Ok, first, you'd need to put way more options, and better understand the difference in each roles.
Producers are the people who manage the ressources of the game : time, money, people.
Designers are the people who actually chose the storyline, the environnements, the monsters who are gonna be in the game.
Programmers are the people who give tools to the designers, artists and integrators to succeed.
Artists do everything art-related in the game : menus art, animations, meshes, etc
Integrators are the people who put the things the artists did in the game with the tools the programmers gave them.
Developers is way too wide a term to define any real job in the domain : a janitor cleaning the workspace as helped in the "developement" as well (ok, that example is maybe a bit farfetched, but you get what I meant).
In the end, it depends on what makes the game bad in your opinion : if it's the story, then the designers are to blame. If it was the glitch/bugs, then the programmers are to blame, etc.