Atmosphere, Weather, and Baseball

Atmosphere, Weather, and Baseball: How Much Farther
Do Baseballs Really Fly at Denver’s Coors Field?
Frederick Chambers, Brian Page, and Clyde Zaidins
University of Colorado at Denver
This article tests the widely held assumption that batted baseballs travel 10 percent farther in Denver than in
major-league ballparks at sea level. An analysis of (1) National League fly-ball-distance data for 1995–1998,
(2) the micrometeorology of Coors Field, and (3) weather dynamics along the Colorado front range shows that
the assumed elevation enhancement of fly-ball distance has been greatly overestimated due to prevailing weather
conditions in downtown Denver. We conclude that the record number of home runs at Coors Field must be
attributed as much to the personnel of the Colorado Rockies team and the effects of mile-high elevation on the
act of pitching a baseball as to the effect of low air density on fly-ball distance. Key Words: baseball, geography of
sports, meteorology, urban climatology, urban geography.
Introduction
oors Field, the home of major-league baseball’s Colorado Rockies, opened in April
1995 in the Lower Downtown (LoDo) district
of central Denver. Just a decade before, LoDo
was a derelict urban landscape of crumbling
warehouses, shuttered factories, old flophouses,
and vacant lots—a place that most Denverites
actively avoided. Today, the district is the hub
of the city’s social life and a magnet for capital
investment. In amazing fashion and at an astounding rate, LoDo’s turn-of-the-century buildings have been converted into residential lofts,
upscale hotels, professional offices, restaurants,
brewpubs, art galleries, bookstores, coffee shops,
and nightclubs. But the jewel in LoDo’s crown
is undoubtedly Coors Field. The ballpark fits
marvelously into its environs. It echoes the scale,
design, and materials of adjacent brick warehouses and in so doing replicates the urbanity and
accessibility found in early twentieth century
ballparks such as Wrigley Field, Fenway Park,
and Ebbets Field—qualities that are sorely
lacking in the multipurpose stadiums built during
the 1960s and 1970s. LoDo’s gentrification was
well underway by the time Coors Field was
completed, but the ballpark nevertheless provided a powerful boost to local business expansion and is now the district’s most prominent
landmark.
While Coors Field has received accolades for
both its architectural beauty and its role in local
economic development, it has acquired quite a
C
different sort of reputation as a place to play
baseball. Since its inauguration, Denver’s Coors
Field has gained national notoriety as the ultimate home-run-hitter’s park—a ‘‘launching
pad’’ of historic proportions. Indeed, Coors
Field led all major-league ballparks in both total
home runs and home runs per at-bat during
seven of its first eight seasons ( James 1995,
1996, 1997, 1998, 1999, 2000; STATS Inc.
2001; Carter, Nistler, and Sloan 2002). Nearly
all observers, from noted physicists to veteran
players to casual fans, attribute the dramatic
home-run output at Coors Field to the effect of
thin air on the flight of a baseball. In theory, the
ball should travel about 10 percent farther in
Denver (elevation 5,280 ft) than it would in a
ballpark at sea level, an elevation enhancement
that prompted one prominent sports columnist
to call Coors Field ‘‘a beautiful joke [that] turns
the sport into a third-rate freak show’’ (Boswell
1998:1D). These comments are hardly atypical.
In fact, throughout the nation, Coors Field is
viewed as a curious anomaly that distorts our
cherished national pastime by transforming
mediocre hitters into stars.
We put such assumptions to the test in
this article. Does the ball really fly 10 percent
farther in Denver, as the laws of physics would
predict? And, is low air density really to blame
for the large number of home runs hit at Coors
Field? We address these questions through a
detailed analysis of the relationships between
atmosphere, weather, and baseball in Denver.
The analysis is presented in four sections. We
The Professional Geographer, 55(4) 2003, pages 491–504 r Copyright 2003 by Association of American Geographers.
Initial submission, July 2001; revised submission, May 2003; final acceptance, May 2003.
Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, and 9600 Garsington Road, Oxford OX4 2DQ, U.K.
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Volume 55, Number 4, November 2003
begin by discussing the physics of baseball, in
order to ascertain just how far the ball should
travel at mile-high elevation versus sea level.
Second, we compare expected fly-ball distances
to observed fly-ball distances through an examination of fly-ball-distance data for fourteen
National League ballparks. Our analysis of flyball distance spans the 1995–1998 seasons,
encompassing the first four seasons in which
baseball was played at the LoDo ballpark. These
data show that compared to other ballparks, fly
balls hit at Coors Field do not travel anywhere
near as far as one would expect given the low air
density in Denver. Third, we seek to explain this
discrepancy through an analysis of the weather at Coors Field, using data collected inside
the stadium during the 1997 season. Finally, we
expand our meteorological analysis by relating
ballpark-scale weather data to regional-scale weather data for northeastern Colorado.
