On the Level of Measurement of Sports Probabilities: Ordinal Behavior in Rare NBA Probability

Probabilities in sports forecasting are shaped by betting-market mechanisms, where expectations are exchanged through prices and transformed into implied probabilities. Although probabilistic predictions are usually treated as quantitative variables, rare events may be represented with lower resolution, making some probability ranges behave closer to ordinal structures. This paper investigates this hypothesis using NBA betting odds. We directly assess ordinality by examining the loss of linearity between implied probabilities and empirical outcome frequencies while evaluating whether monotonicity is preserved across probability ranges. The results show that low-probability odds deviate from the linear behavior expected under quantitative assumptions, while largely maintaining their ordinal ordering. The ordinal hypothesis is independently evaluated through a predictive experiment based on a Gated Recurrent Unit model. The model uses team-level temporal sequences as input features to predict the probability of a target game. We compare the behavior of the ordinal-aware CORAL loss across the analyzed subsets. The results suggest that the subset exhibiting ordinal characteristics attains a lower statistical risk under this ordinal inductive bias than the subset characterized by quantitative behavior. Finally, we discuss the broader applicability of comparative training with loss-function-induced inductive biases as a practical method for identifying the measurement level of target variables.