It is no directly related between the battery capacity and battery current of protection board. Capacity large, not battery large, battery is mainly to see the continuous current.
That is to say, the larger of your motor, the protection board continuous current should be larger. Besides, protection board is also related to the current limit of the controller.
Taking 10s 36V as an example, choose 16A for below 350A, 25A for below 500W, 35A for below 800W, 60A for below 1000W, and contact customer service for below 1200W. In short, the continuous current of the protection board must be larger than the current limit of the controller.