# Home Runs & Hole-in-One Statisticians Show that High Altitude Makes Hits Longer

December 1, 2006 — Two mathematicians at the University of Northern Colorado are taking a fresh statistical look at the effects of elevation on hitting -- specifically at Coors Field in Denver, where the field is at a significantly higher altitude (5,277 feet) than any other major league ballpark in the United States. They found elevation can significantly change the percentage of slugging.

DENVER -- Although baseball season is over, and players are taking a break from training, statisticians are in high gear, calculating who had the league's best batting statistics. Researchers at University of Northern Colorado now know for certain just where balls fly farther.

Sports fans suspect it. Pros know it. Now mathematics confirms it. Balls hit at Denver's Coors Field carry farther than in any other stadium in the country.

"We now actually have statistical data supporting this theory of a 'Coors Field Effect,'" Jay Schaffer, a statistician at University Northern Colorado in Greeley, tells DBIS.

They scored big with their latest findings: proof balls fly farther in thin air. That's because the air has fewer air molecules that normally would slow the ball down.

At Coors Field, the purple seats are one mile high. The Rockies' number of homeruns is often thought to be inflated by the Coors Field Effect. Sure enough, research confirms a homerun that travels 400 feet in Miami, in Denver would travel 420 feet, and in Mexico City, 430 feet.

"You already got this pre-conceived notion that the ball is going to carry so well, so they don't hit it that good," says Colorado Rockies' Brad Hawpe. "You are already breaking back, so you are going to miss the ball then."

This impacts more than just a batter's swing.

"At sea level, it's two clubs for me," says amateur golfer Katrina Steadle. "So, in Vail, I would be hitting a seven iron, and at sea level, I am probably hitting a five iron. It is a big difference." ...But for golfers, their balls are flying high.

Due to the lack of humidity in Colorado, the Colorado Rockies' baseballs are placed in a humidor to keep them from drying out. The moisture is believed to negate some of the effects of the thinner air.

BACKGROUND: Two mathematicians at the University of Northern Colorado are taking a fresh statistical look at the effects of elevation on hitting – 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.

Note: This story and accompanying video were originally produced for the American Institute of Physics series Discoveries and Breakthroughs in Science by Ivanhoe Broadcast News and are protected by copyright law. All rights reserved.

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