Multi-object tracking (MOT) in team sports is particularly challenging due to the fast-paced motion and frequent occlusions resulting in motion blur and identity switches, respectively. Predicting player positions in such scenarios is particularly difficult due to the observed highly non-linear motion patterns. Current methods are heavily reliant on object detection and appearance-based tracking, which struggle to perform in complex team sports scenarios, where appearance cues are ambiguous and motion patterns do not necessarily follow a linear pattern. To address these challenges, we introduce SportMamba, an adaptive hybrid MOT technique specifically designed for tracking in dynamic team sports. The technical contribution of SportMamba is twofold. First, we introduce a mamba-attention mechanism that models non-linear motion by implicitly focusing on relevant embedding dependencies. Second, we propose a height-adaptive spatial association metric to reduce ID switches caused by partial occlusions by accounting for scale variations due to depth changes. Additionally, we extend the detection search space with adaptive buffers to improve associations in fast-motion scenarios. Our proposed technique, SportMamba, demonstrates state-of-the-art performance on various metrics in the SportsMOT dataset, which is characterized by complex motion and severe occlusion. Furthermore, we demonstrate its generalization capability through zero-shot transfer to VIP-HTD, an ice hockey dataset.