Atmosphere, Weather, and Baseball: How Much Farther...

Atmosphere, Weather, and Baseball: How Much FartherDo Baseballs Really Fly at Denver’s Coors Field?

Frederick Chambers, Brian Page, and Clyde ZaidinsUniversity of Colorado at DenverThis article tests the widely held assumption that batted baseballs travel 10 percent farther in Denver than inmajor-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 thatthe assumed elevation enhancement of fly-ball distance has been greatly overestimated due to prevailingweatherconditions in downtown Denver. We conclude that the record number of home runs at Coors Field must beattributed as much to the personnel of the Colorado Rockies team and the effects of mile-high elevation on theact of pitching a baseball as to the effect of low air density onfly-ball distance.KeyWords: baseball, geographyofsports, meteorology, urban climatology, urban geography.

Introduction

Coors Field, the home of major-league base-ball’s Colorado Rockies, opened in April

1995 in the Lower Downtown (LoDo) districtof central Denver. Just a decade before, LoDowas a derelict urban landscape of crumblingwarehouses, shuttered factories, old flophouses,and vacant lots—a place that most Denveritesactively avoided. Today, the district is the hubof the city’s social life and a magnet for capitalinvestment. Inamazing fashionandat anastound-ing rate, LoDo’s turn-of-the-century build-ings 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 crownis undoubtedly Coors Field. The ballpark fitsmarvelously into its environs. It echoes the scale,design, and materials of adjacent brick ware-houses and in sodoing replicates theurbanityandaccessibility found in early twentieth centuryballparks such as Wrigley Field, Fenway Park,and Ebbets Field—qualities that are sorelylacking in themultipurpose stadiumsbuilt duringthe 1960s and 1970s. LoDo’s gentrification waswell underway by the time Coors Field wascompleted, but the ballpark nevertheless pro-vided a powerful boost to local business expan-sion and is now the district’s most prominentlandmark.

While Coors Field has received accolades forboth its architectural beauty and its role in localeconomic development, it has acquired quite a

different sort of reputation as a place to playbaseball. Since its inauguration, Denver’s CoorsField has gained national notoriety as the ulti-mate home-run-hitter’s park—a ‘‘launchingpad’’ of historic proportions. Indeed, CoorsField led all major-league ballparks in both totalhome runs and home runs per at-bat duringseven of its first eight seasons ( James 1995,1996, 1997, 1998, 1999, 2000; STATS Inc.2001; Carter, Nistler, and Sloan 2002). Nearlyall observers, from noted physicists to veteranplayers to casual fans, attribute the dramatichome-run output at Coors Field to the effect ofthin air on the flight of a baseball. In theory, theball should travel about 10 percent farther inDenver (elevation 5,280 ft) than it would in aballpark at sea level, an elevation enhancementthat prompted one prominent sports columnistto call Coors Field ‘‘a beautiful joke [that] turnsthe sport into a third-rate freak show’’ (Boswell1998:1D). These comments are hardly atypical.In fact, throughout the nation, Coors Field isviewed as a curious anomaly that distorts ourcherished national pastime by transformingmediocre hitters into stars.We put such assumptions to the test in

this article. Does the ball really fly 10 percentfarther in Denver, as the laws of physics wouldpredict? And, is low air density really to blamefor the large number of home runs hit at CoorsField? We address these questions through adetailed analysis of the relationships betweenatmosphere, 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.

begin by discussing the physics of baseball, inorder to ascertain just how far the ball shouldtravel at mile-high elevation versus sea level.Second, we compare expected fly-ball distancesto observed fly-ball distances through an ex-amination of fly-ball-distance data for fourteenNational League ballparks. Our analysis of fly-ball distance spans the 1995–1998 seasons,encompassing the first four seasons in whichbaseball was played at theLoDoballpark.Thesedata show that compared to other ballparks, flyballs hit at Coors Field do not travel anywherenear as far as one would expect given the low airdensity inDenver. Third, we seek to explain thisdiscrepancy through an analysis of the wea-ther at Coors Field, using data collected insidethe stadium during the 1997 season. Finally, weexpand our meteorological analysis by relatingballpark-scaleweatherdata toregional-scalewea-ther data for northeastern Colorado.

Our overall argument is that the effect of thinair on the flight of the baseball in Coors Fieldis greatly overestimated, owing to the ways inwhich general atmospheric forces are condi-tioned by specific geographic circumstances. Inthis case, distinctive weather dynamics on thefront range of the RockyMountains, along withtopographic features of the South Platte Rivervalley and urbanization patterns in downtownDenver, act to suppress the effect of low airdensity on the flight of the baseball in CoorsField. We conclude that a better understandingof the ballpark’s dramatic home-run rate can begained by examining (1) the effects of thepersonnel make-up of the Rockies team and(2) the effects of mile-high elevation on the actof pitching a baseball.

