I had a topic like this a month or so ago but not in the same context with regards to sports and your martial art training.
20th century sport scientists in the now defunct U.S.S.R found that athletes could benefit from participating in sports other than the one in which is their main core. This is no suprise as the same idea was used in 19th century western physical culture in the pursuit of all around general vibrance.
By doing so, you could tap a broader array of physiological and psychological skills. For example, it was common in Moscow and other soviet cities for wrestlers, to play twenty minutes of basketball as part of the warmup for their day-to-day training sessions and that their volleyball players trained in soccer exercises and drills for conditioning. During certain periods of training they knew that other sports can be used to make their athletes, quicker, stronger and more flexible.
The same principle can be used for martial training.
As an example last weekend I joined in a game of dodge ball at my gym, yep dodge ball, except this game was composed of athletes like college football players, this gym has a serious sports performance divison, as one of the owners is a college football coach, and they do all sorts of off the cuff biomotor training for strength, speed, agility, and quickness, which means they called it a sports ball reaction drill, but I am still calling it dodge ball.
The goal of the drill was to improve visual stimuli response and total-body quickness. From a martial standpoint you could see how this also translates to footwork, evasion skills, fast changes in direction, first step quickness, and so on.
Just food for thought so get out their and play some sports ball reaction drills-ummm-I mean dodge ball.
Cheers!