this project that suggest areas for further collaboration, namely, how to leverage computational algebra systems (which I have used in this project) and how to visualize ordered data to effectively communicate insights.