How Much Does Coors Field Really Matter?
KEITH WOOLNER
In 1993, Major League Baseball expanded for the first time since 1977. Two teams joined the National League: the Florida Marlins and the Colorado Rockies. The Rockies were the first to reach the playoffs, winning the Wild Card in 1995. But twelve years after joining the league, the Marlins have two World Championships and the Rockies have only that one brief postseason appearance under their belts. In fact, the Rockies haven’t managed to win more than 83 games in any year of their existence (Table 8-2.1).
TABLE 8-2.1 Rockies Year-by-Year Won-Lost Record and Finish
The signature characteristic of the Rockies hasn’t been any individual player, their 1995 Wild Card–winning team, or even their stellar attendance record (they led MLB in attendance for each of their first seven years and didn’t drop below three million fans in a season until 2002). Instead, it’s the ballparks in which they’ve played, Coors Field and Mile High Stadium—or to be more precise, those parks’ legendary effects on offense and run production. In the baseball community, it’s taken for granted that playing at high altitude wreaks havoc with the game. Yet most fans and sportswriters don’t really know how to account for it.
How do we know that Coors Field causes massive spikes in offense, rather than the Rockies simply having terrible pitching and great hitting for a decade? If playing at a mile-high altitude affects the game, which elements are most affected, and by how much? In short, how does a player’s home park affect his value?
A quick glance at the statistical record is enough to raise suspicions. Since 1993 the Rockies have had only two pitchers post a Run Average below 4.00 in at least 100 innings: Marvin Freeman’s 3.11 RA in 112.2 innings in 1994, and Joe Kennedy’s 3.77 RA in 162.1 innings in 2004. No other team has fielded so few stingy pitchers during that time. In fact, only three other teams have fewer than seven such seasons over that span: the Rangers and Brewers with four each and the Tigers with three. The Rockies’ expansion counterparts, the Marlins, have fifteen such seasons.
During the same period, Rockies batters have hit .300 or better in at least 500 PA 34 times, tops in the majors by a wide margin (27 percent more than the #2 team, the Cleveland Indians). Even by a more saber-metrically friendly measure of hitting such as OPS (on-base percentage plus slugging average), the Rockies have had thirty-six players top an 850 OPS, 20 percent more than the next-best teams (Red Sox and Yankees). Of all the 500-PA seasons posted by Rockies batters since 1993, an amazing 62 percent of those topped an 850 OPS, easily the highest ratio in the majors. No other team topped 50 percent (Yankees and Rangers were at 48 percent), and the median was 33 percent.
That combination of stellar hitting and feeble pitching is enough to raise eyebrows, but it alone can’t prove that the Rockies play in an unusual environment. It could very well be that the Rockies have had studly hitters and girly-men pitchers for over a decade. Indeed, the Rockies have never ranked lower than fourth in runs scored per game, often leading the league in that category. Meanwhile, they’ve dominated the top of the list in most runs allowed per game (Table 8-2.2).
To show that it’s the ballpark, not the quality of the team’s players that are most to blame, we have to find a way isolate the park’s influence and keep the quality of players constant. The way to do this is to use just the games played by the team at its home park. So to see the effect of Coors Field, compare the results from Rockies’ home games to their away games. Since a team plays roughly the same mix of opponents at home and on the road, the overall quality of players in the two sets of games are approximately the same. Both sets of data contain Rockies hitters facing opposing pitchers, and opposing hitters facing Rockies pitchers. Even if the Rockies hitters are exceptionally good as a group, they are equally represented and weighted in both Rockies home games and Rockies away games, so overall they balance out. The same is true of the Rockies pitchers: Regardless of their actual quality, the fact that they contribute half the innings in both the home and away totals means that the overall quality of each pitcher is constant between the two sets of totals.
TABLE 8-2.2 Colorado’s League Rank in Best Offense and Worst Defense, by Year
For example, in 2004, the Rockies and their opponents combined for 1,752 hits in 5,739 at-bats over 81 games in Colorado. In the Rockies’ 81 road games, there were 1,413 hits in 5,467 at-bats. Here are the batting averages for both sets of games:
COL Home: 1,752 H/5,739 AB = .30528 AVG
COL Road: 1,413 H/5,467 AB = .25846 AVG
With the same hitters and pitchers, the games in Colorado yielded a .305 batting average, while the games away from Colorado produced a .258 batting average. That 47-point difference can be attributed in large part to the effect of Coors Field. Usually the effect of a park on a particular statistic is expressed as a ratio, as shown below:
.30528/.25846 = 1.18 COL park factor for batting average
Coors Field increases batting averages by 18 percent in the aggregate, compared to the league average (or more accurately, the weighted average of opposing parks the Rockies played in, which are usually close to the overall league average).
