The Physics of Coors Field’s Higher Fence

Coors Field’s outfield fence got an alteration last season. (via Matt Dirksen, Colorado Rockies)

Baseball exhibits the same nuances as humans–not surprising given humans invented the game. Both are governed by a stringent set of rules. Yet, within those tight regulations mankind and baseball both seem to possess nearly infinite variation.

Human life can exist only within very proscribed boundaries. For example, we could have evolved only on a planet that is not too close to a star or it would be too hot, and we can’t be too far away where it would be too cold. We could have happened only within the so-called “Goldilocks Zone.” Indeed, things had to be “just right.”

Yet within these stringent rules, a wondrous carnival of variations emerges. Humans have different eye colors, a variety of skin tones, a broad range of heights and weights, and a wide diversity of other traits that make the human drama so fascinating.

Baseball, too, has highly proscribed rules. The distance between the rubber and home plate must be 60.5 feet. The ball must be between 2.86 and 2.94 inches in diameter and weigh between 5.00 and 5.25 ounces. It must have 216 stitches. The bat can be no larger than 2.61 inches across. As sportswriter Red Smith once put it, “Ninety feet between home plate and first base may be the closest man has ever come to perfection.”

However, within these tight regulations there is such a plethora of possibilities. One of the clearest variations from ballpark to ballpark is in the outfield. Of all things, there are few rules governing the distance to and height of the fences. That brings us to Coors Field, where the game is played a mile high…I guess I could have phrased that better.

Due to the thinner air, balls travel farther there than at other major league parks. To maintain some sense of equity, the fences in Denver are deeper, making the outfield the second-largest in baseball, about 7.5 percent larger than average. The only larger outfield belongs to Kansas City. Yet, since 2007, Kauffman Stadium averaged about three quarters of a homer fewer per game than Coors.

The table above is created using data from ESPN Home Run Tracker. It shows the first-, second-, and third-ranked parks for average home run distance for each year since 2007. You can see Coors Field dominates the list due to two factors. The first, of course, is the thinner air. The second reason is the same reason Kauffman Stadium is ranked consistently high; the fences are simply farther away. Alan Nathan came to the same conclusion regarding the length of homers in Denver using Statcast data.

So, what can be done to make Coors Field more consistent with other ball yards? In 2002, the Rockies began storing their baseballs in humidors, which slightly reduced homer production. Since then, there has been much hand wringing (especially by pitchers) and little done until the 2016 addition of higher fences. The Rockies added green-coated, chain-link fence 8.75 feet high atop the wall from right-center to right field. In addition, they added similar fencing five feet high along the left field line in front of the tunnel next to the bleachers.

The purpose, according to manager Walt Weiss, was to eliminate some of the “cheaper home runs.” The Rockies management hoped these changes would result in a decrease of five to six percent in total homers. How did it all work out?

With only one season of data since the increase in fence height, the results were not consistent with the predictions. In 2015, Coors Field saw 202 dingers while the tally for 2016 actually rose to 215. Oops. The league-wide home run increase last year affected things enough that just looking at the total homers isn’t going to tell much of a story. Let’s instead look at the homers that went into the seats where the new fence in right field was added.

Since Statcast doesn’t share the spray angle or the precise landing location of homers, I used ESPN Home Run Tracker to look for homers in 2015 and 2016 that went into region where the higher fence now exists. In 2015, a total of 53 round-trippers entered the region, while last year only 41 did, a 22 percent decrease despite the overall increase in four-baggers.

Figuring out exactly which of the 2015 homers would not have been homers in 2016 is much more of a challenge, because one would have to very carefully calculate the trajectory of each one and see if it cleared the 2015 wall by 8.75 feet or more. I’m lazy, so instead I used the JE designation in the ESPN Home Run Tracker data base.

JE (just enough) means “the ball cleared the fence by less than 10 vertical feet, or that it landed less than one fence height past the fence. These are the ones that barely made it over the fence.” Clearing the fence by 10 feet is close enough to 8.75 feet in my book, since any trajectory calculations I might have done would have had random errors of a few feet anyway. By this guestimate, there were 17 homers in 2015 that would not be homers in 2016. Here they are ranked by maximum height.

An interesting feature of these results is that the new fence would have stopped only three arcing flyball homers, while it ended the flight of 14 lower trajectories. One could argue the added fence is five times more likely to stop a hard-hit drive than a high arcing “cheap homer.” This might be explained by some basic physics, which I call the Window Blind Effect.

When the blinds are closed, they are perpendicular to your line of sight. When they are open, they are parallel so you can see through the window. So, the amount of light they block depends upon the how they are oriented relative to the direction you are looking.

Now, imagine you are a ball on a flat trajectory headed toward the new fence. The blinds look more closed to you than if you are a high fly ball heading downward toward the top of the fence. The point is, the added fence will block more liners than fly balls.

If only this were the cause of the disparity between lost homers that were fly balls and those that were line drives. Below is a plot of the home runs in 2016 versus their launch angle.

The fact is, the great majority have launch angles below 30˚. Only 25 percent have launch angles greater than 30˚. So there may be no physics needed to explain the disparity in line drive homers and high arcing ones. It is simply a matter of a higher probability of the lower trajectories. So, much for science…I guess it’s just statistics.

References & Resources

• ESPN Home Run Tracker
• Andrew Fox, Fangraphs Community Research, “Complete Outfield Dimensions”
• Alan Nathan, The Hardball Times, “Going Deep on Going Deep”
• David Kagan & David Atkinson, The Physics Teacher, “The Coefficient of Restitution of Baseballs as a Function of Relative Humidity”