Oh, I have played quite competitively (though not baseball). I've played on championship teams as well as hockey teams who didn't win until after Christmas (including the intrasquad scrimmage lol).
I've also been part of teams that were almost as bad with coaches who were bad, but we had players who stepped up as leaders and set the cultural tone for the team.
I'm not saying Pedro needs to stay (quite the opposite) - just stating a fact that, if you're trying to build a positive culture in the organization, you need players who are willing to take a long, hard look at themselves and try to make things better.