However, it’s not quite that easy.
One difficulty in looking at the statistical record is that things don’t even out perfectly over 162 games. Even if parks and environmental conditions were identical, we’d expect to see some random differential between two halves of the season (such as home and road games). Similarly, if you flip a coin 100 times, you are unlikely to have the same number of heads as tails, even if the expected value is 50-50. Also, just because there’s a difference between stats in home and road games doesn’t automatically mean that the differences are due entirely to the influence of the home park itself.
In fact, we can determine mathematically how much variability to expect just from taking a small sample of games. For a single season of stats, the expected standard deviation in an observed park factor due just to chance is about 5 percent. (Standard deviation measures the spread around the mean. Very few, if any, of the data points are exactly at the overall average—each point is some distance away, either higher or lower. The standard deviation is a way to average those distances to find out how far the typical data point is from the average.) So with the +18 percent park factor for batting average being more than three standard deviations away, we can be relatively sure that we’re seeing something real. This is less of a problem for Coors Field than for most other parks in the majors that are less extreme, where it’s harder to distinguish true park effects from other factors influencing the results. To become more confident about what effect a park has on hitters, we look at more players, over more games and plate appearances, spanning more years. Since one-year park factors fluctuate quite a bit for a given park (due to simple random chance as we’ve seen, but also due to actual environmental changes like temperature, humidity, and wind), we usually use three-year or five-year park factors to yield a more stable, reliable result.
The most commonly used park factor is the one employed to measure overall run scoring. A neutral park factor is commonly printed as 100. A 110 park factor thus indicates that a park inflates run scoring by 10 percent (110 = 1.10 = 10 percent above average). A park factor of 85 indicates that a park deflates run scoring by 15 percent (85 = 0.85 = 15 percent below average). The park factor for runs summarizes the overall effect the park has on hitters. We’ll discuss how to properly use the park factor for runs later on.
What Causes Coors Field’s Park Effect?
The underlying causes of park effects are surprisingly varied. There are the obvious ones, such as different outfield dimensions. But there are also subtle ones, such as differences in the quality of hitting backgrounds, lighting and shadows, amount of foul territory, quality of grounds maintenance, height of walls, prevailing wind direction and speed, average temperature, humidity, shape and area of the outfield, grass versus turf, and the proportion of day versus night games. And, of course, altitude, which is one of the key factors that makes Coors Field unique. Robert K. Adair, a professor of physics at Yale, has written an entire book titled The Physics of Baseball in which he explains the underlying physical reasons that a high-altitude ballpark like Coors creates a favorable offensive environment. We’ll let him do the heavy lifting on explaining the science behind the park effect:
Offense
Since the retarding force on a ball is proportional to the density of the air, a baseball will travel farther in ball parks at high altitude. A 400-foot drive . . . near sea level could [be expected] to travel about 430 feet at mile-high Denver. And if the Major Leagues are further internationalized some day with a team in Mexico City, at 7800 feet, [that] blow could be expected to sail nearly 450 feet. . . . Old home run records will be swept away unless the fences are moved out in high parks.
The air in Denver is thinner than at sea level, offering less resistance to a ball in flight. Balls travel farther and faster. This is most apparent with flyballs, which carry farther, and line drives, which are more likely to fall for hits because of both the thin air and the huge expanse of grass in Coors Field’s outfield. The result is an increase in offensive totals (home runs, hits) and rate statistics (batting average, on-base percentage, slugging average) for Rockies players.
Furthermore, swings themselves are more likely to produce a ball in play than a strike at Coors. Looking at the percentage of pitches swung at and not put into play, we see that Coors Field has shown a definite, albeit slight, tendency to help batters miss or foul a pitch off less often. This could be because of the hitting background or the thin air lessening the movement on pitches, thus making them less effective (Table 8-2.3).
Pitching
The pitchers will also be hurt at high altitude. A mile high at Denver, the fast ball will take a little less time to cross the plate—and gain about 6 inches—but the curve will break about 25 percent less. A curve that will break left-right about 8 inches and drop an extra 8 inches (due to the overspin component) at sea level will break about 1 5/8 inches less and drop about 4 inches less in Denver. The ball breaks less because it crosses the plate faster, and thus has a little less time to break; in addition, the Magnus force is smaller. Similarly, the knuckle ball will dance perhaps 25 percent less.
