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Tuesday, March 30, 2004

Trump on Socrates 

Enjoy a taste of Dan Ackman’s hilarious review of Donald Trump’s new biography Trump: How to Get Rich (Note: I refuse to provide a link to this book) from the Tuesday March 30, 2004 WSJ:

Who among us -- ex-wives, former mistresses and spurned business partners excepted -- does not love The Donald? He first entered our world, and allowed us into his, more than 20 years ago, and he has never left. Now the idea of Donald J. Trump not being around seems difficult to imagine. Mr. Trump always saves us the trouble of having to try.

Mr. Trump tells his readers that they should budget quiet time: For Mr. Trump it's between 5 a.m. and 8 a.m., when he reads seven newspapers and catches up on the dozen magazines he receives daily. He also says that you should read books a lot. Mr. Trump does it "in the evening, after a black tie dinner," while munching pretzels. He enjoys biographies. But "now and then I like to read about philosophers -- particularly Socrates, who emphasizes you should follow the convictions of your own conscience, which basically means thinking for yourself, a philosophy I tend to agree with."

The book reads as if it had been dictated in the back of a limousine on the way to a helicopter, which is exactly what you'd want from a Trump production.

Should you read this book? You could read Socrates instead, but he was never as rich as Mr. Trump and not as much fun.


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Advice to Econ Graduate Students 

Fellow GMU alum and now GMU professor Alex Tabarrok gives some excellent advice to graduate students in an interview with Crescat Sententia.

If you go to graduate school be prepared to be bored for at least the first two years. After that it gets much more interesting. And believe it or not the boring stuff will help you to do the fun stuff. (And the boring stuff becomes a lot more fun when it turns out to be useful!) Sure, it's overdone at most places but math and hard-core empirical work have their place.

Intuition is a tricky thing because most of our intuitions are wrong. For most of us, it's only by training ourselves on the boring stuff that we develop good intuitions which we can then use to blog!

Sobering advice, but still excellent.

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Why are Gas Prices so High? 

It is not just OPEC (as Bill pointed out) or greedy oil companies, but environmental regulations. Well, I suspect there is a good chance oil companies have had a hand in supporting these regulations (see Russell Roberts's post on Bruce Yandle's Bootleggers and Baptists hypothesis). Skip has a good post on this, and he is pessimistic about the chances for a fall in gasoline prices anytime soon.

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Monday, March 29, 2004

High Concept Comedy 

On Monday nights Letterman show, Dave presented the following high concept comedy piece - have 1999 Nobel Prize winner for Economics Robert Mundell come out and tell old Jeff Foxworthy “You might be a redneck” jokes. Throughout the entire hour, Dave called on Mundell to tell old chestnuts like:

If you only have one tooth, you might be a redneck.
If you call your sister mom, you might be a redneck.
If you’re too drunk to fish, you might be a redneck.


Brilliantly applied comedic theory! It could only have been improved if they had included my favorite redneck joke “If you job requires you to wear a shirt with your name on it, you might be a redneck” and also if they could have somehow gotton James Buchanan, who is from Alabama, to participate instead of the Canadian Munndell.

Up to this point, whenever I have told someone I am an economist, they reacted with mix of confusion and mild disgust. After this comedy bit, the public’s perception of economists can only improve, although we may get called on to occasionally tell a redneck joke, which I know will be no problem for myself or JC.

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Wisdom from Thomas Sowell 

Here are a couple “Random Thoughts” from the great Thomas Sowell:

It is almost impossible to go to a shopping mall these days without seeing some teenage girl's navel. There was a time when a guy was not likely to see a girl's navel except on some more memorable occasion than a visit to a mall.

I don't want to give false hope to anyone with medical problems. But I remember a doctor telling me, after the end of my finger had been smashed by a powerful machine and looked like hamburger: "I will try to save your finger but you should never expect to see a fingernail there again." Six months later, a fingernail began to grow back

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Introducing Sabernomics 

For those of you who have been following Old Fishinghat from the early days, you have certainly noticed a change in the content of my posts. While my tone remains bitter and sarcastic (like Bill), my main topic of interest has been baseball (unlike Bill). Therefore, I decided to create a new weblog for my baseball studies and commentary.

I am happy to announce the start of Sabernomics: a weblog dedicated to economic thinking about baseball. If you are a regular reader of this site, then you know what to expect. If this interests you, please visit the new site. I have transferred many posts from the Hat over to Sabernomics to get it started -- I always hate it when new weblogs start with just that first post.

What does this mean for Old Fishinghat? Not much. Bill and I will still be posting plenty of commentary.
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Thursday, March 25, 2004

Private Stadiums are Profitable 

Doug Pappas and Baseball Primer discuss a study by Marc Poitras (GMU alum) and Larry Hadley that shows privately funded baseball stadiums can turn a profit.