Our overall argument is that the effect of thin
air on the flight of the baseball in Coors Field
is greatly overestimated, owing to the ways in
which general atmospheric forces are conditioned by specific geographic circumstances. In
this case, distinctive weather dynamics on the
front range of the Rocky Mountains, along with
topographic features of the South Platte River
valley and urbanization patterns in downtown
Denver, act to suppress the effect of low air
density on the flight of the baseball in Coors
Field. We conclude that a better understanding
of the ballpark’s dramatic home-run rate can be
gained by examining (1) the effects of the
personnel make-up of the Rockies team and
(2) the effects of mile-high elevation on the act
of pitching a baseball.
Fly-Ball Physics
The trajectory of any object in flight depends
upon several variables. In particular, the flight
of a batted baseball depends upon its initial
launch circumstances, the force of gravity,
and air resistance. The initial launch variables
include its starting velocity, angle of launch, and
rate of spin. The most important force
on the ball is gravity, and were it possible to
ignore the effect of the air, the trajectory could
be calculated with negligible uncertainty. This
is not the case, however, and predictions of
the exact path a ball will follow depend upon the
nature of the aerodynamic forces on the ball due
to the air.
We have constructed a mathematical model for
the fly ball based upon the discussions in Adair
(1990, 1994) and Brancazio (1984). An object’s
trajectory in a vacuum, where only gravity affects
the flight, was worked out by Galileo four centuries ago. The aerodynamics of an object’s path
in the air is far less well known even today. The
action of the air on the ball can be classified in
terms of the wind (which will vary with time and
location), the drag (which acts with a force that
opposes the motion of the ball), and the Magnus
force (which acts in a direction that is perpendicular to the ball’s velocity). Our model includes
all of these effects. A major goal of the model is
to predict the effect of altitude on the distance
the ball travels.
In our comparison of fly balls at sea level with
those at the altitude of Denver’s Coors Field, we
leave out the wind. For individual situations, the
wind is important, but comparisons among
different ballparks should be made for calm
conditions. Outfield fly balls will inevitably
leave the bat with backspin. In this case, the
Magnus force will provide a lift on the ball and
add a small percentage to the total distance.
This lift is proportional to both the drag and the
backspin rate and is true at sea level and in
Denver. These differences with respect to altitude are not significant.
By far the most important effect of air on the
trajectory is the resistance (drag). The standard
model for air resistance involves a dimensionless parameter known as the drag coefficient,
CD. Although there are experiments to measure
a baseball’s CD, it has a large uncertainty. The
complications in knowing its value are due to
(1) the fact that it is not constant but depends
upon the ball’s velocity and (2) the fact that it
is very sensitive to the smoothness of the ball’s
surface. This surface dependence is further
complicated by the ball’s stitches. The basic
idea is that if all other variables are the same, a
ball will travel farther at higher altitude. This is
due to the dependence of CD upon the density of
the air. The standard assumption that is used in
all such calculations in that CD is proportional
to the air density, r. This density, in turn, is
determined by the temperature, barometric
pressure, and altitude. It is also affected to
a lesser extent by the relative humidity. All
trajectory calculations do show an enhanced
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
fly-ball distance at Denver, but the enhancement
varies considerably with small changes in CD.
If we standardize our comparisons to 400foot fly balls at sea level with no wind, there
are still large variations. Adair (1990) predicts a
10 percent enhancement (4400 Denver vs. 4000
New York), but with some small changes in CD
he later (1994) predicts a 7.5 percent increase
(4300 Denver vs. 4000 New York). We have tried
several forms for CD and find predicted enhancements that range from 7 percent to over 13
percent. Given this, Adair’s original 10 percent
prediction seems a reasonable one, and, moreover, has become the accepted standard measure
of elevation enhancement at Coors Field.
We plan to refine our model and present
the details in another publication. There are
experimental approaches that would help to
clarify the air drag question. One approach
would be to study the baseball’s terminalvelocity behavior as a function of air density.
The terminal velocity is the speed an object reaches in free fall and is where the ball’s weight and
drag force are equal in strength. Another would
be to measure the distance of flight when fly
balls are mechanically launched with controlled
initial conditions at different altitudes. Until we
have a better model for CD, trajectory calculations will be subject to uncertainties. For
this reason, we take a conservative approach
in this article and use the middle-range estimate
of 10 percent.
Observed Fly-Ball Distances
in National League Ballparks
The physics of baseball gives us a very clear idea
of how much farther a baseball should travel
at Coors Field versus ballparks at sea level. Of
course, not all National League stadiums are
located at sea level, so we adjusted our model of
fly-ball trajectories to reflect the actual elevations of the league’s other ballparks. Compared
to the elevation-adjusted average of the other
National League ballparks, the ball should fly
9.3 percent farther in Denver.
Do these theoretical relationships hold true
in actuality? In order to answer this question,
we analyzed fly-ball distance data for fourteen
National League ballparks for 1995 through
1998.1 These data provide an estimate of the
distance traveled by every fly ball hit in fair
493
territory for every game played in the league
over four seasons, a total of nearly 8,000 fly
balls per ballpark and over 100,000 fly balls
overall. This sample size is more than sufficient
to detect any systematic enhancement of fly-ball
distance due to altitude.
