Inflated Players ... and Numbers?

With Barry Bonds, the sports world’s most famous suspected substance abuser, tied with Babe Ruth in career home runs, only 41 shy of Hank Aaron’s all-time record, many observers are fretting that baseball’s ledgers have been permanently compromised.

But those who study the numbers most closely aren’t so sure.

Steroids and other performance-enhancing substances “ought to upset baseball researchers as much as anybody, since we make our bread and butter out of the integrity of baseball’s numbers,” statistician Nate Silver wrote in the recent book “Baseball Between the Numbers,” an anthology of analytical studies published by website Baseballprospectus.com.

The statisticians who pore over baseball’s numbers with a devotion unmatched in any other sport -- the study is known as “sabermetrics,” after the Society for American Baseball Research, or SABR -- have been looking for signs of a “steroid effect” for several years.

They’ve come up largely empty-handed.

“The subject is as hotly debated in the statistical community as it is in the general community,” said J.C. Bradbury, an economist who runs the statistics website Sabernomics.com. Players “are getting bigger, and they’re hitting more home runs. Why? The very obvious answer before us is steroids, but it’s very difficult to test their impact simply by looking at data within the game.”

Some doubt the riddle will ever be solved, partially because there is no solid information about which players used the illegal substances, in what years, and how they might have performed without them.

Of course, there’s no lack of evidence that numerous players turned to steroids and other so-called performance-enhancing drugs in the last decade, and that some improved their statistics in that time. Several, including New York Yankees first baseman Jason Giambi, reportedly confessed to steroid use before a Bay Area grand jury in 2003 and others have admitted in books to illegal drug use while implicating other players.

These disclosures and others have shined a spotlight on some of the sport’s biggest stars with the gaudiest records, including Bonds. Questions have also been raised about lesser players experiencing isolated but unexpectedly productive years.

Nor is there any question that baseball has experienced a surge in offensive power since the mid-1990s, a period that coincides with reports of increased steroid use in the game. In the National League, home runs per game increased to 1.01 from .87 between 1993 and 2005; in the American League, the jump was to 1.09 from .92. Strikeouts per game also increased, but runs and hits per game remained nearly static in both leagues, suggesting that more hitters may have been swinging for the fences and, perhaps, pitchers’ steroid use had increased as well.

None of that identifies steroids as the culprit. “It’s well nigh impossible to ascribe any particular effect to any particular cause,” said Neal D. Traven, co-chairman of the statistical analysis committee at SABR.

For one thing, steroids have not been invariably a magic bullet for the kind of physical improvement that translates into success on the diamond. Some say that steroids, used haphazardly, can work against the kind of physical development needed for baseball or lead to physical breakdown.

According to “Game of Shadows,” a book by two San Francisco Chronicle reporters based on secret grand jury testimony and other material, Bonds’ steroid use initially produced upper-body bulk that damaged his elbow, requiring surgery in 1999 and a nearly two-month layoff.

When he returned, he felt “muscle-bound and inflexible.” Only after he added human growth hormone (another banned substance) to his chemical intake did his muscle quickness and flexibility improve to the point where his home run output might have been affected, the book says.

Some players have improved after quitting steroids, according to Silver, who studied the records of 76 major and minor leaguers suspended during 2005 for use of illegal performance-enhancing substances. Silver observed that most did decline after being suspended and presumably giving up drugs, but the difference was “just on the verge of being statistically significant.” On the whole there was no “systematic, large-scale change.”

“I always point to the difference between Jason Giambi and Jeremy Giambi,” Silver said. “That tells part of the story.”

Jason Giambi reportedly admitted to the 2003 grand jury that he took steroids as early as 2001, after which he hit an average of 40 homers a year for three years for the Oakland Athletics and New York Yankees before a run of injuries in 2004. Now presumably steroid-free, the Yankees’ starting first baseman is leading the team with 12 home runs. His younger brother Jeremy, who admitted 2003 steroid use to the grand jury, according to the Chronicle, failed to match his peak home run season of the year before and was driven out of the major leagues by injuries and poor performance after 2003.

Steroids haven’t been used only by hitters. Nearly half the major and minor league players snared by baseball’s steroids testing program in 2005 were pitchers. “If both pitchers and batters are doing them, the effect would wash out,” Traven said.

At least one analyst even doubts that the rise in home runs is sufficiently remarkable to require any explanation beyond sheer chance. The cluster of six 61-plus home run seasons by Mark McGwire, Sammy Sosa and Bonds from 1998 through 2001 is entirely consistent with the randomness of home run records, according to a 2006 paper by Arthur De Vany, an emeritus professor of economics at UC Irvine who runs a consulting firm.

“Steroids do not come into the picture,” he wrote, “nor is there any need to invoke explanations that go beyond the natural variation of home run hitting, at-bats, chance, and the laws of extreme human accomplishment.”

Statisticians are wary of giving steroids credit for the offensive explosion not only because their effects are hard to pin down, but because of other changes in the game. In his “Historical Baseball Abstract,” published in 2001, Bill James, perhaps the best-known sabermetrician, listed six trends contributing to 1990s offense, of which only one -- the rise of strength training -- could even remotely be connected to steroid use. The others included changes in bat design that enhanced bat speed, changes in pitching and hitting styles that increased opposite-field home runs and, especially, a wave of new, hitter-friendly ballparks.

Seven of the 10 most hitter-friendly parks in major league baseball in 2005 (ranked by comparing home and road statistics by the home team) were built in the 1990s or later. At the top of the list is Denver’s Coors Field, a high-altitude stadium so offense-enhancing that the Colorado Rockies led the National League in home runs in four of their first five years in the park; in 1997 the Rockies out-homered the runners-up in the category (the Dodgers and Atlanta Braves) by 65 homers despite finishing third in their division.

Others conjecture that the relationship between pitching and hitting has lost its equilibrium. “I have a general impression that pitchers have reached some sort of physical limit,” Traven said. There’s evidence that fastball speeds have reached a plateau short of 100 mph, while hitters still have room for improvement. “It may be chemicals, but also technique and training,” he said.

Major league expansion in 1993 and 1998, which added four teams, may have diluted pitching. Bradbury has compiled figures showing that the range of earned-run averages from worst to best among pitchers has reached a historical high. “If you have hitters taking advantage of lesser pitchers, you’ll have an uptick in offense,” he said.

For many fans, the chief exhibit for the effect of performance-enhancing substances on baseball remains the career of Bonds. Reporting by the San Francisco Chronicle and in “Game of Shadows” strongly indicates that Bonds used such substances beginning in the late 1990s, just before embarking on a record-breaking offensive surge in 2000, the year he turned 36, including his record 73 home runs in 2001.

Nevertheless, without independent evidence of Bonds’ drug use, statisticians say, there might be little reason to deduce it from his record alone. Some of Bonds’ skills aren’t commonly regarded as steroid-related, including his hand-eye coordination and his plate discipline.

Late-career power surges like Bonds’ aren’t unprecedented, although none has been so pronounced. Sean Forman, proprietor of the statistical website baseball-reference.com, observed in a study that Aaron recorded the highest home run rates of his career -- that is, homers per balls put in play -- at the ages of 37 and 39, when he hit 47 (the highest total of his career) and 40 homers, respectively. Ted Williams tied his second-best season home run total with 38 at the age of 38. Williams also recorded the best home run rate of his career at the age of 41, his last year as a player, when he hit 29 homers in only 113 games.

Yet no player has ever hit homers as prolifically after age 35 as Bonds -- 220. “Bonds isn’t unique, though he’s certainly the best of the bunch,” Forman said.