Fall risk prediction among hospitalized patients is a critical aspect of patient safety in clinical settings, and accurate models can help prevent adverse events. The Hester Davis Score (HDS) is commonly used to assess fall risk, with current clinical practice relying on a threshold-based approach. In this method, a patient is classified as high-risk when their HDS exceeds a predefined threshold. However, this approach may fail to capture dynamic patterns in fall risk over time. In this study, we model the threshold-based approach and propose two machine learning approaches for enhanced fall prediction: One-step ahead fall prediction and sequence-to-point fall prediction. The one-step ahead model uses the HDS at the current timestamp to predict the risk at the next timestamp, while the sequence-to-point model leverages all preceding HDS values to predict fall risk using deep learning. We compare these approaches to assess their accuracy in fall risk prediction, demonstrating that deep learning can outperform the traditional threshold-based method by capturing temporal patterns and improving prediction reliability. These findings highlight the potential for data-driven approaches to enhance patient safety through more reliable fall prevention strategies.