I think Baseball umpire doesn’t have enough direct influence to dependably determine the outcome of games. Not without a hilariously inconsistent strike zone.
Basketball is much better, they get to call fouls that drive good players off the floor, and give direct scoring opportunities to the favored team.
…and within two weeks fans, coaches, players, owners and TV announcers were screaming for the real ref’s heads for poor officiating and controversial rulings. That’s less about the influence of officials and more about human nature.
One of the things I really like about curling (okay a minor sport outside of Canada and maybe Scotland) is how little effect the officials have. Most of the time none. Occasionally a measure, but I recently watched a tournament (taped in April, but I only recently got round to it) in which the players even did the measurement. A player from one team did, watched closely by his opponent. The only other time you might see an official is if a rock gets accidentally moved. It is supposed to replaced where both teams agree. I once saw one of the most competitive skips in the game (Russ Howard) turn away when one of his teammates accidentally move a rock and said to his opponent, “Put it where you think it should go.” Which the opposing skip. Players call all their own fouls and they really do.
One of the reasons I have more or less lost interest in baseball is the lousy refereeing. I once saw a professional umpire (Hunter Wendelstadt, if you care) fuck up the infield fly rule! Imagine, the first non-obvious rule in the books. Unbelievable.
Certain referees in boxing can benefit boxers based on their style of refereeing. An example would be how much clinching or “hugging” the referee allows. The referee in Mayweather vs Hatton (Joe Cortez?) did not allow much clinching and was very quick to separate the fighters. This put Hatton at a disadvantage since he prefers a rough and tumble, inside fighting style. Hatton would work his way in and be seperated before he could go to work in earnest. It probably didn’t change the ultimate outcome tho since Mayweather is a far better fighter than Hatton anyway. See also Jones vs Ruiz for a similar situation.
Steve Smoger is a referee known for not stopping fights unless absolutely necessary. So a fighter that cuts easily or has poor defense would prefer him over a more conservative referee.
Mills Lane was very tough about enforcing rules and was very stern. If I was facing a fighter known for cheating (Hopkins, Holyfield, Tyson) I may prefer him to referee in hopes that he would be able to control the opponent.