By Patrick Hruby
Page 2

Heads turned. The ball bid the park adieu. With a single, violent swing of his bat, Barry Bonds made baseball history Saturday in Oakland, climbing one home run closer to the immortal Willie Mays. Six hundred sixteen home runs. It's a mind-numbing number, a body of work to rival Tupac's posthumous releases. Congratulations are in order.

Wait. Hold up.

You say Bonds actually has 714 career home runs?

Barry Bonds
Jed Jacobsohn/Getty Images
Next up in his sights: 755.

Er, no. Good one. But no. Sure, if you want to get all technical, there's no arguing that Bonds has forcefully redirected 714 pitches into home run territory over his 21 major-league seasons. Yet according to the ziggurat of evidence compiled in the book "Game of Shadows," Bonds also ingested a Mexican farmacia's worth of performance-enhancing drugs during his peak slugging period, making some of those dingers less authentic than country crooner Kenny Rogers' reconstructed face.

Question is, how many? How many of Bonds' home runs are honest? And how many came courtesy of his reported juicing?

Start with a caveat: There's no way to know. At least not for sure. The homers themselves can't be replicated in a lab, let alone studied. The variables involved in each at-bat are too numerous and complex to tease out completely. The specific physical effects of taking bovine bulk builders and female sex hormones -- Bonds reportedly took both; did he end up lactating buttermilk? -- are poorly understood.

Truth be told, we can only manage a crude approximation. An educated guess, but a guess nonetheless.

On the other hand, that sure beats an unsightly asterisk.

So, how did Page 2 place Bonds' "legitimate" total at 616 homers? In taking away 98 home runs since 1999 -- when Bonds' allegedly began using steroids -- we sought to quantify the performance-enhancing effects of steroids in four hitting-related categories: strength, stamina, longevity and confidence. To do so, we spoke to a swing guru, a major league scout, training and biomechanics specialists, and an expert on the physics of baseball. We looked over hit charts and home run distances, tabulating every Bonds blast from '99 to now. We even got help from a nuclear scientist (albeit a nuclear scientist who really likes baseball).

We then did the math. Follow along ...

1. Strength

"I don't know if steroids are going to help you in baseball. I just don't believe it. I don't believe steroids can help eye-hand coordination [and] technically hit a baseball."
-- Barry Bonds, Jan. 22, 2005

Bonds is correct. Steroids alone won't help you hit a curveball. But coupled with skill and training, they will help you hit that same curveball farther. Here's how:

Barry Bonds
Stephen Dunn/Getty Images
Back in 1988, Bonds hit 24 home runs for the Pirates.

Steroids build size and strength. They allow longer, harder workouts and promote better physical gains than would otherwise be possible.

According to "Game of Shadows," Bonds began using performance-enhancing drugs and training with Greg Anderson following the 1998 season. The results were astounding. In 1997, a team media guide listed Bonds at 206 pounds. By spring training of 1999, he weighed 225, with authors Mark Fainaru-Wada and Lance Williams claiming:

    "...almost all of the gain was rock-hard muscle ... the change in Bonds' physique was startling. Around the Giants, they took to referring to Bonds as The Incredible Hulk. When Bonds took batting practice, he was driving the ball farther than he ever had before."

In 2003, Muscle and Fitness magazine reported that Bonds, then about to turn 39, weighed 230 pounds and was in "the best shape of his life." Bonds himself told the magazine that his improvement as a player was due to "training and nutrition," making him "a better athlete than before."

An accompanying photo shows Bonds and Anderson sitting in front of BALCO ringleader Victor Conte, who has a hand on each man's meaty shoulders. All three are smiling. And why not? At an age when most top athletes have a hard time simply maintaining their chiseled physiques, Bonds had packed on 20-plus pounds of added bulk.

Extra size and strength equals extra bat speed. Robert Adair wrote the book on baseball physics. Literally. His "The Physics of Baseball" has enjoyed multiple editions and is considered the classic text in its field.

BARRY'S HOME RUNS
Here is the complete list of Barry Bonds' home runs since 1999 -- including the 83 we took away from his career total after our analysis.

On page 139, Adair provides an equation relating bat speed (that is, the speed of the bat's sweet spot at the moment it makes contact with the ball) to player weight:

V = k sqrt(M/(m+M/81))

(Note: V is the velocity of the bat in miles per hour, m is the bat weight in pounds, M is the player's weight in pounds, sqrt means square root and k is a constant, 10, in mph. Phew!)

According to Adair's formula -- and don't worry, we asked him to double-check the calculations, since our last math class came in high school -- the 206-pound Bonds generates a bat speed of 67.34 mph, while the 228-pound Bonds swings the same 32-ounce bat at 68.81 mph, an increase of 1.48 mph.

