(Full disclosure: the following was inspired by this post from Jared Wilson)
As a young Christian who worked at a Christian bookstore, I saw a lot of posters, bookmarks, etc. that had this verse beside an athlete doing something spectacular:
"I can do all things through him who strengthens me."
The idea seemed to be that you could be the best athlete in the world because Jesus is your strength. But if Philippians 4:13 had any application to the sports world, I think the context of the passage makes it obvious which one of the guys in this picture that verse was meant for:
No, Philippians 4:13 isn't supposed to make LeBron excited about how wonderfully he can dunk a basketball. It's supposed to help Stackhouse run down the court with his head held high, even though he just got humiliated in front of several thousand people.
"I can do all things through him who strengthens me." I.e., I can be publicly shamed and still find joy and contentment, because I am loved by the Maker of Heaven and Earth at the cost of His own Son, and His love is more precious than my personal pride and dignity.
So put that verse on a coffee mug, or a sports poster, and find strength in suffering well.