Bonds Hits 644 Not 715

Since its rules have undergone only marginal change over parts of three centuries, much is made of the continuity and stability of the game of baseball. Part of the charm of baseball is the conceit or illusion that players from different eras can be fairly compared. How does Babe Ruth, for example, compare to Hank Aaron?

By definition all-time records — the most homeruns in a single season, the longest consecutive hitting streak, the most career hits — are statistics that form the basis of judging players of different eras. In swimming or running records fall like clockwork as players grow bigger and faster because of improved training methods, better nutrition, faster tracks and pools, and sometimes chemical aides. In baseball, players play directly against one another. As hitters grow bigger and faster, so too do pitchers and defensive players. Balance is generally maintained. Longtime records fall sporadically as rare players raise their game above the level of their contemporaries.

However, baseball too has it discontinuities that provide the grist of arguments when comparing players. The meaning of hitting records changed when livelier balls with a cork center were introduced in 1926. Cumulative records must certainly be affected by the introduction of night games since it is more difficult to hit the ball under the lights.

The facts that

  • stadiums have been redesigned and new ones constructed,
  • the size of the pitcher’s mound has changed,
  • the designated hitter was introduced into the American League,
  • relief pitching is used now more than in the past,
  • leagues have expanded,
  • the season has grown from 154 to 162 games, and
  • the strike zone has shrunken and grown at the collective whims of baseball umpires

have all changed the game.

Of course the most profound transformation in baseball came when black Americans were finally allowed to play major league baseball. In what sense can any record before Jackie Robinson broke the color barrier in 1947 be considered legitimate without the pool of black players to compete against? Though we can speak as if the game has remained the same, it is really profoundly different as it has changed to accommodate to new American sensibilities and sometimes American sins.

If you believe the evidence offered in Game of Shadows by Mark Fainaru-Wada and Lance Williams, the late 1990s will be known as the era of the “juiced” player, where the introduction of steroids and growth hormones made players stronger, enabled them to train harder, and to play with less fatigue. Hitting records washed away in a deluge of chemical enhancement.

Babe Ruth’s single-season homerun record of 60 in 1927 stood for 34 years until Roger Maris’s bested it by one run in 1961. That record held up for 37 years. Then from 1998 to 2001 Mark McGwire, Sammy Sousa, and Barry Bonds broke the 61 homerun mark six times, with Barry Bonds besting them all with 73 homeruns in 2001. The single-season homerun record was not broken in a single extraordinary performance by a single player, but six times by three different players. Something dramatic had happened and steroid use is a chief suspect.

As of this writing, Barry Bonds has just surpassed Babe Ruth’s career mark of 715 homeruns, though at Bonds’s reduced production rate, Hank Aaron’s 754 mark still seems along way off. Nonetheless, the question arises, how would Barry Bonds have faired has his training not been pharmaceutically augmented.

Of course, this is a question that cannot ever be definitively answered, but on can make reasoned estimates. Patrick Hruby of ESPN used an at-bat-by-at-bat approach to estimate Bonds’s hypothetical performance. Using empirical formulas relating player weight to bat speed and bat speed to distance traveled, Hruby estimates that Bonds’s hits traveled about nine feet further as a consequence of 20 lbs of steroid-induced muscle mass. Taking the distance all of Bonds’s homeruns from 1999 to 2004, Hruby computes how many would have fallen harmlessly on the warning track rather than landing in the stands. Assuming that fatigue would have reduced homerun production late in the season, Hruby then makes an adjustment for increased energy steroids might have provided to arrive at a total of 616 homeruns, nearly a hundred short of Bonds’s present total. We must now add one to Hruby’s total to 617 given Bonds’s 715th homerun.

Hruby’s computations are intriguing but they are focused too narrowly. While it is possible to go back and adjust all of Bonds’s hits for distance, doing so ignores the fact that if Bonds were hitting fewer homeruns, pitchers would have pitched differently to him. During Bonds’ most productive seasons, he was intentionally walked an extraordinary number of times. In 2004, he garnered over 232 walks of which 120 were obviously intentional. An unknown number of walks were just the result pitchers giving nothing for Bonds to hit. If Bonds were not such a dangerous hitter, he would have had far more at-bats. This increased number of at-bats would have given Bonds more opportunity to hit homeruns in a way unaccounted for by Hruby’s analysis.

Here we offer an alternative estimate. Many people have examined the trajectory in player careers, with player performance increasing at the beginning of a career and then gradually ebbing as a player ages. Though there are exceptions, the trajectories can be modeled as quadratic functions which usually peak about 27 years of age. Using a simple curve fit, we estimate Bonds’ homerun trajectory.

The attached graph shows Bonds’s actual homerun production. The solid black line shows a quadratic curve fit for Bonds’s homerun production, only using homerun data from 1986 to 1998. The standard deviation about the curve fit to 1998 is 4.8 runs per season. We assume that the homeruns from 1999 to 2004 were tainted.


From the beginning of his career through 1998 Bonds accumulated 411 homeruns. If we add the curve-fit-predicted homeruns from 1999 to 2004, when we assume steroid enhancement, and then add the small number of homeruns from 2005 and 2006, we arrive at an estimate of 644 homeruns. Given the assumptions that the curve fit reasonably estimates homerun production, then the 95% confidence limits on the estimate of homeruns, would bound this value to between 640 to 648 homeruns. These numbers would have Bonds fourth on the on-time list just behind Willie Mays’s 660 mark. Although here we challenge Hruby’s overly pessimistic estimate of Bonds’s likely homerun total without drug enhancement, we echo Hruby’s conclusion: “Without steroids, Bonds was a damn good player. With steroids, he’s a good player damned.”

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