The fly-ball distance data was obtained from
STATS Inc. This company records a wide range
of information for each baseball game played
in the major leagues, including the distance
traveled by every ball put into play. Our analysis focuses only on fly balls, as this is the type
of batted ball most affected by the dynamics of
atmosphere and weather. In every major-league
ballpark, STATS Inc. estimates the distance that
each fly ball travels by locating the final position
of the ball on a chart of the field. This method
yields estimated distance, not precise distance.
However, we believe that this data is reliable
because: (1) a consistent method is used at each
ballpark, and (2) the sample size is more than
large enough (over 100,000) to account for any
individual errors in fly-ball measurement (that
is, incidents of overestimation or underestimation should cancel each other out).
We averaged the 1995–1998 fly-ball-distance
data for fourteen National League ballparks,
including Coors Field. The results of our
analysis are quite surprising. The average flyball distance at Coors Field is 302.8 feet, while
the average at the other 13 ballparks is 284.5
feet. This is a difference of only 18.3 feet, not the
26.5 feet that Adair (1990) would predict on
the basis of decreased air density at mile-high
elevation. Thus, the ball does travel farther at
Coors Field, but not the expected 9.3 percent.
Compared to the average of the other National
League ballparks, the ball flies just 6 percent
farther in Denver (see Table 1).
Why do fly balls travel just 6 percent farther in
Denver? One possible answer is that variation
in fly-ball distance can be explained by baseball factors alone. After all, no two at-bats
are alike, and how far any batted ball travels is
the result of a complicated and unique set of
circumstances having to do with the particular pitcher and batter involved—including, for
instance, the pitcher’s skill level and orientation (left- or right-handed), the type and speed
of pitch thrown, the batter’s orientation, the
batter’s hand-eye coordination, and so forth.
For these reasons, we would expect fly-ball
distances to vary somewhat from ballpark to
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Volume 55, Number 4, November 2003
Table 1 Average Fly-Ball Distance in National
League Ballparks
Stadium
Coors Field
Atlanta (composite of
Turner and Fulton)
Chicago
Cincinnati
Florida
Houston
Los Angeles
Montreal
New York
Philadelphia
Pittsburgh
San Diego
San Francisco
St. Louis
NL Avg. w/out Coors Field
Four-Year Average
Distance (ft)
d Coors
(%)
302.8
290.8
4.0
283.8
284.9
282.2
286.7
291.6
281.3
282.5
290.8
282.2
277.6
271.1
293.1
284.5
6.3
5.9
6.8
5.3
3.7
7.1
6.7
4.0
6.8
8.3
10.5
3.2
6.0
ballpark over the course of several seasons. To
determine the influence of this routine, baseball-driven variation in fly-ball distance, we
analyzed average fly-ball distances for just those
National League stadiums located at sea level,
thus eliminating the elevation factor. We found
a standard deviation of plus or minus 6 feet in
fly-ball distance for this set of ballparks over
the four-year study period, which is far short
of the 18.3-foot difference between average flyball distance at Coors Field and average fly-ball
distance at the other National League parks.
According to our statistical analysis (a single
tailed Student’s t-test), this means that the
lower-than-expected difference between Coors
Field and the other National League ballparks
does not derive from baseball variables alone
(at the 90 percent confidence level).
If the routine vagaries of baseball cannot
account for the fact that fly balls do not travel
as far as expected in Denver, then we must
look elsewhere to address the question. Another
possible answer—and the one that we wish to
highlight in the next section—has to do with the
distinctive geographic circumstances of Coors
Field, particularly the weather.
Coors Field Meteorology
There have been several previous attempts to
link weather and baseball, although the results
of these studies have been inconclusive at
best (Kingsley 1980; Skeeter 1988; Kraft and
Skeeter 1995). In one study, Mark Kraft
and Brent Skeeter (1995) examined the effects
of temperature, humidity, and wind—both
direction and velocity—on fly-ball distances
in several major-league ballparks throughout
North America. Multiple regression analysis on
these variables yielded an R2 value of 0.062.
In other words, 6.2 percent of the variance
in fly-ball distance could be assigned to the
meteorological variables. Of these variables,
temperature, with an R2 value of 0.036, was
the single greatest contributor. Humidity and,
surprisingly, wind were considered to be relatively unimportant in the determination of how
far a baseball flies in major-league ballparks.
Part of the reason that this study showed no
significant relationship between weather variables and fly-ball distance has to do with the
source and character of the weather data upon
which the study was based. To begin with, the
weather data were collected at regional weather
stations that were not located in close proximity
to the ballparks. In addition, these data were
reported on only at the beginning of the game,
with no further updates on conditions as the
game progressed, even though all of the measured variables can and do change radically
over the span of an average three-hour baseball game. Further, wind was reported only
in descriptive terms as either ‘‘blowing in,’’
‘‘blowing out,’’ or ‘‘blowing across,’’ providing a
somewhat limited analytical basis. The authors
(1995, 48) readily acknowledge the limitations
of their data and conclude their article by stating
that ‘‘much more detailed studies, including
microclimatological analyses’’should be performed within the confines of individual ballparks
to better assess how meteorological variables
affect fly-ball distances.
