# Home Runs & Hole-in-One

## Statisticians Show that High Altitude Makes Hits Longer

December 1, 2006

The physics of atmospheric pressure was well known -- air resistance is lower at higher altitudes. Statisticians have now demonstrated that the average hit at Denver's Coors Field -- the highest Major League field in the United States -- carries farther than at any other stadium in the country. A homerun that travels four hundred feet in Miami,would travel 420 feet in Denver.

## Science Insider

BACKGROUND: Two mathematicians at the University of Northern Colorado are taking a fresh statistical look at the effects of elevation on hitting ý specifically at Coors Field in Denver, Colorado, where the field is at a significantly higher altitude (5,277 feet) than any other major league ballpark in the United States. They found that elevation can significantly change the percentage of slugging.

ABOUT THE STUDY: Jay Schaffer and Erik Heiny studied the effects of elevation on slugging percentages -- the total number of bases divided by the number of at bats -- in major league baseball in 2003. They did this by applying a statistical model to determine whether elevation was a significant factor on the hitting statistics for both major leagues. They found that the slugging percentage at Coor's Field is about 9.2. percentage points than for stadiums at middle elevations (between 500 and 1,100 feet), and about 12.5 percentage points higher than at elevations below 500 feet. Other analysts have argued that the effect could also be attributed in part to the ballpark dimensions. However, although it is one of the largest ballparks in the major leagues, its dimensions aren't much different from other stadiums.

THE AIR UP THERE: The "thin air" at such a high elevation means that a baseball carries father, so it's easier for players to hit a home run. Specifically, the high altitude decreases the amount of air resistance on batted balls, so they travel farther when hit. The low air pressure means the pitches "break" less severely and are also easier to hit. To combat this effect, baseballs used in games at Coors Field are placed in a humidor beforehand to increase their weight. Earlier mathematical studies have shown that because of the elevation, a baseball travels roughly 10 percent farther at Coors Field than it does in other stadiums.

The American Mathematical Society and the Mathematical Association of America contributed to the information contained in the TV portion of this report.

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## Did you know?...

The Denver Rockies are known as the "Blake Street Bombers," because of the stadium's location (on Blake Street) and the high rate of home runs at the stadium. In 2001, 58 percent of the tea's home runs occurred at Coors Field, while batters for visiting teams made 60 percent of their home runs at the "mile-high" stadium.

Jay Schaffer
Tel: 970-351-1676
Jay.Schaffer@unco.edu

American Mathematical Society
Providence, RI 02904-2294
Tel: 1-800-321-4267

The Mathematical Association of America
Washington, DC 20036-1358
Tel: 1-800-741-9415