Trust us: That's more impressive than it sounds.

Bat speed is the key to power hitting. Jack Mankin is an electrical engineer. He also is a youth baseball coach and something of a baseball swing junkie.

Way back in 1986, Mankin bought a VCR that featured frame-by-frame replay, a rare and exotic luxury at the time. He taped about 100 major league games, then set out to chart the swing mechanics that separated great hitters from average ones.

Mankin taped plastic strips to his television screen. He used a grease pencil to trace body movement. He plugged his findings into computer spreadsheets. He's still at it today.

Recently, Mankin looked over clips of Bonds, from 1988 and the present. Conclusion?

"There's absolutely no change," said Mankin, who runs a Web site devoted to bat speed. "The only difference is that back then, most of his home runs were just enough to clear a 360-foot fence. Now, he's up to 400-some with the same dang swing."

The same dang swing. Only faster. In an excellent 2005 San Diego Union-Tribune article detailing the effects of steroid use on power hitting, major league scouts claim Bonds' bat speed not only stopped declining but also increased during the time he worked with Anderson -- an observation consistent with Adair's weight-to-bat speed formula.

Barry Bonds
Jonathan Daniel/Getty Images
In his first year with the Giants in 1993, Bonds won his third MVP award, hitting .336 with 46 home runs.

"I've seen [Bonds'] bat speed improve," a longtime major league scout told Page 2. "But I can't say it's because of steroids."

How does extra bat speed help a hitter? Simple. While many factors influence the height and distance of a flyball, the most important variable is the speed of the bat at the instant it connects with a pitch.

Mont Hubbard, a mechanical and aeronautical engineering professor at the University of California-Davis, co-authored a 2003 American Journal of Physics article examining home run ball flight. An accompanying graph plots bat speed against flyball distance -- and like a rising homer, the curve sloped upward, almost in a straight line.

The faster the swing, the longer the long ball.

"We work with bat speed a lot, especially with a lot of the [major league] guys who come down here before spring training," said David Donatucci, director of the International Performance Institute at the IMG Academies in Bradenton, Fla. "If you're working [at] the skill [of hitting] and increasing in strength at the same time, you'll become a more powerful hitter."

Alan Nathan, a baseball physics buff and nuclear physics professor at the University of Illinois at Urbana-Champaign, estimates every one mph of extra bat speed translates into roughly six feet of added flyball flight distance. Back to Bonds. By bulking up and increasing his bat speed, he added about nine feet to his average flyball distance -- the difference between the warning track out and reaching the outfield seats.

ANGRY BLOGGER FAQ
Q: I'd like to pick apart this article. Where should I start?

A: Pretty much anywhere. Everything in the article -- especially the number 616 -- is rooted in educated guesswork.

Q: Such as?

A: The player mass to bat speed formula. Physically modeling a big-league swing -- what physicist Robert Adair calls "a rather complex energy transfer system" -- isn't easy. Adair's formula is a logical approximation rooted in the assumption that the total energy a batter can generate is linearly proportional to his muscle mass. The root assumption is pretty sound; the bat speeds it produces are estimates.

Q: Let's talk distance. Are Bonds' home run lengths totally accurate?

A: No. Home run distances are historically -- and notoriously -- inaccurate, calculated via mathematical formulas, specialized cameras, inexact eyeballing and old fashioned walking out the distance by foot. Some teams, like Boston, don't even bother. Check out this excellent Wall Street Journal article for more information.

Q: OK, so the home run distances are approximations. How about your estimates of where they cleared the park?

A: Also guesses. And fairly crude ones at that. Along with date, opponent and distance, each Bonds home run came tagged with a letter code marking the general area it left the stadium. Stats, Inc. provided Page 2 with a radial chart (click to see popup) matching each letter to a portion of the field. Page 2 then matched groups of letters to the outfield distances available for each stadium: center, right, left, down both foul lines, and sometimes a few additional (often quirky) markers. In general, we broke things up as follows: C-E, left-field line; F-K, left; L-O, center: P-U, right; T-X, right-field line.

Could these estimates be more accurate? Definitely. Watching videotape of each Bonds home run, for instance, would be a good place to start. Unfortunately, Page 2 has neither the time nor the access. (If anyone out there wants to take up the gauntlet, drop us a line. We'd love to know what you find out).

Q: How about all those extra walks the supposedly juiced-up Bonds started receiving? Even if a non-juiced Bonds hit home runs less often, he would have seen more pitches. Shouldn't Barry get a few home runs back?

A: We struggled with this, but ultimately decided to leave it out, mostly because walks are highly dependent on: a) game situation; b) the pitcher on the mound; c) manager discretion.

