How can we separate referee bias from other sources of home-field advantage?

Are umpires and referees biased in favor of home teams?

The evidence seems to say they are. In "Scorecasting," Tobias Moskowitz and Jon Wertheim listed many bits of evidence that suggest such bias. While I don't agree with them that refereeing is the *only* thing that causes home-field advantage, they make a pretty good case that it at least causes *some* of it.

Next month, I'll be giving a presentation on this topic at the SABR convention in Long Beach. My tentative plan is, first, to show evidence (mostly baseball) showing umpire bias. For that, I'll use examples from "Scorecasting." In addition, there's a great study from John Walsh in the 2011 Hardball Times book, which uses Pitch f/x data to show that umpires miscall the strike zone in favor of the home team by about 0.8 pitches a game (which is worth .015 in winning percentage, or about one-third of observed HFA). And, there was some work done my Mitchel Lichtman at "The Book" blog.

Second, I plan to show evidence that some of the performance differential is very unlikely to be caused by umpires or referees. For instance, suppose I find out that when putting the ball in play with nobody on and nobody out on a 2-1 count, home teams have significantly better outcomes than road teams. If that's the case, it can't have much to do with umpires, right? Because if the ball is put in play, the umpire doesn't have to make a call, except, perhaps, on a safe/out play, and we know those are rarely missed.

That sounds reasonable, but it's not necessarily right. Perhaps the reason road teams have worse ball-in-play outcomes (if in fact, they do) is that, knowing that umpires are biased against them, they have to swing at worse pitches to avoid taking an unwarranted strike. For that reason, it could be that the effect of umpires is much more than the 0.8 pitches a game. Indeed, it's logically possible that the *entire* home field advantage is caused by umpires. For instance, if the batter knows that he'll *never* get a called ball on a certain outside pitch, he'll swing at all of them. The bias will then show up only in the outcome of balls in play, and in extra (swinging) strikes, but not in extra called strikes.

So, you can't really be sure that the 0.8 figure isn't a biased, lowball estimate of the umpire's bias.

Still, you can probably argue that a large extra effect of this sort is implausible. If two-thirds of umpire bias was hidden by batters compensating, it would leave some evidence. You'd see a lot more swinging strikes for the visiting batters. You'd see a lot more balls in play for the visiting batters. You'd see lower pitch counts for the home pitcher, because the visiting hitters would be making contact more often.

Or would you? Maybe even those effects are too small to be seen with the naked eye, as it were. If it took many years of Pitch f/x data, and many years of waiting for John Walsh to notice an umpire bias of .015, who's to say that an additional umpire bias of .030 can immediately be seen in other stats?

Does anyone see a way out of this dilemma, or have any suggestions on what kind of evidence would help resolve the issue? The only one I can think of is NBA foul shooting, where there's absolutely no referee influence, but still a significant HFA. For baseball, though ... there's nothing like that that I can think of.

I might just have to bite the bullet and go with the argument I'm making here: that a large hidden umpire bias effect is implausible, but not impossible.

But if you have any ideas or comments, let me know.