TABLE 8-2.3 Percentage of Swings That Were Misses or Fouled Off
In 2001, Colorado General Manager Dan O’Dowd undertook a bold (and expensive) experiment. He signed two starting pitchers, Mike Hampton and Denny Neagle, who rely primarily on changing speeds to fool hitters, for a combined $170 million. The rationale was that if breaking pitches break less at Coors than at sea level, then breaking-ball pitchers should be hampered disproportionately by the altitude. Adair’s commentary supports this notion. Pitchers with exceptional change-ups, the Rockies thought, wouldn’t be affected by the thin air and thus could succeed in Denver.
Hindsight being twenty-twenty, we can see now that neither Hampton nor Neagle had dominant strikeout rates, which meant that they were relying on getting outs on balls in play—balls that at Coors carry farther and go faster, as we’ve seen. Neagle was already prone to giving up home runs, a problem that was exacerbated by pitching in Coors. Hampton’s HR rate tripled in his first season with the Rockies. Adair comments that fastballs seem to be a little bit faster, and change-ups lose less velocity during flight than they would at sea level for the very same reason. The batter’s timing is less disrupted because the velocity difference between a good change-up and what he’s used to seeing is reduced. What was a dominating change-up in most parks turns into a third-rate fastball at Coors. Both pitchers were considered massive disappointments, and their ERAs soared after they landed in Colorado. The team’s record regressed by 9 games in the first Rockies season for Hampton and Neagle.
TABLE 8-2.4 Colorado Park Factors for Groundball Percentage (of balls in play)
One explanation sometimes cited for the increase in hitting at Coors is that, even after home runs are accounted for, Coors plays as a “flyball” park—it increases the tendency of batters to hit the ball in the air, resulting in more doubles and triples than would be expected. That turns out not to be the case, though. Looking at the number of batted balls that stay in the park, broken down by groundballs or flyballs, the percentage of groundballs is actually slightly higher at Coors than in Rockies road games—although the park factor is less than 2 percent, well within the margin for error (Table 8-2.4).
Another effect of the higher overall offense at Coors is that it takes more pitches to get through a game. Because it’s harder to get batters out, more of them come to the plate in a typical game. Each game averages 6.5 percent more pitches when played in Colorado—that equates to an extra 5 or 6 games’ worth of pitches per year that the Rockies have to get out of their staff. Just about all that difference is a direct result of there being more batters; there’s virtually no difference in the number of pitches each batter sees per plate appearance between Coors and the rest of the league (Table 8-2.5).
In an effort to weigh other factors that might make the ball travel farther, the Rockies have experimented with keeping baseballs in a humidor prior to games at Coors, believing that higher humidity will make it easier for pitchers to keep the ball in the park. There is some scientific basis for that belief. Adair says that “long flies hit with balls stored under conditions of extreme humidity could be expected to fall as much as 30 feet short of the distance expected for normal balls.”
After the Rockies’ experiment became public, there were attempts to experimentally determine the effect of humidity on a baseball’s “coefficient of restitution,” which measures how elastic, or lively, a ball is. One such experiment was done by David Kagan (CSU Chico Department of Physics) and David Atkinson. Their results (documented at http://phys.csuchico.edu:16080/kagan/profdev/COR.pdf) agree with Adair’s findings. High humidity results in a less lively baseball.
TABLE 8-2.5 Colorado Park Factors for PA per Game and Number of Pitches per Game
However, the effect of the humidor is overstated. The Rockies were keeping the humidor at about 40 percent humidity, versus the Denver air, which can often be 10 percent or lower. While the difference between zero and 100 percent humidity can produce an effect of 30 feet distance on a batted baseball, the 30 percent difference between the humidor and the ambient air would produce an effect of only about a nine-foot reduction in distance. But even more importantly, the Rockies claimed they were keeping the balls in the humidor at around 90 degrees Fahrenheit, which turns out to be self-defeating. A warmer ball is more elastic than a colder ball, and thus will travel farther. The effect from temperature would completely counteract the effect of the wetter air. So other than providing a little physics lesson on the sports pages, the great humidor experiment really didn’t amount to much.
Fielding
But even if the fences are adjusted, the high-altitude stadiums will still be a batter’s boon, and a pitcher’s bane. With fences moved back, there will be acres of ground for balls to fall in for base hits. . . .
With the smaller drag, the ball will also get to the outfielder faster in Denver than at Fenway Park in Boston. Indeed, a hard-hit “gapper” hit between the outfielders will reach the 300-foot mark about 0.3 second sooner in Denver than at sea level, thus cutting down the range of the pursuing outfielder 8 or 9 feet, a not inconsiderable amount in this game of inches. Even the range of a shortstop covering a line drive or one-hopper will be cut by nearly a foot in Denver.
