I was wondering how much would I have to pay an artist that works at RIOT to make me a splash-art of a character that I have created in my mind. I know it takes lots of time to make and still, I have the urge to see my character in real life, not just in my mind. so does anyone have a guesstimation?
You don't need an artist from Riot to draw what you want. There's a lot of talented peolpe out there that would give color and shape to your idea. You just need to search for artists that have a style that you like.
To answer your question more directly: No, you probably can't pay a Riot's artist to draw for you. Not that it would cost you too much, but because they wouldn't have time/interest in doing so. To be sure, the best you can do is to contact them via social media: List of Riot Games Artists
Good luck.
