There are so many great writers who were also drunks. Is there some sort of link between writing and alcoholism?

I recently read Leaving Las Vegas by John O'Brien and it prompted this train of thought.

Why are so many great writers also alcoholics? Especially great American writers?

Off the top of my head F. Scott Fitzgerald, Charles Bukowski, Hunter Thompson, Ernest Hemmingway, Stephen King and Truman Capote were all alcoholics.