Lack of rapidly available neurological expertise, especially in rural areas, is one of the key obstacles in stroke care. Stroke care networks attempt to address this challenge by connecting hospitals with specialized stroke centers, stroke units, and hospitals of lower levels of care. While the benefits of stroke care networks are well-documented, travel distances are likely to increase when patients are transferred almost exclusively between members of the same network. This is particularly important for patients who require mechanical thrombectomy, an increasingly employed treatment method that requires equipment and expertise available in specialized stroke centers. This study aims to analyze the performance of the current design of stroke care networks in Bavaria, Germany, and to evaluate the improvement potential when the networks are redesigned to minimize travel distances. To this end, we define three fundamental criteria for assessing network design performance: 1) average travel distances, 2) the populace in the catchment area relative to the number of stroke units, and 3) the ratio of stroke units to lower-care hospitals. We generate several alternative stroke network designs using an analytical approach based on mathematical programming and clustering. Finally, we evaluate the performance of the existing networks in Bavaria via simulation. The results show that the current network design could be significantly improved concerning the average travel distances. Moreover, the existing networks are unnecessarily imbalanced when it comes to their number of stroke units per capita and the ratio of stroke units to lower-care hospitals.