As Barry Bonds slowly claws his way to the all time homerun record, I thought I would do some analysis to give some perspective to Bonds surpassing of Aaron's record. There has been much talk of circumstantial evidence implicating sluggers like Bonds, McGwire, Sosa and Palmiero. The Game of Shadows, Victor Conte and the lurking investigations of BALCO have created a lot of uncertainty around the "purity" of Bonds pursuit of homerun record. As a Padres fan, I have not enjoyed the fact that Bonds has hit more homeruns against the Padres than any other team, and I was present at AT&T Park when Bonds hit #700 off of Jake Peavy. But, it is hard to know what percentage of baseball players are using performance enhancing drugs, so you still expect, that if everyone were clean, Bonds would still be creating havoc, and it is very difficult to finesse out how much of Bonds domination of the sport in the last few years was due to drugs given the allegations of widespread use by his competitors.

That said, want rankles me, and most of the people that dislike Bonds breaking Aaron's record, is that he is competing against a player when the technology of today's performance enhancing drugs was not well developed, and no one expects that any of Aaron's performance was influenced by drugs.

To help me understand whether I should cheer or boo Bonds pursuit of the record, circumstantial evidence aside, I decided to analyze how the two players compare against each other, as well as the universe of 500+ HR sluggers (through the end of 2006 season).

The chart below makes me want to boo, loudly:

A little busy, but this chart shows a few things. The left vertical axis is HR's in a given year, the X axis is the player's age. I have three main HR lifecycles shown. The dark, thick blue line is the average of 20 hitters who had 500 or more HR's in their career at the end of 2006. That line shows an intuitive trend: the players gradually hit more home runs through their early years, starting to peak in their late 20's, plateau through their early 30's, then gradually decline into their mid-30s, with a sharp decline in their late 30s and early 40s. That trendline most likely understates the impact of decline because of selection. The only players in this chart for ages 35+ are the ones that were still productive in those ages. Some charts below show the number of active players and the cumulative plate appearances for the sluggers; few stay productive late in their careers.

The orange line and the brown line are the HR's for each year of Bonds and Aaron's career by age. Hank Aaron had more HR's early in his career and stayed remarkably productive late into his 30s, thus making him the all time HR leader. While each year jumps around a bit, his HR pattern roughly follows the average for the group: rising numbers in his youth, a prolonged, productive plateau and then decline. What is striking about Aaron is the length of his plateau. By the age of 23, he was hitting over 30 HR's a year, and more less maintained that through age 39, dropping off sharply at the age of 40.

Bonds has a more curious trajectory. He played college, so did not start in the majors as quickly, but showed a similar rise in power, though he did not seem to reach is productive peak until his late 20s. During that period, he actually had fewer HR's per year than the group of sluggers, modestly outperforming them through his prolonged plateau. Ages 32 to 35 suggest the he was gradually losing his power, completely in line with the slugger universe. Age 36 he hit 49 home runs, the more than any of his seasons, albeit only slightly more than some prior seasons (46 at age 29, 42 to age 32). Aaron had a very productive mid to late 30s as well, so that may not look that anamolous. Then things got very unusual. He hit is record-breaking 73 home runs at the age of 37. Aside from that, he averaged 45 home runs per season ages 38-40, almost 5 home runs higher than his "peak" years of ages 29-32. Things That Make You Go Hmmmm.

The final line on the chart (red-doted, values are on the right vertical axis) is the differential between Bonds and Aaron in their career home runs at a given age. As described, Aaron entered the majors younger and hit his peak earlier than Bonds, so when both sluggers were at age 28, Aaron had over 120 more home runs than Bonds did at age 28. That differential slid a bit as Bonds entered his "peak", but the gap stayed fairly steady through their 30s. At the end of the season when they were 35, Aaron had 554 HR's, Bonds had 445, for a difference of 109. Given that Aaron had a strong, late career, his record looked comfortably intact.

But, as the chart shows, this did not happen. The differential between Aaron and Bonds plummetted, even though Aaron had solid HR seasons ages 36-39. As described earlier, Bonds' numbers went ballistic, by absolute standards (73 HR's at age 37) but even more mystifying given his age. No way.

So, when I look at these trends, I have to either accept that Bonds was truly an anamolous player, able to generate unprecedented power in his career very late in his career at a age when most other sluggers were declining, or, as alleged, he used drugs to alter his performance in a material way. If you believe him despite this data, that is your choice. But as sluggers accumulate data, and Bonds continues to look freakishly out of line, it will be harder and harder to accept that position. No wonder Bonds is pulling for A-Rod; he has to be hoping that someone passing him makes his late career surge look less crazy. The problem with that is that A-Rod has averaged over 44 home runs a year from ages 23 to 31 (not counting this year), and done so consistently. If he passes Bonds and Aaron, his numbers will look a lot more like Aaron's than Bonds.

Any Other Late Power Hitters?
To be fair, I did want to see if there we other 500+ HR hitters that did have a late career surge. Clearly Bonds had a odd looking surge compared to Aaron and the "average", but perhaps the average masked at least one other late career power surge player. To do this, I looked at the % of HR's hit after the age of 37. The chart below summarizes all 20 hitters:

This chart shows the percentage of home runs the hitter hit age 37 and older out of their career home run total. The leftmost two (highest %; in orange) are both Barry Bonds: Bonds at the end of 2006 and the percentage that Bonds will have when he catches Aaron. The third highest is Ted Williams (in green). When you look at Ted Williams career, he did play into his 40s (he hit 29 HRs at the age of 42), he also missed three years of his prime years for serving in the Army in WWII. If you assume he would have hit some HRs instead of playing (I gave him 99; 33 per year, the average of the four years before and after his tour of duty), the percentage that came 37 and older is still high (25.0%) but much closer to Aaron (21.6%; in brown) than Bonds when he breaks the record (34.6%). The adjusted Williams total is also in green, the fifth from the left. You may notice another player over 30%, so perhaps giving Bonds some comfort? That is Rafael Palmeiro; cold comfort.

So, in conclusion, there are not any other sluggers that have a comparably high portion of their HRs so late in their career. Palmeiro is the closest, and he is, of course, faces similar suspiscions around drug as does Bonds, except he was actually caught.

Just to show it, below is a similar chart (HR by Age) I showed above with Bonds and Aaron, but this time it shows Williams, Bonds, Palmeiro and the same average.

While Williams has the gap I described above when he served in the military, and also two very low years ages 34 & 35, presumably due to injury. Without those injuries, his % past the age of 36 would have been even lower, pulling him near Aaron and away from Bonds. Palmeiro's data is also a bit damning. He was well below the average of the HR club for most of his career, then strongly above the average of sluggers starting in his mid-30s and lasting until he was 40 and then just before testing positive for a banned substance, reported by the New York Times to be stanozolol, made famous by the sprinter Ben Johnson.

This data says to me, with almost no doubt, that Bonds used performance enhancing drugs to catch the HR record. Bud Selig is a lame weasel, so I have no sympathy or much respect for his views, but I wish someone currently active in the game with the respect of his or her peers, would make a simple statement to the effect of: Based on the data of the freakish late career HR surge by Bonds, coupled with the allegations of intense performance enhancing drug use, we cannot celebrate Bonds' catching and passing of Hank Aaron's record. How can you celebrate this?