Fly-Ball Physics

The trajectory of any object in flight dependsupon several variables. In particular, the flightof a batted baseball depends upon its initiallaunch circumstances, the force of gravity,and air resistance. The initial launch variablesinclude its starting velocity, angle of launch, andrate of spin. The most important forceon the ball is gravity, and were it possible toignore the effect of the air, the trajectory couldbe calculated with negligible uncertainty. Thisis not the case, however, and predictions ofthe exact path a ball will follow depend upon the

nature of the aerodynamic forces on the ball dueto the air.Wehave constructed amathematicalmodel for

the fly ball based upon the discussions in Adair(1990, 1994) and Brancazio (1984). An object’strajectory in a vacuum, where only gravity affectsthe flight, was worked out by Galileo four cen-turies ago. The aerodynamics of an object’s pathin the air is far less well known even today. Theaction of the air on the ball can be classified interms of the wind (which will vary with time andlocation), the drag (which acts with a force thatopposes the motion of the ball), and the Magnusforce (which acts in a direction that is perpendi-cular to the ball’s velocity). Our model includesall of these effects. A major goal of the model isto predict the effect of altitude on the distancethe ball travels.In our comparison of fly balls at sea level with

those at the altitude ofDenver’s Coors Field, weleave out thewind. For individual situations, thewind is important, but comparisons amongdifferent ballparks should be made for calmconditions. Outfield fly balls will inevitablyleave the bat with backspin. In this case, theMagnus force will provide a lift on the ball andadd a small percentage to the total distance.This lift is proportional to both the drag and thebackspin rate and is true at sea level and inDenver. These differences with respect to alti-tude are not significant.By far the most important effect of air on the

trajectory is the resistance (drag). The standardmodel for air resistance involves a dimension-less parameter known as the drag coefficient,CD. Although there are experiments to measurea baseball’s CD, it has a large uncertainty. Thecomplications in knowing its value are due to(1) the fact that it is not constant but dependsupon the ball’s velocity and (2) the fact that itis very sensitive to the smoothness of the ball’ssurface. This surface dependence is furthercomplicated by the ball’s stitches. The basicidea is that if all other variables are the same, aball will travel farther at higher altitude. This isdue to thedependence ofCDupon thedensity ofthe air. The standard assumption that is used inall such calculations in that CD is proportionalto the air density, r. This density, in turn, isdetermined by the temperature, barometricpressure, and altitude. It is also affected toa lesser extent by the relative humidity. Alltrajectory calculations do show an enhanced

492 Volume 55, Number 4, November 2003

fly-ball distance at Denver, but the enhancementvaries considerably with small changes in CD.

If we standardize our comparisons to 400-foot fly balls at sea level with no wind, thereare still large variations. Adair (1990) predicts a10 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 triedseveral forms for CD and find predicted en-hancements that range from7percent to over 13percent. Given this, Adair’s original 10 percentprediction seems a reasonable one, and, more-over, has become the accepted standardmeasureof elevation enhancement at Coors Field.

We plan to refine our model and presentthe details in another publication. There areexperimental approaches that would help toclarify the air drag question. One approachwould be to study the baseball’s terminal-velocity behavior as a function of air density.The terminal velocity is the speed an object rea-ches in free fall and iswhere the ball’sweight anddrag force are equal in strength. Another wouldbe to measure the distance of flight when flyballs are mechanically launched with controlledinitial conditions at different altitudes. Until wehave a better model for CD, trajectory calcu-lations will be subject to uncertainties. Forthis reason, we take a conservative approachin this article and use themiddle-range estimateof 10 percent.

Observed Fly-Ball Distancesin National League Ballparks

The physics of baseball gives us a very clear ideaof how much farther a baseball should travelat Coors Field versus ballparks at sea level. Ofcourse, not all National League stadiums arelocated at sea level, so we adjusted our model offly-ball trajectories to reflect the actual eleva-tions of the league’s other ballparks. Comparedto the elevation-adjusted average of the otherNational League ballparks, the ball should fly9.3 percent farther in Denver.

Do these theoretical relationships hold truein actuality? In order to answer this question,we analyzed fly-ball distance data for fourteenNational League ballparks for 1995 through1998.1 These data provide an estimate of thedistance traveled by every fly ball hit in fair

territory for every game played in the leagueover four seasons, a total of nearly 8,000 flyballs per ballpark and over 100,000 fly ballsoverall. This sample size is more than sufficientto detect any systematic enhancement of fly-balldistance due to altitude.The fly-ball distance data was obtained from

