Any time someone is talking about the ref's influence on sports I get to plug one of my favorite books, Scorecasting by Moskowitz and Wertheim. The premise of the book is simple: using statistical analysis, can you prove or disprove various beliefs about sports? Several chapters are dedicated to various ways that officials influence the games that they're calling. The book does make a compelling case that they do, but in the least expected and to my mind genuinely most noble way: it seems that when officials do bend the rules, it's usually to avoid doing anything at all. In baseball, strike zones shrink on an 0-2 count because a called third strike feels like the official deciding the outcome but a swing and miss, or contact in-play, feels like the two teams playing the game and deciding the winner. In Association Foot-the-Ball, the tendency in big matches, in close matches and later on in matches isn't to call more penalties on any one team than the others, it's to penalize less overall. In matches that aren't that close or important the tendency is that the underdog will receive fewer penalties, or in blowouts the team in the lead tends to take more penalties than the team that's behind. What's really fun is that because human behavior is feedback loops that accept feedback loops as input even the appearance of bias can sometimes introduce bias. When they studied hockey they went with the assumption that, all other things being normalized for, each team should be equally likely to be the next to take a penalty. Some individual teams might be more likely than others to take a penalty, but across dozens of teams and dozens of seasons it should more or less shake out square. But it turns out that similar patterns apply: in close games, or during the playoffs fewer penalties overall but also the first strong evidence of something that hockey folk have always suspected: make-up calls. You're right, sometimes it's really close and sometimes the officials just get it wrong, and this book demonstrates statistically that after close or incorrect calls, or calls that seemed to have an inordinate effect on the game, the team that was put at a disadvantage is
much more likely to be the next put at an advantage.
So yeah, officials do influence play and frankly I think it's a good and healthy thing for the sport overall when they do. In the case of balls and strikes I support automated calls because that's very simple (the ball is either in the box or not, and we can hem and haw about how we define the box during the off-season) and the infra to do it is already in-place. But in difficult, judgment-call situations (to take american football as an example, what's the actual, objectively-defined line between a corner getting handsy and defensive pass interference?) I not only think humans are necessary despite their biases but because of them. Obv bias in favor of any one team or style of play needs to be rooted out but the way that officials actually call games, even when it varies from the rules, seems to actually benefit the sport, the athletes and the fans in a lot of unexpected ways.