Add a field on the user profile for handedness (right/left/ambidextrous/unknown).
Then, on the team page, include an icon beside each player showing their handedness.
You could use some of these icons:
https://p.yusukekamiyamane.com/icons/se ... yword=hand
right: hand-point
left: hand-point-180
ambidextrous: either hand-ily or hand-horns or hand-finger
Player Handedness
Re: Player Handedness
Will put this on the todo list, though it'll be a lower priority than a number of things already on there.
Re: Player Handedness
Lower priority is obviously understandable. 