STATS Inc. This company records a wide rangeof information for each baseball game playedin the major leagues, including the distancetraveled by every ball put into play. Our analy-sis focuses only on fly balls, as this is the typeof batted ball most affected by the dynamics ofatmosphere and weather. In every major-leagueballpark, STATS Inc. estimates the distance thateach fly ball travels by locating the final positionof the ball on a chart of the field. This methodyields estimated distance, not precise distance.However, we believe that this data is reliablebecause: (1) a consistent method is used at eachballpark, and (2) the sample size is more thanlarge enough (over 100,000) to account for anyindividual errors in fly-ball measurement (thatis, incidents of overestimation or underestima-tion 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 ouranalysis are quite surprising. The average fly-ball distance at Coors Field is 302.8 feet, whilethe average at the other 13 ballparks is 284.5feet.This is a difference of only 18.3 feet, not the26.5 feet that Adair (1990) would predict onthe basis of decreased air density at mile-highelevation. Thus, the ball does travel farther atCoors Field, but not the expected 9.3 percent.Compared to the average of the other NationalLeague ballparks, the ball flies just 6 percentfarther in Denver (see Table 1).Why do fly balls travel just 6 percent farther in

Denver? One possible answer is that variationin fly-ball distance can be explained by base-ball factors alone. After all, no two at-batsare alike, and how far any batted ball travels isthe result of a complicated and unique set ofcircumstances having to do with the particu-lar pitcher and batter involved—including, forinstance, the pitcher’s skill level and orienta-tion (left- or right-handed), the type and speedof pitch thrown, the batter’s orientation, thebatter’s hand-eye coordination, and so forth.For these reasons, we would expect fly-balldistances to vary somewhat from ballpark to

How Much Farther Do Baseballs Really Fly at Denver’s Coors Field? 493

ballpark over the course of several seasons. Todetermine the influence of this routine, base-ball-driven variation in fly-ball distance, weanalyzed average fly-ball distances for just thoseNational League stadiums located at sea level,thus eliminating the elevation factor. We founda standard deviation of plus or minus 6 feet infly-ball distance for this set of ballparks overthe four-year study period, which is far shortof the 18.3-foot difference between average fly-ball distance at Coors Field and average fly-balldistance at the other National League parks.According to our statistical analysis (a singletailed Student’s t-test), this means that thelower-than-expected difference between CoorsField and the other National League ballparksdoes not derive from baseball variables alone(at the 90 percent confidence level).

If the routine vagaries of baseball cannotaccount for the fact that fly balls do not travelas far as expected in Denver, then we mustlook elsewhere to address the question. Anotherpossible answer—and the one that we wish tohighlight in the next section—has to dowith thedistinctive geographic circumstances of CoorsField, particularly the weather.

Coors Field Meteorology

There have been several previous attempts tolink weather and baseball, although the resultsof these studies have been inconclusive at

best (Kingsley 1980; Skeeter 1988; Kraft andSkeeter 1995). In one study, Mark Kraftand Brent Skeeter (1995) examined the effectsof temperature, humidity, and wind—bothdirection and velocity—on fly-ball distancesin several major-league ballparks throughoutNorth America. Multiple regression analysis onthese variables yielded an R2 value of 0.062.In other words, 6.2 percent of the variancein fly-ball distance could be assigned to themeteorological variables. Of these variables,temperature, with an R2 value of 0.036, wasthe single greatest contributor. Humidity and,surprisingly, wind were considered to be rela-tively unimportant in the determination of howfar a baseball flies in major-league ballparks.Part of the reason that this study showed no

significant relationship between weather vari-ables and fly-ball distance has to do with thesource and character of the weather data uponwhich the study was based. To begin with, theweather data were collected at regional weatherstations that were not located in close proximityto the ballparks. In addition, these data werereported on only at the beginning of the game,with no further updates on conditions as thegame progressed, even though all of the mea-sured variables can and do change radicallyover the span of an average three-hour base-ball game. Further, wind was reported onlyin descriptive terms as either ‘‘blowing in,’’‘‘blowing out,’’ or ‘‘blowing across,’’ providing asomewhat limited analytical basis. The authors(1995, 48) readily acknowledge the limitationsof their data and conclude their article by statingthat ‘‘much more detailed studies, includingmicroclimatological analyses’’should be perfor-med within the confines of individual ballparksto better assess how meteorological variablesaffect fly-ball distances.Acting upon this suggestion, we set up two

meteorological stations inside Coors Fieldfor the duration of the 1997 baseball season.2

These stations were constructed atop conces-sion stands along the rear concourse of theballpark. One station was located down the left-field line, while the other was in straightawaycenter field just beyond and above the bull-pens (Figure 1). Weather variables monitoredincluded temperature, relative humidity, baro-metric pressure, and wind. Temperature andrelative humidity measurements were deter-mined by a Campbell Scientific HMP35C

Table 1 Average Fly-Ball Distance in NationalLeague Ballparks

StadiumFour-Year Average

Distance (ft)d Coors

(%)

Coors Field 302.8

Atlanta (composite of

Turner and Fulton)