Still, for the sake of argument, suppose that a non-juiced Bonds walks in 1999-2005 at the same rate he did in 1996-98, once every 4.84 plate appearances. He gets 223 extra at-bats, and at his 1996-98 home run rate (one per 13.45 at-bats), hits another 17 home runs.

Complete Angry Blogger FAQ.

Now for the fun part. Using statistics and a chart provided by STATS, Inc., Page 2 examined every home run hit by Bonds from 1999 to May 2 of this year, 301 in all.

The entry for each home run lists the ballpark where it was hit, the estimated distance it traveled and the approximate area where the ball cleared the field of play. Comparing each homer to the ballpark dimension diagrams found at andrewclem.com, we sought to answer a single question:

If you take away the extra nine feet of flyball distance Bonds generated by putting on 20 pounds of muscle, how many of his home runs fall short?

Here's how the answer breaks down:

• 1999: four home runs out of 34.
• 2000: nine out of 49.
• 2001: 18 out of 73.
• 2002: 11 out of 46.
• 2003: 10 out of 45.
• 2004: 13 out of 45.
• 2005: one out of five.
• 2006: zero out of five.

In total, Page 2 estimates that 66 Bonds home runs would have landed inside the fence sans his alleged steroids use. Again, this is an approximation. But is our guess wholly unreasonable?

According to Adair, a 1 percent change in flyball distance translates into a roughly 7 percent change in the probability of hitting a home run. Since Bonds enjoyed a 2.4 percent increase in flyball distance, he should have seen a 16 percent increase in home run production.

Our number -- 66 home runs -- represents about 22 percent of Bonds' home runs since 1999. The numbers are in the same ballpark. Emphasis on in.

2. Stamina

"Before, I would train really hard in the offseason and work out just a little bit during the season, trying mostly to keep my flexibility. Then I'd hit a wall in August. But the last few years I've been training all year, and that has changed my whole career, because I don't get weaker during the year. I don't suffer a down spell or hit bottom. I stay strong all year."
-- Bonds, in Muscle and Fitness magazine, 2003

Perhaps you've heard the term: The dog days of summer. Temperatures rise. Injuries nag. Fatigue sets in, mental and physical. The season seems endless. Older players feel the grind most acutely.

Some switch to lighter bats. Others skip batting practice. Anything to conserve precious energy.

Enter steroids. In "Juiced," Jose Canseco writes that performance-enhancing drugs kept him feeling fresh, as if the last day of the season was the first day of spring training. "Game of Shadows" reports that using human growth hormone helped Bonds retain his buffed-up body without rigorous training.

That August wall? Knocked down like the one in Berlin. Get pumped, stay pumped, with more pep to boot.

Without steroids, how much would Bonds have sagged in the stretch? We don't really know. But we can make another reasonable guess. Assume that instead of gaining 1.8 mph in bat speed, an aging Bonds would have lost that amount by the end of July.

Subtract nine more feet from Bonds' charted home runs from August through October, and here's how many die on the warning track:

Barry Bonds
Otto Gruele Jr./Getty Images
In 1998, Bonds hit 37 home runs -- 33 fewer than Mark McGwire.

• 1999: six home runs.
• 2000: three home runs.
• 2001: five home runs.
• 2002: zero home runs.
• 2003: one home run.
• 2004: one home run.
• 2005: one home run.

Add it up, and that's 17 more homers we're taking away from Bonds, bringing our running total to 83. Time to check our work.

3. Longevity
"I don't have to [use steroids]. I mean, I'm a good enough ballplayer as it is. I don't need to be any better. I can't get any better at this age."
-- Bonds, in an interview with Bob Costas, 2002

No kidding. At age 39 in 2004, Bonds hit a home run every 8.3 at bats -- the second-best rate of his career, and far superior to Babe Ruth (16.6), Willie Mays (17.1) and Ted Williams (15.8) at the same age.

Is Bonds simply a marvelous athlete, benefiting from advances in training and nutrition unavailable to the sluggers of yore? Perhaps. Or perhaps Bonds has access to better chemicals.

Testosterone levels decline with age. Typically, so does athletic performance. Recent research suggests that both testosterone and human growth hormone may have significant anti-aging effects.

Now consider: At ages 31-33, the top 10 home run hitters not named Barry Bonds (and not including contemporaries Sammy Sosa, Mark McGwire, Rafael Palmeiro and Ken Griffey Jr.) collectively averaged a dinger every 13.8 at-bats. From age 34 through 39, however, that average fell to one home run per 15.6 at bats, a drop-off of 1.8.

Similarly, Bonds at ages 31-33 averaged a home run every 13.5 at bats. But from age 34 onward -- when he allegedly started using performance-enhancing drugs -- Bonds has averaged one home run per 8.5 at bats, an unprecedented surge.

