For those of you who took advanced math courses on the promise that the knowledge gained would pay off handsomely and have spent decades waiting for that payoff, here it is (and sorry in advance for the letdown).

If two statistics are completely independent of one another, then I can change statistic #1 as much as I want and statistic #2 will stay the same. For instance, no matter how much I may think otherwise, whether I wear my Steelers jersey on autumn Sunday afternoons has no impact on whether Pittsburgh wins or loses on that day.

So as a test, I looked at various aspects of major league games to determine how they affect the number of runs that are scored. Obviously, the most important determinant is who is pitching. Ranked in various orders after that; who is hitting, the stadium in which the game is played, who is catching, how good the defensive players are behind the pitchers, and the weather.

One could look at statistics to figure things like this out. An easier way to figure out what impacts sporting events is to look at what gamblers consider. According to The Logical Approach, a site which provides information to gamblers to see what they feel gamblers need to know about before they bet on baseball games, the factor they provide the most information on might surprise you: umpires.

Why do they look at umpires? Well, it turns out that one of the most reliable ways to figure out whether a game will be high scoring is to know who is umpiring behind home plate. For example, when Clint Fagan was behind the plate in 2016, pitchers had an ERA of 5.62 and a K/BB ratio of 2.02, but when Lance Barrett was calling balls and strikes pitchers had an ERA of 3.94 and a K/BB ratio of 3.92. Each of these guys was behind the plate for thirty games in 2016, which is enough to rule out random variations, especially when we are talking about one guy calling strikes almost twice as much as the other.

This is not meant to be a gambling primer, although if you choose to use it that way, good luck to you. If you are betting the over/under on how many runs are scored in a game, you would think your most important piece of information would be who is pitching. But it turns out that umpires are almost as important. There were 74 pitchers last season with enough innings to qualify for the ERA title. 18 finished with better K/BB ratios with Barrett as an umpire. 11 finished with worse ratios with Fagan. Essentially, Barrett turned every pitcher into Corey Kluber, while Fagan turned them into Jered Weaver.

It’s not just these two guys either. The variability among the entire list of umpires is almost as great as it is among those 74 pitchers. Statistically speaking, there is no plausible explanation for this other than that Barrett has a strike zone that is substantially larger than Fagan’s, and that every other umpire defines the strike zone according to his peculiar tastes. Just to be fair, though, I figured maybe Fagan had a disproportionate number of games involving Jose Altuve, so I looked at 2017. This season, through games of July 31, pitchers had an ERA of 5.32 and a K/BB ratio of 2.44 with Fagan, and an ERA of 3.91 and K/BB ratio of 2.89 with Barrett. So both have moved toward the average, but each is still distinctly on the same side as their history suggests.

This isn’t just a baseball thing. You can find stats showing that some officiating crews in the NFL call pass interference or holding much more than others. But everyone involved in the NFL up to Roger Goodell himself will tell you that the pass interference rule is too vaguely worded and leaves itself open to arbitrary interpretation. The strike zone, on the other hand, is defined as “the area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the bottom of the knees, determined by the batter’s stance as the batter is prepared to swing.” Not much wiggle room there, but Barrett and Fagan seemed to have found some.

Actually, one of them could be right, but there’s no way that both of them are. Pitchers and hitters spend hours prior to each game scouting each other; they should not have to scout the umpires as well. By allowing this much discretion in the interpretation of the strike zone, Major League Baseball is stoking the fire for some sort of automated solution in the near future.