290.8 4.0

Chicago 283.8 6.3

Cincinnati 284.9 5.9

Florida 282.2 6.8

Houston 286.7 5.3

Los Angeles 291.6 3.7

Montreal 281.3 7.1

New York 282.5 6.7

Philadelphia 290.8 4.0

Pittsburgh 282.2 6.8

San Diego 277.6 8.3

San Francisco 271.1 10.5

St. Louis 293.1 3.2

NL Avg. w/out Coors Field 284.5 6.0


Temperature and Relative Humidity Probe,housed in a twelve-plate Gill radiation shield.A Campbell Scientific CS105 Barometric Pres-sure Sensor measured barometric pressure,whilewinddatawas collected usingR.M.Young,Gill U-V-W Anemometers. These anemo-meters allow for three-dimensional profilingof the wind: an east-west vector (U), a north-south vector (V), and a vertical-angle vector(W). From this data, wind azimuth, velocity,and elevation angle may also be calculated.

Measurementswere takencontinuouslyduringgame time and averaged every fifteen minutes.Both the averaged and instantaneous values

were downloaded on the quarter-hour using aCampbell Scientific21Xdata-loggerwith storagemodule. These results were then transferred andanalyzed utilizing the Microsoft Excel spread-sheet program. For each game for whichweatherdata were collected, averages of temperature,relative humidity, barometric pressure, and windwere determined (wind averages included allpermutations listed above).This game-specific Coors Field weather data

was then related to game-specific Coors Fieldaverage fly-ball-distance data. A correlationmatrix was developed on the data as part ofthe initial statistical analysis (Table 2). As with

Figure 1 Location of weather instruments within Coors Field. Image courtesy of Landiscor Aerial

Information. Graphic illustration by Chris French.


the results obtained byKraft andSkeeter (1995),it can be seen that temperature and relativehumidity have little, if any, correlative valuewith fly-ball distance. Unlike the case withthat previous study, however, wind—especiallythe U- (east-west) vector—does seem to becorrelative.

Stepwise multiple regression analysis was em-ployed to determine the explanatory value (ifany) that could be attributed to meteorologicalvariables with respect to the fluctuation in fly-ball distance at Coors Field (Table 3). Only onevariable—the U-vector again—was statisticallysignificant (at a 95 percent confidence level)

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. 1.00

Temp. 0.13 1.00

RH �0.12 �0.83 1.00

U-vector �0.47 0.15 �0.07 1.00

V-vector �0.11 �0.03 0.25 �0.01 1.00

W-vector 0.18 �0.42 0.45 �0.59 �0.09 1.00

Azimuth �0.14 �0.17 0.41 0.08 0.60 �0.04 1.00

Wind Vel. 0.02 0.42 �0.40 0.17 0.18 �0.46 �0.19 1.00

Elev. Angle 0.14 �0.12 0.04 �0.11 0.17 0.14 �0.13 0.65 1.00

Table 3 Stepwise Multiple Regression of Coors Field Average Fly-Ball Distance and MeteorologicalVariables

Dependent variable: Average fly-ball distance

Parameter Estimate Standard Error T Statistic p-value

Constant 299.052 3.87306 77.2134 0.0000

U-vector �16.1962 6.05091 �2.67665 0.0129

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio p-value

Model 2901.54 1 2901.54 7.16 0.0129

Residual 10124.8 25 404.992

Total (Corr.) 13026.3 26

R-squared¼ 22.2744 percent

R-squared (adjusted for d.f.)¼ 19.16544 percent

Standard error of estimate¼ 20.1244

Mean absolute error¼ 17.0508

Durbin-Watson statistic¼ 1.86565

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-squared¼ 0.00% Adjusted R-squared¼ 0.0% MSE¼ 501.013

Step 1:

Adding variable U-vector with F-to-enter¼7.16445

R-squared¼ 22.27% Adjusted R-squared¼ 19.17% MSE¼ 404.992

Final model selected.


enough to enter the model in this test. Thisresulted in an R2 value of 0.223, or an R2 valueof 0.192 when adjusted for degrees of freedom.Simply stated, this indicates that almost 20percent of the variation in fly-ball distance atCoors Field can be attributed to differences inwinds along the east-west vector, with all othervariables playing an insignificant role.

Further examination of the U-vector revealssome interesting information. During the 1997season, winds blowing with an easterly compo-nent inside Coors Field exhibited almost twicethe intensity of westerly winds—approximately12 miles per hour, versus 6. Additionally, ave-rage fly-ball distances decreased under an east-erly wind regime (approximately 290 feet witheasterly winds versus over 303 feet with awestern component). Correlation analysis ofwind direction and fly-ball distances verifiedthese results. Average fly-ball distances dis-played a negative correlation with east winds(r-value¼�0.45), and a positive correlationwith west winds (r-value¼ 0.49).