Here we see that Coors alters the game for everyone on the field. Hitters feast on pitches with less movement, driving them farther than at sea level. Those batted balls move faster, so fielders have less time to react and catch the ball. The result is that more balls hit in play will fall for base hits. We can measure the batting average on balls in play (often abbreviated BABIP) against a team as well as Defensive Efficiency (created by Bill James), which measures the percentage of batted balls turned into outs as a measure of overall team defense. Defensive Efficiency is just 1 minus BABIP—thus, we’ll speak of either a .700 Defensive Efficiency or a .300 BABIP. We’ll stick with the batting average representation (BABIP), as its scale is more familiar to most readers:
TABLE 8-2.6 Colorado Park Effect for Defensive Efficiency
BABIP = (H – HR)/(AB – HR – SO)
The vast majority of home runs are hit out of the field of play, so removing them from the hit total leaves us with just the hits where the defense had at least a fighting chance of retiring the batter. Similarly, strikeouts end at-bats without putting the ball into play, so they, along with home runs, are removed from the denominator. By calculating the park factor for BABIP, we can see how much harder Coors Field is on fielders (Table 8-2.6).
We saw before that Coors does not really change the mixture of groundballs and flyballs that are produced, so we can’t attribute the change in BABIP to a shift in distribution. In fact, the effect is pronounced and roughly the same magnitude regardless of the type of batted ball. Whether a groundball that scoots by a diving shortstop or a line drive hit past a sprinting right fielder, balls fall for hits roughly 15 percent more often (Table 8-2.7).
TABLE 8-2.7 Colorado Park Effects for Different Types of Batted Balls in Play
The Proper Use and Interpretation of Park Effects
Since we now know that Coors Field has genuine and pronounced effects on player statistics and team offense, the next question to consider is this: How can we make use of that knowledge to better understand player value in an extreme environment like that of the Rockies’ home field?
Consider the 1997 National League MVP race, where Larry Walker beat out Mike Piazza, getting 22 first-place votes to Piazza’s 3 (Jeff Bagwell, who finished third overall, also got 3 first-place votes). Walker had more home runs (49 to 40), hits (208 to 201), runs (143 to 104), and RBI (130 to 124). He also posted a higher batting average (.366 to .362), on-base percentage (.452 to .431), and slugging average (.720 to .638). Seems like a clear case for Walker, at least offensively. However, Piazza played for the Dodgers in pitcher-friendly Dodger Stadium, while Walker played half his games in Coors Field. The two players’ aggregate park factors were almost 15 percent different, in Walker’s favor. If we make the proper adjustments, we can see what a performance in a neutral park that’s equivalent to each hitter’s stats would be (Table 8-2.8).
TABLE 8-2.8 Mike Piazza vs. Larry Walker Park-Adjusted Statistics, 1997
Taking park effects into account to put both hitters on a level playing field, Piazza and Walker are now much closer. Piazza has a 21-point advantage in adjusted batting average, an 11-point advantage in adjusted on-base percentage, and has narrowed the gap to 32 points in adjusted slugging average. Taking into account the difficulty in finding good-hitting catchers compared to good-hitting right fielders, there’s a compelling argument that Piazza should have won the MVP in ’97 in a landslide, given that he and Walker were almost equivalent in value as hitters before considering their positions.
The careful reader will note that we didn’t rely upon Walker’s home-versus-road stats and Piazza’s home-versus-road stats to determine whether to adjust their stats or not. Rather, we used the park factor observed for all players aggregated together. Walker actually posted comparable or better numbers on the road in 1997 (.346/.443/.733 on the road versus .384/.460/.709 at home). Yet we penalized him for his home park, even though his personal stats were not better at home. Is this fair?
Whether or not it’s fair depends on what you are trying to accomplish. As we’ve seen, park factors are calculated using the league-wide change in offensive production for the park in question. For an MVP discussion, which is centered on player value, the average park adjustment is exactly what we want.
Park factors are used to adjust for the value of a player’s performance, not to project how a particular player’s stats would change in another park. The entire league got a huge boost from playing in Coors. As a result, each individual run was less valuable in Colorado than it was elsewhere in the NL, because it takes more runs to win a game there.
