Let's say a player have 20 in every stat, but 1 in consistent. Does anyone know how that will affect the players stats in a game?

Not sure if it affects the skill itself but the overall behavior of the player in the game.
What I'm saying is that, if for example consistency affects 20% and the player in your example is a QB and he usually throws 80% according to his skills, he may drop to 80% - 80%*20% = 64%
It is not necessary the same as dropping each skill to 20 - 20%*20 = 16.

Of course, both above formulas would be the same, if performance would be a linear function of skills.