In their study, the researchers took into account team performance, ticket prices, the honeymoon period of a new stadium, stadium capacity and player salaries. With the first season in a typical $268 million stadium expected to produce about $33 million, half the cost of construction would be recovered in five years and all of the cost in 12 years, the study said. After 20 years, revenues would exceed construction costs by more than $100 million and by $200 million after 30 years, the study said.



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The Old Fishinghat Revealed 

Q: Why is this weblog, which is mostly about baseball economics, named "Old Fishinghat?"

A: Here is a picture of this site's namesake.




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Wednesday, March 24, 2004

Measuring the Quality of Competition in MLB 

This article by Chris Dial caused me to revisit some of my thinking about the quality of competition in baseball over time. Judging player ability over time when player performance is a function of other participants in the game is not easy. For example, in sports such as running, where the outcome is measured by time, it is very easy to compare athletes over time using absolute measures of performance. The runner with the fastest time is clearly the best. However, sports such as baseball, where outcomes are a function of the relative performance of players, comparing abilities becomes much more difficult. While Babe Ruth was the greatest hitter of his era it does not mean that he is any better than the players in today's game. The pitchers of today differ from the pitchers of Ruth's era. While Ruth may have dominated in his own time, few would argue that this beer-swilling slugger would be the same player in today's game. But, it is possible that Ruth performed better against his competition than Barry Bonds does to his.

So if we cannot use absolute statistics to measure achievement, how can we compare player performance across eras. Stephen Jay Gould suggests such a method: compare the distribution of playing talent in the game. The talent spectrum in baseball ranges from AAA call-ups to superstars. As the talent pool expands more fringe players enter the game. This means that the best hitters (pitchers) in the league get more opportunities against low-quality pitchers (hitters), giving the best players a greater opportunity to excel. Gould takes his argument a step further to say that the compression of talent in today's game -- due to the rising population compared to stagnant number of teams -- reduces the occurrence of abnormal excellence. He views the decreased dispersion, as measured by the standard deviation of several baseball statistics, as the reason that no player has batted .400 since Ted Williams in 1941.

I decided to use Gould's argument in a different way. I want to see how competitive the game was, as measured by talent dispersion, during different eras in baseball history. I am curious as to the quality of the game as measured by the distance between the best and the worst players. An instructive example occurs every four years in soccer with the World Cup. The best players in major leagues around the world form all-star teams by country and compete. I am not a huge soccer fan, but I have watched both MLS and World Cup soccer. There is huge difference in quality of play, with the World Cup being at a much higher level of play. This makes me wonder, has the talent distribution in baseball become more like the World Cup over time, as Gould predicts?

First, I want to look at the percent of the US population playing Major League Baseball over time. This table lists the population per MLB player at the start of each decade.

Date Pop/Player Ratio
1900 238,163
1910 288,214
1920 265,054
1930 308,007
1940 330,411
1950 378,314
1960 358,646
1970 338,687
1980 348,532
1990 382,631
2000 375,229

Century 328,353
Post-1940 352,557


Since 1940 MLB has been above the average ratio of the century, but it has not continually increased. Why not? Expansion. Also, I am excluding some other important measures that understate dispersion in the early part of the century such as racial segregation and the lack of international players. However, this may be counterbalanced by the emergence of other sports with which baseball competes for talent. Therefore, I am not sure how useful this information is.

Second, I want to directly examine the dispersion of baseball talent in hitting and pitching. Instead of using the pure standard deviation of baseball statistics, I am going to use the coefficient of variation (CoV) as a measure of dispersion. The CoV is simply the SD/Mean, and it is superior to the non-normalized SD because it is not biased by the mean. For example, a year with a high mean batting average is likely to have a higher SD of batting average than a year with a low batting average. Using the Lahman database I use all pitchers that face at least 50 batters and players that have 100 at-bats to calculate the CoV of quasi-OBP allowed [(hits +walks)/(AB+walks)] and batter OPS for all pitchers and hitters. I would prefer to calculate OPS against for pitchers, but this data needed to calculated this is not in the Lahman data. I pick the cut-off of 50 and 100 for pitchers and batters to cut-out the players who do not have enough observations to for reliable statistics, but I don't want to cut out all of the fringe players. I set a lower standard for pitchers, because raising the cut-off excludes a good number of relief pitchers. This figure lists this dispersion by decade relative to the 1920-2003 average. Higher bars mean greater dispersion, lower bars mean more similarity across players.



One thing that is quite interesting is the difference in fluctuations across hitters and pitchers. They do not seem to move together. For example, in the 1980s and 1990s hitters were not widely dispersed though pitchers were very dispersed. This leaves a few questions to ponder.