Dingers!
In an excerpt from "Dingers: A Short History of the Long Ball", Peter Keating explains that Bonds dominated his league like no player in history.

If "Game of Shadows" is correct, steroids helped Bonds throttle Father Time, becoming more powerful at an age when most players slip significantly. How many fewer home runs would he have hit had his production declined at the rate of his non-juiced peers?

Let's crunch the numbers:

• At 31-33, Bonds' home run rate is 13.5. He suffers a drop of 1.8, making his 34-39 rate 15.3;
• At 34-39, Bonds had 2,477 at-bats;
• Divide 2,477 by 15.3, and you get 162.

By the standards of his historic peers, Bonds should have have hit about 162 homers from age 34 through 39; in reality, he smacked 292. The difference: 130 home runs.

Are all of those bogus? Hard to say. Give Bonds the benefit of the doubt. Suppose, for argument's sake, he's as ageless as the man he's chasing, Hank Aaron.

Barry Bonds
Jed Jacobsohn/Getty Images
Bonds cracks his record 71st home run in 2001.

At ages 34-39, Aaron enjoyed a rare rise in his home run rate, from 15.4 to 13.0 (explained, in part, by a move from Milwaukee's County Stadium to more homer-friendly Atlanta Fulton County Stadium). Assign the same moderate 2.4 boost to Bonds. Then divide his at-bats accordingly.

Bonds ends up with 223 homers, much closer to his real-life total of 292. And the difference between the two -- 69 fewer home runs -- is pretty close to the 83 we've already taken away.

Confidence

"There are some things I don't understand right now. The balls I used to line off the wall are lining out [of the park]. I can't tell you why. Call God. Ask Him."
-- Bonds, to the San Francisco Chronicle, 2001

So Bonds is stronger. More energetic. In goes the needle. Out go the long balls. His confidence surges.

Out go more long balls.

Feel good. Play better. Self-assurance is the great sports intangible, nearly as important as raw talent. Think you can do it? You're halfway there.

"Look, steroids make you better," says the major league scout, a former player himself. "But the other factor is confidence. You can't measure that. But there is a value there, and athletes all thrive on it. They need to know that they can perform."

Call God. Spoken like a man who knows he can perform. Bolstered by steroids, would a supremely self-assured Bonds swing for the fences more often? Seems likely. From 1987 to 1998, Bonds' average ground ball to flyball ratio was 0.81; between 1999 and last season, it was 0.62 -- an increase of about 19 extra flyballs for every 300 balls put into play. Maybe a pumped-up Bonds was trying harder to go deep. Maybe he belted additional home runs as a result.

More on confidence: "Game of Shadows" reports that performance enhancers improved Bonds' eyesight, helping him track pitches. Coincidence? Not necessarily. Extra bat speed means extra time to differentiate between a fastball and a slider.

Moreover, a 2002 University of California San Francisco study found that older men with higher testosterone levels performed better on cognition tests than men with lower levels. Two years later, Harvard researchers discovered that men with higher testosterone levels are quicker to solve spatial-relationship problems.

Really, what is spotting and crushing a major league fastball if not a spatial-relationship problem ... played out at warp speed?

"People talk about bat speed, but nobody talks about [Bonds'] eyesight," said the major league scout. "He sees a pitch so quick, so early. He can see it and relay that information to his muscles faster than anyone else. That's what all good hitters do. They know what the ball is when it has been out of the pitcher's hand for just 10, 15 feet. Only special people do this."

How many home runs are quicker reactions and a juice-boosted feeling of invincibility worth? Could be five. Could be 25. Could be more, if fearful opposing pitchers lack confidence and fail to summon their best stuff.

What seems clear is this: Confidence helps, same as muscle. Let's say increased self-assurance allowed Bonds to belt 15 more home runs -- about three per season. That brings our grand total of tainted dingers to 98, a number that corresponds nicely with 1998 -- Bonds' last clean year, if "Game of Shadows" has it right. And even if the book is wrong, the photographs don't lie: Bonds today is a swollen sponge, a hulking parody of his lithe former self. Of course he bashed like never before. The laws of physics demand nothing less.

In his book, Adair states that if 140-pound Paul Waner uses a 32-ounce bat to hit a 90 mph fastball 338 feet, 225-pound Mark McGwire can use the same swing and same bat to drive the same pitch nearly 50 feet farther. Hello, andro!

"Bigger is better," Adair said in an e-mail interview. "But Waner was a damn good player."

Six hundred sixteen home runs. Our best guess. A long way from 715, but still an incredible number. Such is the shame in having to wonder: Without steroids, Bonds was a damn good player. With steroids, he's a good player damned.

Patrick Hruby is a columnist for Page 2. Sound off to Page 2 here.



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