Acting upon this suggestion, we set up two
meteorological stations inside Coors Field
for the duration of the 1997 baseball season.2
These stations were constructed atop concession stands along the rear concourse of the
ballpark. One station was located down the leftfield line, while the other was in straightaway
center field just beyond and above the bullpens (Figure 1). Weather variables monitored
included temperature, relative humidity, barometric pressure, and wind. Temperature and
relative humidity measurements were determined by a Campbell Scientific HMP35C
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
495
Figure 1 Location of weather instruments within Coors Field. Image courtesy of Landiscor Aerial
Information. Graphic illustration by Chris French.
Temperature and Relative Humidity Probe,
housed in a twelve-plate Gill radiation shield.
A Campbell Scientific CS105 Barometric Pressure Sensor measured barometric pressure,
while wind data was collected using R. M. Young,
Gill U-V-W Anemometers. These anemometers allow for three-dimensional profiling
of the wind: an east-west vector (U), a northsouth vector (V), and a vertical-angle vector
(W). From this data, wind azimuth, velocity,
and elevation angle may also be calculated.
Measurements were taken continuously during
game time and averaged every fifteen minutes.
Both the averaged and instantaneous values
were downloaded on the quarter-hour using a
Campbell Scientific 21X data-logger with storage
module. These results were then transferred and
analyzed utilizing the Microsoft Excel spreadsheet program. For each game for which weather
data were collected, averages of temperature,
relative humidity, barometric pressure, and wind
were determined (wind averages included all
permutations listed above).
This game-specific Coors Field weather data
was then related to game-specific Coors Field
average fly-ball-distance data. A correlation
matrix was developed on the data as part of
the initial statistical analysis (Table 2). As with
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Volume 55, Number 4, November 2003
Table 2 Correlation Matrix of Coors Field Average Fly-Ball Distance and Meteorological Variables
Avg. Dist.
Temp.
RH
U-vector
V-vector
W-vector
Azimuth
Wind Vel.
Elev. Angle
Avg. Dist.
Temp.
RH
U-vector
V-vector
W-vector
Azimuth
Wind Vel.
Elev. Angle
1.00
0.13
0.12
0.47
0.11
0.18
0.14
0.02
0.14
1.00
0.83
0.15
0.03
0.42
0.17
0.42
0.12
1.00
0.07
0.25
0.45
0.41
0.40
0.04
1.00
0.01
0.59
0.08
0.17
0.11
1.00
0.09
0.60
0.18
0.17
1.00
0.04
0.46
0.14
1.00
0.19
0.13
1.00
0.65
1.00
the results obtained by Kraft and Skeeter (1995),
it can be seen that temperature and relative
humidity have little, if any, correlative value
with fly-ball distance. Unlike the case with
that previous study, however, wind—especially
the U- (east-west) vector—does seem to be
correlative.
Stepwise multiple regression analysis was employed to determine the explanatory value (if
any) that could be attributed to meteorological
variables with respect to the fluctuation in flyball distance at Coors Field (Table 3). Only one
variable—the U-vector again—was statistically
significant (at a 95 percent confidence level)
Table 3 Stepwise Multiple Regression of Coors Field Average Fly-Ball Distance and Meteorological
Variables
Dependent variable: Average fly-ball distance
Parameter
Estimate
Standard Error
Constant
U-vector
299.052
16.1962
3.87306
6.05091
T Statistic
77.2134
2.67665
p-value
0.0000
0.0129
Analysis of Variance
Source
Sum of Squares
Model
2901.54
Residual
10124.8
Total (Corr.)
13026.3
R-squared ¼ 22.2744 percent
R-squared (adjusted for d.f.) ¼ 19.16544 percent
Standard error of estimate ¼ 20.1244
Mean absolute error ¼ 17.0508
Durbin-Watson statistic ¼ 1.86565
Df
Mean Square
F-Ratio
p-value
1
25
26
2901.54
404.992
7.16
0.0129
Stepwise Regression
Method: forward selection
F-to-enter: 4.0
F-to-remove: 4.0
Step 0:
0 variables in the model. 26 d.f. for error.
R-squared ¼ 0.00%
Adjusted R-squared ¼ 0.0%
Step 1:
Adding variable U-vector with F-to-enter ¼ 7.16445
R-squared ¼ 22.27%
Adjusted R-squared ¼ 19.17%
Final model selected.
MSE ¼ 501.013
MSE ¼ 404.992
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
enough to enter the model in this test. This
resulted in an R2 value of 0.223, or an R2 value
of 0.192 when adjusted for degrees of freedom.
Simply stated, this indicates that almost 20
percent of the variation in fly-ball distance at
Coors Field can be attributed to differences in
winds along the east-west vector, with all other
variables playing an insignificant role.
Further examination of the U-vector reveals
some interesting information. During the 1997
season, winds blowing with an easterly component inside Coors Field exhibited almost twice
the intensity of westerly winds—approximately
12 miles per hour, versus 6. Additionally, average fly-ball distances decreased under an easterly wind regime (approximately 290 feet with
easterly winds versus over 303 feet with a
western component). Correlation analysis of
wind direction and fly-ball distances verified
these results. Average fly-ball distances displayed a negative correlation with east winds
(r-value ¼ 0.45), and a positive correlation
with west winds (r-value ¼ 0.49).
