Isn't that part of the issue: as a player approaches 40, his ability should decline relative to league average. If, like Bonds, every player took steroids so they could play in their late-30's like the were still in their 20's, you'd have much different league averages.

Why not list Barry's stats with similar hitters through the years and compare the relative dropoff in production -- or, in Barry's case, non-dropoff -- as they age?

The thing now is that too many people who might actually know are accusing him. Suppose there's an 80% probability that each of them are lying. If their behavior is independent, then the probability that 6 people are lying is about 25%.

Age Bonds Not-Bonds
20 to 24 4.0% 5.6%
25 to 29 7.2% 6.8%
30 to 34 7.6% 7.3%
35 to 39 12.2% 6.6%
40+ 11.9% 4.1%

Graphing it and adding a trendline only accentuates the fact that Bonds somehow evaded the aging process that the rest succumbed to.

I know that a batters eye gets better as he gains experience, but this is in most cases tempered by a decline in strength and speed- which simply doesn't seem to be the case with Mr. Barry. It's too bad so many modern sluggers are tainted, or we could run comparisons vs them to account for the current era of expansion pitching and smaller ballparks. The only sluggers I could think of that I'd venture to be relatively clean would be Griffey and Thomas, but their injury histories screw things up anyway.

Wouldn't you like that heroism to stand up?
Wouldn't you like their feats to be real and actually mean something, not be clouded by suspicion?

And this whole juicing thing hasn't tainted everyone. Sure, it's hit Bonds, Giambi, Sheffield, Sosa, McGwire, Palmiero, Canseco, Caminiti, and the guys Canseco implicated (Juan Gone and Pudge Rodriguez).

But there are plenty of great hitters NOT implicated: A-Rod, Frank Thomas, Jim Thome, Ken Griffey, Hideki Matsui, Andruw Jones, Mike Piazza, David Ortiz, Vladimir Guerrero, Albert Pujols, Carlos Delgado, Derek Jeter, Carlos Beltran, Ichiro, Magglio Ordonez, Alfonso Soriano, Michael Young, Mark Texiera, Hank Blalock, Troy Glaus, Manny Ramierez, and on and on.

Sure, you want to root for the guys setting the records, and we ALL did when it happened. But now, those records, the most cherished in all of sports, are being clouded by suspicion, allegations, admissions and proof. (Not to even mention the whole BALCO mess)

I'd suggest rooting for different players. History will not look well upon the recent past well. Every player under suspicion of using steroids will likely have trouble getting into the Hall, if ever. Even Barry.

As for Bonds, I'm so tired of steriods. I know that it matters and it's a big scandal, but I wish it would just go away. The season is about to start and it is time to be happy about baseball, and Bonds and all of this crap is just messing it up. I honestly wish he would just retire so that this whole era can fade into the past. Oh, well. The game will go on.

I really don't think that you can use %Change from the year before as a way of saying that Bond's stats didn't change much. 2001 was a huge jump from the year before. But that is also amazing is that the next few years didn't really fall back 50%. Instead his performance went from out this world to merely stratospheric. 2002 had a 18% drop FROM a 50% jump. That means he still had a 28% jump from 2000.

I decided to take the comparison to League Average that you gave and plotted them out in a variety of ways.

You will see that with no statistical manipulation that will simple plots of the numbers you gave, that there is a real difference in Bonds' performance before and after 1998 when he started taking steroids. Every measure of performance jumps.

http://tinyurl.com/k7roq

But if you want a statistical basis for it, I don't thin it'll be quite so easy as people expect.

If I take the 7 years from 1999-2005 (starting with the first full year after he allegedly starting using), and compare to the previous 7 years:

1a) HR/AB: Two sample T-test: 12.1% vs. 7.8%, p=.0005. That's statistically significant, even with just 14 data points.

1b) HR and AB, totals: Chi-squared analysis*: 10.5% vs 7.1%, p=0.0000009. That's statistically significant. Way significant.

*This adjusts for varying AB levels per year, a potential flaw in #1a.

2) HR/AB prorated to league average: Two-sample T-test: 3.7 vs. 3.0, p=.028. That's statistically significant.

3) HR/AB prorated to team average: Two-sample T-Test: 4.2 vs. 3.6, p=.15. Not significant.

Actually, that was very easy. Three out of four analyses, viewed from a hypothesis testing perspective, show a statistically significant increase between the two sets of 7 years there. Fact: Bonds hit significantly more HR per AB from age 34 to 40 than from age 27 to 33.

If you want to suggest that the 'roids were the reason, well... Correlation does not prove causation. But there is a correlation here.

If I were hitting a homerun every time I got to see a pitch in the strike zone, then naturally people would pitch around me. So then the only way to really measure my home run power is to look at the pitches that are near the plate that is the times were you don't walk.

Take two scenarios:
I play four game series. I get 20 plate appearances. I hit a 12 homeruns because no one pitches around me. So HR/PA = .6, my HR/AB = .6

Now imagine we replay those games. But this time the pitchers read the scouting reports properly. They pitch me tentatively. In 20 plate appearances, I get 10 walks. So I only get 10 real at bats where I get to see real pitches. In those I mash my usual .6 rate, giving me 6 home runs.

So my true power rate is HR/AB of .6. But if you look at HR/PA, it is 6/20 giving me a rate of .3 which suppresses the real homerun rate.

Thus I would say that you should really only look at HR/AB for the discussion that we are having.

Thanks for running the numbers. I was about to run the same analyses. I figured the pictures I posted would be a simpler way of showing the pre/post 1998 Bonds. But in the end, the numbers are necessary as well.

I did notice that you and I chose different ranges by one year -- I didn't assume an immediate impact. Either way, your graphs, my stat tests... same conclusion. There's something different in the alleged steroid era for Bonds, and it is statistically verifiable.

Mike? Do you stand by your statement?

that seems incredibly naive considering the extent of specificity in the new book (and we've only seen bit and pieces on SI).

one of the other aspects of the game that 'roids are supposed to affect is speed. while i am sure age has played a significant part in bonds's decline in the SB department, it's intersting to note that his SB #'s (per 162 games) dropped off by 65% in 98-05. that's significant. (from avg 41 per 162 up to '97 to 14 per 162 thereafter - and if we look at the "change" season of 98 as part of the first group, the numbers are even more dim)

http://tinyurl.com/kc4jh

http://tinyurl.com/kc4jh

http://tinyurl.com/kc4jh

http://tinyurl.com/kc4jh

This does not prove causation. This does not prove steroid use. It just demonstrates that he hit significantly more home runs during those years than in the years prior. Do with that what you will.