Easterly winds are clearly implicated in theobserved suppression of fly-ball distance atCoors Field. In order to get a better under-standing of this relationship, however, it is firstnecessary to examine the broader wind regimein and around the Denver ballpark.

Regional Wind Patterns inNortheastern Colorado

The summer wind pattern in northeasternColorado is dominated by a persistent upslope-downslope regime.This diurnal pattern, similarto that seen in smaller-scale mountain valleylocales, occurs on a regional scale here. JamesToth and Richard Johnson (1985) describe thepattern as occupying the entire South PlatteRiver valley drainage system. The CheyenneRidge to the north, the Continental Divide tothe west, and the Palmer Divide to the southenclose this basin (Figure 2).Under this regime,heating of the east-facing foothills in themorning hours causes air to flow up the SouthPlatte River valley in the late morning throughthe evening hours. This flow reaches a peakin the vicinity of Denver at around 1500 to 1600hours local standard time (LST). Thereafter inthe Denver area, winds weaken and eventuallyshift to a southerly direction before becomingwesterly beginning in the hours between 2200and midnight LST. This downslope patternpersists until the process reverses itself thefollowing morning.The South Platte River flows from the south-

west to the northeast in the vicinity of CoorsField (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.


winds will be northeasterly, while down-valley winds will be southwesterly. In an effortto verify this wind pattern in the vicinity ofCoors Field, we examined data provided byDenver’s Air Quality Control Division, whichhas several air-quality monitoring stations inand around the Denver metropolitan area.3

These stations measure pollution as well aswind direction and velocity. Wind data wasanalyzed from the two stations closest to theballpark; one of these stations is within two cityblocks of Coors Field. Data on wind directionand velocity from these stations were averagedhourly for each month of the baseball season,

April through September, for the years 1995to 1998.The results verify the regional-scale diurnal

pattern described above. Northeasterly windsdominated the afternoon and evening hours ofthis four-year long period. In fact, our resultsshowed that during this time there was never awesterly component to the average wind vectorbetween the hours of noon and 2200 hoursLST,the time period in which almost all Rockiesgames are played. Certainly, this is not to saythat westerly winds do not occur. Indeed, theydo, as we found during our data collection in-side Coors Field. It would seem, however, that

Figure 3 Proximity ofCoors Field toPlatteRiver Valley andRockyMountains. Image courtesyof Landiscor

Aerial Information. Graphic illustration by Chris French.


these wind vectors are the exception to the rule.A westerly component to the wind duringthe months in question most likely occurs inresponse to either (1) local convective systemsor (2) synoptic-scale atmospheric features (e.g.,frontal passages). In any event, westerly flow

regimeswould seem to be relatively brief events,followedbya return to themore routineupslope-downslope pattern.Northeasterly winds would thus appear to

be the causal mechanism that explains shorter-than-expected average fly-ball distances atCoors

Figure 4 Relative location of Coors Field to South Platte River. Satellite photo courtesy of Space Imaging.

Graphic illustration by Chris French.


Field. These winds flow up the South PlatteRiver valley and enter the vicinity of the ballparkfrom the northeast. Within Coors Field, north-easterly winds blow from center field towardhome plate, directly into the face of the batterand into the path of batted balls hit to all seg-ments of the outfield (Figure 4).

Further, we believe that this regional windregime is accentuated by the location of CoorsField with respect to other geographic featuresin the area. The first of these is the topographyof the SouthPlatteRiver valley,which rises to thenorthwest and also narrows in the vicinity ofthe ballpark. The other feature is the patternof urbanization in downtownDenver, one char-acterized by a massing of buildings runningparallel to the South Platte River Valley on itssoutheastern bank beginning just to the north-east of Coors Field. We believe that during theup-valley period (northeasterly winds duringthe day and evening hours), the air flowingto the southwest is constricted somewhat bythe combined effects of topography and urbandevelopment (Figures 3, 4). In all likelihood,this produces a funnel-like effect on windsstreaming into LoDo and may result in in-creased wind velocities in this area. Additionalresearch will be necessary to validate this claim.

Conclusion

The laws of physics tell us that a baseball shouldtravel 10 percent farther in the mile-highatmosphere of Denver than at sea level. More-over, fly balls should travel 9.3 percent farther inDenver than the elevation-adjusted average ofthirteen other National League ballparks. Ourconclusion, however, is that these theoreticalfly-ball trajectories, calculated on the basis ofcomparative air density, do not hold true uponthe examination of fly-ball distance data. In fact,for the 1995–1998 seasons, fly balls traveledjust 6 percent farther in Denver compared tothe average of thirteen other National Leagueballparks. The results of our meteorologicalanalysis of Coors Field and its surrounding areasuggest that the key factor in this suppressionof fly-ball distance is weather—specifically, thedominance of northeasterlywinds in the vicinityof the ballpark during afternoon and eveninghours. These wind conditions exists due toa regional-scale, diurnal, upslope-downslope