Easterly winds are clearly implicated in the
observed suppression of fly-ball distance at
Coors Field. In order to get a better understanding of this relationship, however, it is first
necessary to examine the broader wind regime
in and around the Denver ballpark.
497
Regional Wind Patterns in
Northeastern Colorado
The summer wind pattern in northeastern
Colorado is dominated by a persistent upslopedownslope regime. This diurnal pattern, similar
to that seen in smaller-scale mountain valley
locales, occurs on a regional scale here. James
Toth and Richard Johnson (1985) describe the
pattern as occupying the entire South Platte
River valley drainage system. The Cheyenne
Ridge to the north, the Continental Divide to
the west, and the Palmer Divide to the south
enclose this basin (Figure 2). Under this regime,
heating of the east-facing foothills in the
morning hours causes air to flow up the South
Platte River valley in the late morning through
the evening hours. This flow reaches a peak
in the vicinity of Denver at around 1500 to 1600
hours local standard time (LST). Thereafter in
the Denver area, winds weaken and eventually
shift to a southerly direction before becoming
westerly beginning in the hours between 2200
and midnight LST. This downslope pattern
persists until the process reverses itself the
following morning.
The South Platte River flows from the southwest to the northeast in the vicinity of Coors
Field (Figures 3, 4). Therefore, any up-valley
Figure 2 Diurnal wind patterns in northeastern Colorado. (A) 6:00 a.m.: peak down-valley winds. (B) 4:00
p.m.: peak up-valley winds.
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Volume 55, Number 4, November 2003
Figure 3 Proximity of Coors Field to Platte River Valley and Rocky Mountains. Image courtesy of Landiscor
Aerial Information. Graphic illustration by Chris French.
winds will be northeasterly, while downvalley winds will be southwesterly. In an effort
to verify this wind pattern in the vicinity of
Coors Field, we examined data provided by
Denver’s Air Quality Control Division, which
has several air-quality monitoring stations in
and around the Denver metropolitan area.3
These stations measure pollution as well as
wind direction and velocity. Wind data was
analyzed from the two stations closest to the
ballpark; one of these stations is within two city
blocks of Coors Field. Data on wind direction
and velocity from these stations were averaged
hourly for each month of the baseball season,
April through September, for the years 1995
to 1998.
The results verify the regional-scale diurnal
pattern described above. Northeasterly winds
dominated the afternoon and evening hours of
this four-year long period. In fact, our results
showed that during this time there was never a
westerly component to the average wind vector
between the hours of noon and 2200 hours LST,
the time period in which almost all Rockies
games are played. Certainly, this is not to say
that westerly winds do not occur. Indeed, they
do, as we found during our data collection inside Coors Field. It would seem, however, that
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
499
Figure 4 Relative location of Coors Field to South Platte River. Satellite photo courtesy of Space Imaging.
Graphic illustration by Chris French.
these wind vectors are the exception to the rule.
A westerly component to the wind during
the months in question most likely occurs in
response to either (1) local convective systems
or (2) synoptic-scale atmospheric features (e.g.,
frontal passages). In any event, westerly flow
regimes would seem to be relatively brief events,
followed by a return to the more routine upslopedownslope pattern.
Northeasterly winds would thus appear to
be the causal mechanism that explains shorterthan-expected average fly-ball distances at Coors
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Volume 55, Number 4, November 2003
Field. These winds flow up the South Platte
River valley and enter the vicinity of the ballpark
from the northeast. Within Coors Field, northeasterly winds blow from center field toward
home plate, directly into the face of the batter
and into the path of batted balls hit to all segments of the outfield (Figure 4).
Further, we believe that this regional wind
regime is accentuated by the location of Coors
Field with respect to other geographic features
in the area. The first of these is the topography
of the South Platte River valley, which rises to the
northwest and also narrows in the vicinity of
the ballpark. The other feature is the pattern
of urbanization in downtown Denver, one characterized by a massing of buildings running
parallel to the South Platte River Valley on its
southeastern bank beginning just to the northeast of Coors Field. We believe that during the
up-valley period (northeasterly winds during
the day and evening hours), the air flowing
to the southwest is constricted somewhat by
the combined effects of topography and urban
development (Figures 3, 4). In all likelihood,
this produces a funnel-like effect on winds
streaming into LoDo and may result in increased wind velocities in this area. Additional
research will be necessary to validate this claim.
Conclusion
The laws of physics tell us that a baseball should
travel 10 percent farther in the mile-high
atmosphere of Denver than at sea level. Moreover, fly balls should travel 9.3 percent farther in
Denver than the elevation-adjusted average of
thirteen other National League ballparks. Our
conclusion, however, is that these theoretical
fly-ball trajectories, calculated on the basis of
comparative air density, do not hold true upon
the examination of fly-ball distance data. In fact,
for the 1995–1998 seasons, fly balls traveled
just 6 percent farther in Denver compared to
the average of thirteen other National League
ballparks. The results of our meteorological
analysis of Coors Field and its surrounding area
suggest that the key factor in this suppression
of fly-ball distance is weather—specifically, the
dominance of northeasterly winds in the vicinity
of the ballpark during afternoon and evening
hours. These wind conditions exists due to
a regional-scale, diurnal, upslope-downslope
wind pattern in the South Platte River valley
and, we suggest, are accelerated by local topography and urban massing.
