The concept of local intrinsic dimensionality (LID) has seen increasing adoption in similarity search and data science. As its use expands, it becomes important to develop new perspectives for interpreting LID, and to clarify its relationships with foundational concepts in statistics and data analysis. In this paper, we examine how LID relates to two key concepts in statistics, degrees of freedom and odds. These connections yield new insights into LID as a measure of dominance over uniformity, and introduce novel analogies for interpreting widely used performance metrics, such as area under the ROC curve and Bayes factors.