wind pattern in the South Platte River valleyand, we suggest, are accelerated by local topo-graphy and urban massing.Our assessment is that these daily north-

easterly winds suppress fly-ball distances atCoors Field. These winds flow up the SouthPlatte River valley and enter the vicinity of theballpark from the northeast. Within CoorsField, the winds blow from center field towardhome plate into the face of the batter and intothe path of batted balls hit to all parts of theoutfield. The expected advantage of playingat mile-high elevation (as far as home runsare concerned) is decreased substantially undersuch conditions. However, when the winds areout of the west, the full elevation advantagecan be realized. Such conditions can leadto spectacular fly-ball trajectories, especially toright field. Thus, the effect of the wind is varia-ble: during some games, altitude’s enhance-ment of fly-ball distance will occur, and in othergames it will be suppressed. But over the courseof a season—or several seasons—wind acts tominimize the effect of low air density and thusaccounts for the shorter-than-expected fly-balldistances at Coors Field.Finally, let us return to the question raised

at the outset concerning the character of base-ball games played at Coors Field. While thesuppression of fly-ball distance due toprevailingnortheasterly winds is significant, keep in mindthat the boosting effect of altitude on home-runproduction in Denver is further minimizedby the generous outfield dimensions at CoorsField, the league’s most spacious ballpark. In-deed, in order to come up with ameasure of justhow much more likely it is for home runs tooccur at Coors Field due to low air density, onemust take into consideration actual field dimen-sions around the league. We made this adjust-ment by calculating average fly-ball distance as apercentage of average outfield dimension forfourteen National League ballparks (Table 4).4

This calculation yields a measure of how far theaverage fly ball travels relative to the averageposition of the outfield fence in each ball-park. As the table shows, when field dimensionsare taken into account, the effective differencebetween Coors Field and the other NationalLeague stadiums is not even 6 percent—it isjust 3 percent. Moreover, the difference be-tween Coors Field and the stadiums in Phila-delphia, Los Angeles, and Atlanta is minimal,


while the average fly ball actually carries closerto the outfield wall at St. Louis’s Busch Stadiumthan it does at Coors Field.5 Faced with thesenumbers, the facile assumption that elevationenhancement of fly-ball distance is responsiblefor the large number of home runs in Denvervanishes into so much thin air.

What else might account for the impressivehome run statistics in Denver? After all, duringthe 1995 through 2002 seasons, Coors Fieldwitnessed a rate of .044 home runs per at bat,while the combined averageof theotherNation-al League parks was just .029 home runs per atbat. In other words, home runs occur at CoorsField at a rate that is 52 percent greater than atthe other ballparks—far more than would beexpected even if the mile-high atmosphericenhancement was realized to its fullest ( James1995, 1996, 1997, 1998, 1999, 2000; Carter,Nistler, and Sloan 2002; STATS Inc. 2001).Webelieve that the answer to this question has to dowith two factors: first, the personnel make-upof the Colorado Rockies ball club in terms ofboth hitters and pitchers; and second, thegeneral problems of pitching at altitude.

During the first several seasons played atCoors Field, the Rockies team was stackedwith notable power hitters. Simply put, theywere a team designed to produce large numbersof home runs. However, over the past severalyears, these ‘‘Blake Street Bombers’’ have beentraded or allowed to leave via free agency, asteam management has shifted focus fromhome-run hitters to high-average hitters with

less power. This personnel shift is verified in therecord of Coors Field hitting statistics. Since1995, there has been an overall downwardtrend in the number of home runs per at-bat—a trend that is accounted for by a reduction inthe number of home runs hit by theRockies (thetrend in home runs per at-bat for the oppositionat Coors Field has risen) (Figure 5). In fact,by the 2000 season, Coors Field had been

Table 4 Average Fly-Ball Distance versus Stadium Dimensions in National League Ballparks

StadiumAverage Outfield

Dimension (ft)d Coors

(%)

Avg. Flyball Dist.* (100)

Outfield Dimension d Coors (%)

Coors Field 375.4 80.7

Atlanta (composite of Turner and Fulton) 366.7 2.3 79.3 1.7

Chicago 368.8 1.8 77.0 4.6

Cincinnati 362.8 3.4 78.5 2.6

Florida 369.8 1.5 76.3 5.4

Houston 360.0 4.1 79.6 1.3

Los Angeles 365.0 2.8 79.9 1.0

Montreal 360.8 3.9 78.0 3.3

New York 368.4 1.9 76.7 4.9

Philadelphia 362.0 3.6 80.3 0.4

Pittsburgh 364.0 3.0 77.5 3.9

San Diego 360.2 4.0 77.1 4.5

San Francisco 358.6 4.5 75.6 6.3

St. Louis 362.0 3.6 81.0 �0.4

NL Avg. w/out Coors Field 363.8 3.1 78.2 3.1

Total HRs/AB

00.010.020.030.040.050.06

1995 1996 1997 1998 1999 2000 2001 2002

Rockies HRs/AB

Opposing Team HRs/AB

00.010.020.030.040.050.06

1995 1996 1997 1998 1999 2000 2001 2002

00.010.020.030.040.050.06

1995 1996 1997 1998 1999 2000 2001 2002

Figure 5 Coors Field home runs per at-bat,

1995–2002.