Our assessment is that these daily northeasterly winds suppress fly-ball distances at
Coors Field. These winds flow up the South
Platte River valley and enter the vicinity of the
ballpark from the northeast. Within Coors
Field, the winds blow from center field toward
home plate into the face of the batter and into
the path of batted balls hit to all parts of the
outfield. The expected advantage of playing
at mile-high elevation (as far as home runs
are concerned) is decreased substantially under
such conditions. However, when the winds are
out of the west, the full elevation advantage
can be realized. Such conditions can lead
to spectacular fly-ball trajectories, especially to
right field. Thus, the effect of the wind is variable: during some games, altitude’s enhancement of fly-ball distance will occur, and in other
games it will be suppressed. But over the course
of a season—or several seasons—wind acts to
minimize the effect of low air density and thus
accounts for the shorter-than-expected fly-ball
distances at Coors Field.
Finally, let us return to the question raised
at the outset concerning the character of baseball games played at Coors Field. While the
suppression of fly-ball distance due to prevailing
northeasterly winds is significant, keep in mind
that the boosting effect of altitude on home-run
production in Denver is further minimized
by the generous outfield dimensions at Coors
Field, the league’s most spacious ballpark. Indeed, in order to come up with a measure of just
how much more likely it is for home runs to
occur at Coors Field due to low air density, one
must take into consideration actual field dimensions around the league. We made this adjustment by calculating average fly-ball distance as a
percentage of average outfield dimension for
fourteen National League ballparks (Table 4).4
This calculation yields a measure of how far the
average fly ball travels relative to the average
position of the outfield fence in each ballpark. As the table shows, when field dimensions
are taken into account, the effective difference
between Coors Field and the other National
League stadiums is not even 6 percent—it is
just 3 percent. Moreover, the difference between Coors Field and the stadiums in Philadelphia, Los Angeles, and Atlanta is minimal,
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
501
Table 4 Average Fly-Ball Distance versus Stadium Dimensions in National League Ballparks
Avg. Flyball Dist.
Average Outfield
Dimension (ft)
d Coors
(%)
Coors Field
Atlanta (composite of Turner and Fulton)
Chicago
Cincinnati
Florida
Houston
Los Angeles
Montreal
New York
Philadelphia
Pittsburgh
San Diego
San Francisco
St. Louis
375.4
366.7
368.8
362.8
369.8
360.0
365.0
360.8
368.4
362.0
364.0
360.2
358.6
362.0
2.3
1.8
3.4
1.5
4.1
2.8
3.9
1.9
3.6
3.0
4.0
4.5
3.6
80.7
79.3
77.0
78.5
76.3
79.6
79.9
78.0
76.7
80.3
77.5
77.1
75.6
81.0
1.7
4.6
2.6
5.4
1.3
1.0
3.3
4.9
0.4
3.9
4.5
6.3
0.4
NL Avg. w/out Coors Field
363.8
3.1
78.2
3.1
Stadium
while the average fly ball actually carries closer
to the outfield wall at St. Louis’s Busch Stadium
than it does at Coors Field.5 Faced with these
numbers, the facile assumption that elevation
enhancement of fly-ball distance is responsible
for the large number of home runs in Denver
vanishes into so much thin air.
What else might account for the impressive
home run statistics in Denver? After all, during
the 1995 through 2002 seasons, Coors Field
witnessed a rate of .044 home runs per at bat,
while the combined average of the other National League parks was just .029 home runs per at
bat. In other words, home runs occur at Coors
Field at a rate that is 52 percent greater than at
the other ballparks—far more than would be
expected even if the mile-high atmospheric
enhancement was realized to its fullest ( James
1995, 1996, 1997, 1998, 1999, 2000; Carter,
Nistler, and Sloan 2002; STATS Inc. 2001). We
believe that the answer to this question has to do
with two factors: first, the personnel make-up
of the Colorado Rockies ball club in terms of
both hitters and pitchers; and second, the
general problems of pitching at altitude.
During the first several seasons played at
Coors Field, the Rockies team was stacked
with notable power hitters. Simply put, they
were a team designed to produce large numbers
of home runs. However, over the past several
years, these ‘‘Blake Street Bombers’’ have been
traded or allowed to leave via free agency, as
team management has shifted focus from
home-run hitters to high-average hitters with
* (100)
Outfield Dimension
d Coors (%)
less power. This personnel shift is verified in the
record of Coors Field hitting statistics. Since
1995, there has been an overall downward
trend in the number of home runs per at-bat—
a trend that is accounted for by a reduction in
the number of home runs hit by the Rockies (the
trend in home runs per at-bat for the opposition
at Coors Field has risen) (Figure 5). In fact,
by the 2000 season, Coors Field had been
Total HRs/AB
0.06
0.05
0.04
0.03
0.02
0.01
0
1995 1996 1997 1998 1999 2000 2001 2002
Rockies HRs/AB
0.06
0.05
0.04
0.03
0.02
0.01
0
1995 1996 1997 1998 1999 2000 2001 2002
Opposing Team HRs/AB
0.06
0.05
0.04
0.03
0.02
0.01
0
1995 1996 1997 1998 1999 2000 2001 2002
Figure 5 Coors Field home runs per at-bat,
1995–2002.