Think of it as a currency exchange between runs and wins. Suppose I get paid for doing some kind of work at two different parks (Coors Field, and let’s pick Busch Stadium in St. Louis, which not only played as a roughly neutral park but also has a beer-related name) and get paid in the form of a voucher that I can convert into cash. I earn both 10 Coors vouchers and 10 Busch vouchers. I’m able to convert 10 Coors vouchers into a dollar, but it takes only 8 Busch vouchers to get a dollar. Which is worth more? The 10 Coors vouchers are worth $1, but the 10 Busch vouchers are worth $1.25. I can’t say 10 vouchers = 10 vouchers, because one voucher buys less than the other. To normalize this discrepancy, we use a currency converter, or a park factor, to say that 10 Coors vouchers and 8 Busch vouchers have equivalent purchasing power.
The run-park factor is a currency conversion from Coors runs to NL league-average runs because the typical number of runs to earn a win is different in those environments. Walker spent half his games producing Coors runs, the other half producing NL runs. Even if he was more productive on the road, we still need to deflate the value of the home stats because the rest of the world cares about wins, and Coors runs purchase fewer wins than NL runs do. The fact that Walker did not perform better at Coors, relative to the league-wide improvement at Coors, means that his production was worth relatively less at home than away.
Suppose I buy the most expensive house on the block with a market value of $80,000 in a neighborhood where the average price is $50,000—then I have the most valuable asset of any of the houses. But if that house appreciates at a slower rate than the rest of the homes over the next ten years (say 4 percent instead of 10 percent annually), then my house will eventually be worth less than the average: $118,419 to $129,687. My house’s value didn’t get the same economic boost from my environment as those of other homeowners, so now that asset is worth less than other assets even though it started as the most valuable.
Similarly, Walker’s observed offensive production didn’t appreciate as much at Coors as most players’ hitting did, so his relative value compared to those players drops. He was still tremendously valuable at Coors and overall, but not quite as valuable as the raw numbers might have you think.
Trying to project what that particular player would do in another park or league, rather than estimating the value of his performance, requires a different type of analysis because each park can have a different specific effect on players. A park may influence right-handed and left-handed batters differently. A park may have the most effect on an aspect of the game that isn’t part of a player’s repertoire; on the other hand, the player’s skill set may be uniquely positioned to take better advantage of a park’s quirks than average.
Consider Dante Bichette, an extreme flyball hitter whose statistics soared when he got to Colorado. If because of his tendencies to loft the ball he gained more in batting average and power than usual, he was more valuable in Coors than elsewhere. Suppose Bichette had hit .310/.380/.600 in raw stats, and that a clairvoyant was able to tell us that if Bichette had played in a neutral park, such as Busch Stadium, he would have hit .250/.310/.440. That’s an 80 percent boost in offense, compared to the typical 20 percent to 40 percent jump. That extra run-creating ability above and beyond what’s typical has real value at Coors. When we apply the regular park adjustment to Bichette’s production, we might find that his park-neutral value of his Coors-enhanced performance may in fact be .280/.350/.510—higher than what the clairvoyant told us he would actually hit at sea level, reflecting the value of his taking extra advantage of Coors.
On the other hand, consider Walt Weiss, who posted OBPs of .375 or higher for several years in Colorado but had no power. Would he have done much worse at sea level? His batting average at Coors would be expected to go up because more of his groundballs would go for hits (as we showed earlier). But groundballs rarely turn into doubles and triples, so Weiss’s slugging average was likely not enhanced as much as Bichette’s (or indeed, an average hitter’s).
The run-based park effect that we’ve been discussing can give you only a rough approximation, based on how the average player gained (or lost) in a particular park. It’s imprecise to project those general adjustments down to specific players and say, “This is what they would have done if it weren’t for the home park.” It’s difficult to answer that question with any certainty without a much deeper analysis of specific types of hitters. These include contact hitter versus free-swinger, righty versus lefty, and groundball versus flyball in different kinds of parks.
Since it takes more runs on average to win in a high-offense ballpark than in a low-offense ballpark, the value of a run is proportionally lessened. If a player at Coors, such as Walker, produces at the same level at home and away, then his bat is worth less at home than it is on the road. When the value of a run is taken into account, Piazza’s bat was comparable in value to Walker’s.
How much does Coors Field matter? It’s critically important for a variety of reasons:
For not overrating hitters with superficially superior statistics.
For planning for how taxing it will be on a pitching staff.
For evaluating fielding, recognizing that reaction times are lessened.
For understanding the value of hitters and pitchers contributing toward winning.
And for Mike Piazza, it might matter even more than that. Coors Field probably cost him the 1997 NL MVP Award.
Consistent, but Not in a Good Way
Of the teams in existence during the Rockies’ inaugural season, there’s only one sub-.500 team that has been more consistent (defined by the standard deviation in seasonal winning percentage) than the Rockies year after year.
Most Consistent Teams Since 1993, Ranked by Lowest Standard Deviation