surpassed in home runs per at-bat bybothBuschStadium in St. Louis and Enron Field inHouston. Thus, the large number of home runshit at Coors Field can be attributed, in part, tothe specific group of hitters assembled early onby the Rockies. Once the franchise changedthe character of the team, the preeminence ofCoors Field as the league’s ultimate home-runballpark was somewhat diminished.

The Rockies have also lacked successful pitch-ing for most of their history. Colorado pitchershave had more than their share of problemsover the past eight years, both at home and onthe road. Between 1995 and 2002, the teamwas either last or next to last in most pitch-ing categories, leading the league in home runsallowed seven times. Had the Los Angeles orNew York staffs pitched at Coors Field foreighty-one games per year, the ballpark’s home-run totals would most likely have been sig-nificantly less. Put Atlanta’s pitching staff inDenver for half of their games and this reduc-tion is a virtual certainty.Remember thatAtlanta’sFulton County Stadium was known as the‘‘launching pad’’ until the Braves put togetherthe league’s premier group of pitchers in theearly 1990s.

But perhaps the most important factor inexplaining the home-run numbers in Denveris the ‘‘Coors Field Effect’’—the not-so-subtleinfluence of the ballpark on pitchers from boththe home and visiting teams. Most of theseprofessional athletes are clearly intimidatedby Coors Field. As one player recently obser-ved, the ballpark causes ‘‘an identity crisis’’ forpitchers, leading them to change their approachto the game, move away from their strengths,and ultimately lose confidence in their abili-ties (pitcher Denny Neagle of the ColoradoRockies, quoted in Renck 2003, 14D). Even theleague’s best pitchers often come unglued inDenver. Pitching is undeniably more difficultin Coors Field than in other National Leagueballparks because of the very limited foulground and the cavernous outfield spaces. Thisfield configuration gives hitters more chances,allows more balls to drop in front of outfielders,and permitsmore balls to find the gaps for extra-base hits. Yet beyond this, most pitchers arebeset with a range of other problems once theytake themound.Chief among these are a suddenlack 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 heartof the plate, and more balls hit high, deep, andout the park.Thus, whatwe suggest is thatmorehome runs are hit at Coors Field, not becauseroutine fly balls carry farther, but because ahigher proportion of pitched balls are hit harderthan in other ballparks.These pitching problems inDenver have also

been attributed to low air density. Theoreti-cally, thin air reduces ball-to-air friction, cut-ting down on ball movement between themound and home plate and thus decreasingthe overall control of the pitcher and the effec-tiveness of the pitches thrown. In addition, thelow relative humidity at altitude promotesevaporation from the baseball itself, makingthe ball lighter, drier, and slicker inDenver thanin other parks around the league. Because ofthis, pitchers at Coors Field have a very difficulttime getting a proper grip on the ball, which, inall likelihood, further reduces their control aswell as the movement on their pitches.6 Duringthe 2002 season, in an effort to counteract thepresumed effects of thin air on pitching,the Colorado Rockies began using a ‘‘humidor’’to store baseballs at Coors Field. This devicemaintains the balls in a controlled environmentof 90 degrees Fahrenheit and 40 percenthumidity. According to the Rockies organiza-tion, the intent of the humidor is to ensurethat the baseballs do not shrink to a weight lessthan the 5.0 to 5.25 ounces specified by theleague. The Rockies ball club also believesthat these baseballs, having not yet lost watercontent to evaporationwhen they enter play, areeasier to grip and thus will ‘‘level the playingfield’’ for pitchers in Denver. This might just bewishful thinking, however: a comparison of thestatistics for the 2002 season versus the previ-ous seven seasons indicates that the humidorhad little, if any, effect upon games played atCoors Field.7

Ultimately, these altitude-related issues mayprove to be important contributors to the poorpitching in Denver. For now, however, difficul-ties on the mound would seem to be more theresult of the fragile psychology of pitchers facedwith the imagined specter of baseballs floatingout of Coors Field like weather balloons. Basedupon the analysis presented above, we believethat the answer to why so many home runs arehit at Coors Field lies as much on the field as itdoes in the air. ’


Notes

1 Because the time frame of our analysis is 1995–1998,we used only those cities with ballparks that wereutilized for National League games during all fouryears. County Stadium inMilwaukee and Bank OneBallpark in Phoenix were excluded from the analysisbecause National League games were not playedin these stadiums in 1995, 1996, or 1997 (seeTable 1).