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Volume 55, Number 4, November 2003
surpassed in home runs per at-bat by both Busch
Stadium in St. Louis and Enron Field in
Houston. Thus, the large number of home runs
hit at Coors Field can be attributed, in part, to
the specific group of hitters assembled early on
by the Rockies. Once the franchise changed
the character of the team, the preeminence of
Coors Field as the league’s ultimate home-run
ballpark was somewhat diminished.
The Rockies have also lacked successful pitching for most of their history. Colorado pitchers
have had more than their share of problems
over the past eight years, both at home and on
the road. Between 1995 and 2002, the team
was either last or next to last in most pitching categories, leading the league in home runs
allowed seven times. Had the Los Angeles or
New York staffs pitched at Coors Field for
eighty-one games per year, the ballpark’s homerun totals would most likely have been significantly less. Put Atlanta’s pitching staff in
Denver for half of their games and this reduction is a virtual certainty. Remember that Atlanta’s
Fulton County Stadium was known as the
‘‘launching pad’’ until the Braves put together
the league’s premier group of pitchers in the
early 1990s.
But perhaps the most important factor in
explaining the home-run numbers in Denver
is the ‘‘Coors Field Effect’’—the not-so-subtle
influence of the ballpark on pitchers from both
the home and visiting teams. Most of these
professional athletes are clearly intimidated
by Coors Field. As one player recently observed, the ballpark causes ‘‘an identity crisis’’ for
pitchers, leading them to change their approach
to the game, move away from their strengths,
and ultimately lose confidence in their abilities ( pitcher Denny Neagle of the Colorado
Rockies, quoted in Renck 2003, 14D). Even the
league’s best pitchers often come unglued in
Denver. Pitching is undeniably more difficult
in Coors Field than in other National League
ballparks because of the very limited foul
ground and the cavernous outfield spaces. This
field configuration gives hitters more chances,
allows more balls to drop in front of outfielders,
and permits more balls to find the gaps for extrabase hits. Yet beyond this, most pitchers are
beset with a range of other problems once they
take the mound. Chief among these are a sudden
lack of control, breaking balls that do not break,
and sinker balls that do not sink. The result is
more pitches thrown straight and over the heart
of the plate, and more balls hit high, deep, and
out the park. Thus, what we suggest is that more
home runs are hit at Coors Field, not because
routine fly balls carry farther, but because a
higher proportion of pitched balls are hit harder
than in other ballparks.
These pitching problems in Denver have also
been attributed to low air density. Theoretically, thin air reduces ball-to-air friction, cutting down on ball movement between the
mound and home plate and thus decreasing
the overall control of the pitcher and the effectiveness of the pitches thrown. In addition, the
low relative humidity at altitude promotes
evaporation from the baseball itself, making
the ball lighter, drier, and slicker in Denver than
in other parks around the league. Because of
this, pitchers at Coors Field have a very difficult
time getting a proper grip on the ball, which, in
all likelihood, further reduces their control as
well as the movement on their pitches.6 During
the 2002 season, in an effort to counteract the
presumed effects of thin air on pitching,
the Colorado Rockies began using a ‘‘humidor’’
to store baseballs at Coors Field. This device
maintains the balls in a controlled environment
of 90 degrees Fahrenheit and 40 percent
humidity. According to the Rockies organization, the intent of the humidor is to ensure
that the baseballs do not shrink to a weight less
than the 5.0 to 5.25 ounces specified by the
league. The Rockies ball club also believes
that these baseballs, having not yet lost water
content to evaporation when they enter play, are
easier to grip and thus will ‘‘level the playing
field’’ for pitchers in Denver. This might just be
wishful thinking, however: a comparison of the
statistics for the 2002 season versus the previous seven seasons indicates that the humidor
had little, if any, effect upon games played at
Coors Field.7
Ultimately, these altitude-related issues may
prove to be important contributors to the poor
pitching in Denver. For now, however, difficulties on the mound would seem to be more the
result of the fragile psychology of pitchers faced
with the imagined specter of baseballs floating
out of Coors Field like weather balloons. Based
upon the analysis presented above, we believe
that the answer to why so many home runs are
hit at Coors Field lies as much on the field as it
does in the air. ’
How Much Farther Do Baseballs Really Fly at Denver’s Coors Field?
503
Notes
Literature Cited
1
Adair, Robert K. 1990. The Physics of Baseball. New
York: HarperPerennial.
———. 1994. The Physics of Baseball. 2nd ed. New
York: HarperPerennial.
Boswell, Thomas. 1998. Coors Field is a mistake that
mustn’t be repeated. Denver Post 10 July: 1D, 6D.
Brancazio, Peter J. 1984. SportScience: Physical Laws
and Optimum Performance. New York: Simon and
Schuster.
