The NIV has a better translation. "Patience" is translated as "perseverance". It makes it passage more understandable.

(James 1:2-4 NIV) Consider it pure joy, my brothers, whenever you face trials of many kinds, {3} because you know that the testing of your faith develops perseverance. {4} Perseverance must finish its work so that you may be mature and complete, not lacking anything.