2 The Colorado Rockies Baseball Club allowed usaccess to Coors Field in order to set up our weatherequipment and to periodically check on the instru-ments and download data. It should be emphasizedthat the Rockies organization did not solicit thisstudy, nor did they offer or provide any support forthe research.

3 These data were provided by the Colorado De-partment of Public Health and Environment, AirPollution Control Division (APCD) for the years1995–1998.

4 Average outfield dimension was obtained by aver-aging the distances at five points along the outfieldwall for each ballpark: the left field line, left centerfield, center field, right center field, and the rightfield line. In a few cases, the dimensions of theoutfield were changed in an existing ballpark duringour four-year study, or a team changed ballparksaltogether. In these cases, we used an average ofthe old and new dimensions. The source used forestablishing average outfield dimension was James(1996, 1997, 1998, 1999).

5 IfMarkMcGwirehadplayed for theColoradoRockiesduring 1998, his pursuit of the single-season home-run record would have been hounded by the aster-isk of elevation-enhanced play. Instead, McGwireconducted his quest in St. Louis, protected by ahallowed baseball tradition and unfettered by anylingering doubts, while nevertheless enjoying theadvantages of a ballpark that is every bit as conduciveto home-run production as Coors Field in terms ofhow far the average fly ball carries relative to theaverage position of the outfield fence.

6 For years, manager Bobby Cox of the Atlanta Braveshas blamedDenver’s aridity for the pitchingproblemsat Coors Field, citing the dryness of the ball and hispitchers’ problems with grip (Moss 1999).

7 For the 2002 season, runs per at-bat and hits perat-bat were down slightly but registered at levelsvery similar to past seasons, while home runs perat-bat were higher than some previous years. Inaddition, strikeouts per at-bat were significantlylower 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; Carteret al. 2002).

Literature Cited

Adair, Robert K. 1990. The Physics of Baseball. NewYork: HarperPerennial.

———. 1994. The Physics of Baseball. 2nd ed. NewYork: HarperPerennial.

Boswell, Thomas. 1998. Coors Field is a mistake thatmustn’t be repeated. Denver Post 10 July: 1D, 6D.

Brancazio, Peter J. 1984. SportScience: Physical Lawsand Optimum Performance. New York: Simon andSchuster.

Carter, Craig, Tony Nistler, and David Sloan. 2002.Baseball Guide, 2003 Edition. St. Louis, MO: TheSporting News.

James, Bill. 1995. Major League Baseball Handbook1996. Skokie, IL: STATS, Inc.

———. 1996. Major League Baseball Handbook 1997.Skokie, IL: STATS, Inc.





Kingsley, R. H. 1980. Lots of home runs in Atlanta?Baseball Research Journal 2:66–71.

Kraft,MarkD., andBrentR. Skeeter. 1995.The effectof meteorological conditions on fly ball distance inNorth American major league baseball games. TheGeographical Bulletin 37 (1): 40–48.

Moss, Irv. 1999. Braves contend Coors baseballs areslicker. Denver Post 9 May:18C.

Renck, Troy. 2003. Neagle staying true to form.Denver Post 5 March: 14D.

Skeeter, Brent R. 1988. The climatologically optimalmajor league baseball season inNorthAmerica.TheGeographical Bulletin 30 (2): 97–102.

STATS, Inc. 2001. Major League Baseball Handbook2002. Skokie, IL: STATS, Inc.

Toth, James J., and Richard H. Johnson. 1985.Summer surface flow characteristics over north-eastern Colorado. Monthly Weather Review 113 (9):1458–69.

FREDERICKCHAMBERS is an associate professorin the Department of Geography and EnvironmentalSciences, University of Colorado at Denver, Denver,CO 80217-3364. E-mail: [email protected]. His current research includes investigating mi-crometeorological variables over new and recent lavaflows, detection of ‘‘urban heat island’’ effects in themeteorological records of Colorado mining towns,and western North American glacier-climate inter-relationships.


BRIANPAGE is an associate professor in theDepart-ment ofGeography and Environmental Sciences, Uni-versity of Colorado at Denver, Denver, CO 80217-3364.E-mail:[email protected] researchinterests include the interpretation of cultural land-scapes in the American past, the historical geographyof regional growth and change in the West andMidwest, and the political ecology of agricultureand resource development.

CLYDE ZAIDINS is a professor in the Departmentof Physics,University ofColorado atDenver,Denver,CO 80217-3364. Email: [email protected]. His areas of research interest are in astrophysicsand nuclear physics, and he has taught all levels ofundergraduate physics courses. His father, MorrisZaidins, worked for the Cincinnati Reds from 1937to 1974.


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