Carter, Craig, Tony Nistler, and David Sloan. 2002.
Baseball Guide, 2003 Edition. St. Louis, MO: The
Sporting News.
James, Bill. 1995. Major League Baseball Handbook
1996. Skokie, IL: STATS, Inc.
———. 1996. Major League Baseball Handbook 1997.
Skokie, IL: STATS, Inc.
———. 1997. Major League Baseball Handbook 1998.
Skokie, IL: STATS, Inc.
———. 1998. Major League Baseball Handbook 1999.
Skokie, IL: STATS, Inc.
———. 1999. Major League Baseball Handbook 2000.
Skokie, IL: STATS, Inc.
———. 2000. Major League Baseball Handbook 2001.
Skokie, IL: STATS, Inc.
Kingsley, R. H. 1980. Lots of home runs in Atlanta?
Baseball Research Journal 2:66–71.
Kraft, Mark D., and Brent R. Skeeter. 1995. The effect
of meteorological conditions on fly ball distance in
North American major league baseball games. The
Geographical Bulletin 37 (1): 40–48.
Moss, Irv. 1999. Braves contend Coors baseballs are
slicker. Denver Post 9 May:18C.
Renck, Troy. 2003. Neagle staying true to form.
Denver Post 5 March: 14D.
Skeeter, Brent R. 1988. The climatologically optimal
major league baseball season in North America. The
Geographical Bulletin 30 (2): 97–102.
STATS, Inc. 2001. Major League Baseball Handbook
2002. Skokie, IL: STATS, Inc.
Toth, James J., and Richard H. Johnson. 1985.
Summer surface flow characteristics over northeastern Colorado. Monthly Weather Review 113 (9):
1458–69.
Because the time frame of our analysis is 1995–1998,
we used only those cities with ballparks that were
utilized for National League games during all four
years. County Stadium in Milwaukee and Bank One
Ballpark in Phoenix were excluded from the analysis
because National League games were not played
in these stadiums in 1995, 1996, or 1997 (see
Table 1).
2
The Colorado Rockies Baseball Club allowed us
access to Coors Field in order to set up our weather
equipment and to periodically check on the instruments and download data. It should be emphasized
that the Rockies organization did not solicit this
study, nor did they offer or provide any support for
the research.
3
These data were provided by the Colorado Department of Public Health and Environment, Air
Pollution Control Division (APCD) for the years
1995–1998.
4
Average outfield dimension was obtained by averaging the distances at five points along the outfield
wall for each ballpark: the left field line, left center
field, center field, right center field, and the right
field line. In a few cases, the dimensions of the
outfield were changed in an existing ballpark during
our four-year study, or a team changed ballparks
altogether. In these cases, we used an average of
the old and new dimensions. The source used for
establishing average outfield dimension was James
(1996, 1997, 1998, 1999).
5
If Mark McGwire had played for the Colorado Rockies
during 1998, his pursuit of the single-season homerun record would have been hounded by the asterisk of elevation-enhanced play. Instead, McGwire
conducted his quest in St. Louis, protected by a
hallowed baseball tradition and unfettered by any
lingering doubts, while nevertheless enjoying the
advantages of a ballpark that is every bit as conducive
to home-run production as Coors Field in terms of
how far the average fly ball carries relative to the
average position of the outfield fence.
6
For years, manager Bobby Cox of the Atlanta Braves
has blamed Denver’s aridity for the pitching problems
at Coors Field, citing the dryness of the ball and his
pitchers’ problems with grip (Moss 1999).
7
For the 2002 season, runs per at-bat and hits per
at-bat were down slightly but registered at levels
very similar to past seasons, while home runs per
at-bat were higher than some previous years. In
addition, strikeouts per at-bat were significantly
lower than the previous season, and base-on-balls
(walks) per at-bat did not register historic lows,
as might have been expected ( James 1995, 1996,
1997, 1998, 1999, 2000; STATS, Inc. 2001; Carter
et al. 2002).
FREDERICK CHAMBERS is an associate professor
in the Department of Geography and Environmental
Sciences, University of Colorado at Denver, Denver,
CO 80217-3364. E-mail: [email protected].
edu. His current research includes investigating micrometeorological variables over new and recent lava
flows, detection of ‘‘urban heat island’’ effects in the
meteorological records of Colorado mining towns,
and western North American glacier-climate interrelationships.
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Volume 55, Number 4, November 2003
BRIAN PAGE is an associate professor in the Department of Geography and Environmental Sciences, University of Colorado at Denver, Denver, CO 802173364. E-mail: [email protected]. His research
interests include the interpretation of cultural landscapes in the American past, the historical geography
of regional growth and change in the West and
Midwest, and the political ecology of agriculture
and resource development.
CLYDE ZAIDINS is a professor in the Department
of Physics, University of Colorado at Denver, Denver,
CO 80217-3364. Email: [email protected].
edu. His areas of research interest are in astrophysics
and nuclear physics, and he has taught all levels of
undergraduate physics courses. His father, Morris
Zaidins, worked for the Cincinnati Reds from 1937
to 1974.