# The Myth of the 500-Foot Home Run

## Do men always exaggerate the length of their long balls?

On June 24, fans at Seattle's Kingdome witnessed one of the most dramatic pitcher-hitter confrontations since Walter Johnson faced Babe Ruth. On the mound, the Mariner's Big Unit, 6'-10" Randy Johnson, the tallest man ever to play in the majors, and the most proficient strikeout pitcher in history. At the plate, Oakland's Mark McGwire, the best and strongest home-run hitter since Ruth.

Although Johnson whiffed McGwire twice on the way to a record-breaking total of 19 strikeouts, McGwire hit what was estimated as the longest home run in at least a decade. He got all of a 97-mph fastball, and launched it at 105 mph in the general direction of Canada.

On the radio, Mariner announcer Dave Niehaus marveled, "A high fly ball, belted, and I mean *belted*, deep to left field, into the upper deck! My, oh my, what a shot by Mark McGwire! That is probably the longest home run ever hit here. ... It will be interesting to see how far that ball will be guesstimated. ... We have often wondered if McGwire got ahold of a Randy Johnson fastball how far he could hit it, and I think we just saw it."

Shortly after, Niehaus gave the estimated distance: "538 feet--unbelievable, absolutely unbelievable. The longest home run ever hit here in Seattle ... the longest home run I think I have ever seen hit." Not only that, it seems to be the longest ball hit since 1988, when the distance of major-league home runs was first estimated on a wide scale. Sports pages and broadcasters across the country are still heralding McGwire's homer as one of the great feats in slugging history.

But there's a catch: The 538-feet figure, announced by the Mariners about 40 seconds after the ball landed, was an overstatement worthy of P.T. Barnum. According to three physicists who have worked independently and have written extensively on the science of baseball, the human limit for hitting a baseball at sea level, under normal temperatures and with no wind, is somewhere between 450 feet and 470 feet.

Curious that anyone could hit a ball 538 feet in an indoor park near sea level, I called the Mariners to see how they devised such a spectacular number. The team repeatedly refused to explain how they arrived at the figure or to allow me to speak to whoever made the estimate. Mariners PR Director Dave Aust stresses that the figure is "a guesstimate." "We don't really believe in the process," Aust says, distancing the team from the McGwire number.

That "process" has evolved over time. In 1988, IBM established the "Tale of the Tape" program, devising a system by which home-run distances could be estimated. Sponsorship of the Major League Baseball-licensed program was assumed by telecom giant MCI in 1992 and redubbed the "MCI Home Run Program." The program's Web site lists the 10 longest home runs of the year and provides a searchable database of the home runs of the previous two years.

"We do not measure the home runs," says MCI spokesman Cal Jackson. The distances are estimated by the individual clubs and then provided to MCI. "We act as a warehouse for the numbers that Major League Baseball sends us."

U nsatisfied with the 538-feet number, I did my own figuring. I consulted the 1976 Kingdome blueprints, a more recent laser-survey diagram of the stadium, and the *Seattle Times* game story, and visited the park twice. Here are the facts: McGwire's homer landed in the eighth row of the left side of section 240 in the second deck--439 feet (measured horizontally) from home plate and 59 feet above the playing field.

How much further could the ball have gone? Based on a review of the trajectory charts in *The Physics of Baseball* and *Keep Your Eye on the Ball: The Science and Folklore of Baseball*, conversations with University of Puget Sound physicist Andrew Rex, and correspondence with aerospace engineer and baseball researcher Roger Hawks, I determined that the McGwire home run would have traveled about 474 feet. A mighty home run, yes, but still 64 feet short of the length claimed.

Rex and Hawks agree that any home run hit that far must approximate the "maximum-distance trajectory"--that is it can only be a high fly or a normal fly, not a line drive. McGwire's homer was a high fly, as Niehaus attested, and as was confirmed by his broadcast partner Rick Rizzs, who marveled at the ball's hang time. According to the Major League Baseball system, a high fly will descend at an angle whose cotangent is 0.6. In trigonometry-for-dummies terms, what that means is that for every foot the ball would have continued to drop vertically, it would have traveled another 0.6 feet horizontally. Here's the math: 439 feet + (59 feet x 0.6) = 474 feet.

McGwire's "538-footer" isn't the only questionable long ball of the season. The MCI Web site claims six 500-footers in 1997, five by McGwire and one by Colorado Rockies star Andres Galarraga, hit in Miami. Galarraga's home run, originally announced as 573 feet, then revised at the park to 529 feet, is listed at 529 feet by MCI. By my calculations, it probably went about 479 feet. And yet another reason to doubt the 1997 numbers: Apparently, the IBM/MCI program recorded no 500-footers from 1988 to 1996.

D on't get me wrong--all the homers listed on the MCI top-ten list were remarkable shots. And I'm not arguing that 500-footers are impossible. A few have been hit, but all were aided by altitude, the elements, or both. The best-known of these, Mickey Mantle's mythical 565-foot blast on a windy day at Washington's Griffith Stadium, probably traveled about 506 feet, according to *The Physics of Baseball* author Robert K. Adair.

The MCI Web site spells out the intended method of measuring these home runs. "Distances are measured using a grid system matched to each ballpark's unique parameters and configuration. Each home run is estimated based on how far it would have traveled from home plate on a horizontal line had it not been obstructed by something (seats, fence, roof, foul pole, other stadium parts, etc.)."

If every team worked according to the MCI plan, each stadium would be accurately diagramed with a fine-grained grid related to its seating sections, level by level. This would tell the estimator how far the ball was from home plate when it landed in the seats, bullpen, or other stadium area, and how high it was above field level when it landed. (In today's stadiums, very few home runs touch the ground before hitting something higher first.)

Working with the distance and height, the estimator would assess the ball's trajectory--was it a liner? a normal fly? a high fly?--and use a formula to determine the ultimate distance the ball would have traveled. Click for the formula.

In theory this is not a bad system, but in practice it's not always fully observed. Some teams work from arcs rather than grids, making the estimators' jobs more difficult. Some teams measure only to the point of impact, rather than to the likely field-level landing point. The Rockies don't have height data, and must estimate that dimension. The Red Sox can't see where balls, hit beyond "The Monster" into the street, land. If McGwire had hit his home run in Baltimore, for example, it would have been measured at about 448 feet under the Orioles' point-of-impact house rules. Such departures make the various major-league home-run distances inconsistent, and usually make them less accurate as well.

Major League spokesman Patrick Courtney acknowledges that there have been questions about the MCI program, and says that the measurement issue will be discussed at league PR meetings next month "so everyone will be on the same page for next year."

L et's hope so. Baseball, a game of inches and meticulous record-keeping, deserves accurate and consistent data, and these awful numbers have already tainted one set of record books. Click for the story. The pity is that the home-run-measurement program, as conceived by IBM in 1988, was never uniformly implemented. Now is the time for scientists to review and refine the system and for Major League Baseball to ensure compliance and train the estimators.

After a period of adjustment, during which many long home runs will seem puny, we'll slowly reacclimate ourselves to reality. Weaned off the inflated estimates, numbers that add 60 feet to big home runs, we'll finally appreciate the majesty of a 440-footer.