Essentially, force (strength), velocity and speed-strength (power) are the three main characteristics that are present in ballistic movements, and you can train all of them in the weight room.
Running around and practicing soccer skills while wearing a weighted vest, attaching a band to a hockey stick or a baseball bat, and a myriad of other ridiculous activities in the weight room do not count as sport-specific activities.
You can vastly improve the effectiveness of your in-season programming by understanding submaximal maintenance training and programming flexibility, the use of concentric-only exercises, and high-rep work for recovery.
Rotational power is important for both swinging and throwing. This article includes a three-exercise progression to not only develop better, more efficient rotational ability, but also to improve proficiency in weight transfer.