1) Why does the dispersion of hitting and pitching talent differ? If it were just the result of changes in the size of the population from which MLB draws players, they should move together.

2) How can baseball fans use this data to compare individual players across eras? Though pitching talent is more dispersed than in Ruth's era, the average offense of the league is much higher now. How can we combine both of these metrics to compare players from different eras to each other versus their competition? Bonds has done well in an era of pitchers that are on average worse than Ruth's pitchers, and the modern day pitchers are much more varied in quality. I want to give Ruth the edge here -- not because I like him, but because it seems the right thing to do -- but I would like a more objective way to quantify this. Maybe the historical win shares database will do it, but I don't know.

Finally, I would like to figure out which decade from the past is most like today in terms of the quality of competition. The clear winner is the 1950s, certainly a good decade for baseball. Hitting and pitching dispersion were very similar to today, and Steve Treder seems to like it for some other reasons. It is also interesting that the population to player ratio of today is very similar to 1950.

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Tuesday, March 23, 2004

A Thought from Steven Levitt 

Skip posts an interesting observation from Steven Levitt.

I spent the summer on the couch trying to think seminal thoughts. Not a single one came to me.

Though not intended to be advice, but I think it is instructive.

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Monday, March 22, 2004

Need a Feed Aggregator?  

I just found out about a cool new feature on Yahoo! that allows you to create a news aggregator. The news aggregator receives RSS feeds from all of your favorite sites (up to 20) and displays the updates for each site. To get an account you need to:

1) Get a Yahoo! account.
2) Go to My Yahoo and select "Choose Content"
3) Click on "RSS Headlines"

From there you can search for your favorite websites using the search tool. For example, searching for "fishinghat" will get you Old Fishinghat's site feed. Some site may be harder to find than others. If you cannot find the site you are looking for, you can go to your site and put the site feed into the search box.
Or, look for a button like this (also available on the right sidebar),





which will add Old Fishinghat to your personal feed list.

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Saturday, March 20, 2004

Brady Anderson and Caminiti 

It now seems that the only criterion needed to prove a player is on steroids is for a player to have one season out of the ordinary. The latest victim of this new metric is Brady Anderson, who hit 50 home runs in 1996 -- about double the amount he hit in any other season. This week, Jim "Head and Shoulders" Palmer used this standard to accuse Anderson of using steroids during the 1996 season. It is a stupid standard and Palmer ought to be ashamed of himself for saying it, but I thought I would run the "Caminiti test" on Anderson's 1996. I want to compare Anderson's improvement to Ken Caminiti's improvement, which coincidently both happened in 1996. Caminiti admitted that his career year in 1996 was fueled by steroids, so I think it would be interesting if the improvement was similar.

Anderson Caminiti
OBP ISO OBP ISO
93-95 0.363 0.167 0.351 0.184
1996 0.396 0.340 0.408 0.295
Change 9% 104% 16% 61%


Both players improved, but in different ways. The improvements in isolated-power are big jumps for both, but Brady's improvement was much larger. In terms of on-base-percentage, both improved, but Caminiti's improvement was nearly twice Anderson's.

I want to remind my readers that this is really a crappy test that I am doing mostly for fun, and there is not much information here. BUT, if you are one of those people who thinks the Palmer standard is a good one, then you would have to say that if Anderson had some help from steroids, he also had to improve quite a bit on his own. His hitting power grew a lot more than Caminiti's, and we know he was on the juice.
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First Fish of the Season 

We are having fantastic weather here today, which caused me to get out the old fishinghat (yes, it really exists) and hit the water. I went down to The Depot, bought my fishing license, and went to "Lake" Running Knob Hollow with my ultra-light. I caught a bass on the first cast, but I only caught one more after that. Both of the fish barely fought, but it sure was nice to feel the bend in the rod again. A few more weeks of warm weather and the fishing will be great!

Update: Check out my buddy Travis's webpage (www.qualitytimeflies.com) for some fishing pictures. When I lived in Georgia we were like John Gierach and A.K. Best, except Travis embodied the qulalities of both of these men while I just tagged along and enjoyed the fishing. I guess these pictures will have to do for now since the cool weather returned today; postponing the start of good local fishing for another two weeks :-(.
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Friday, March 19, 2004

Age and Pitching Performance 

After looking into the aging patterns of hitters, the next step is to look at pitchers. How does pitcher performance improve and decline with age? I used the same regression technique I used for hitters to estimate the effect of age on pitching performance using this model.

ERA+ or K/BB+ = X(Age) + B1(Lag of ERA+ or K/BB+) + B2 (# Batters Faced by Pitcher) + V (player constants) + e

ERA+ is the pitcher's season ERA divided by the league ERA that season multiplied by 100; where 100 is a league average pitcher for that season. K/BB+ is the pitcher's strikeout-to-walk ratio for the season divided by the league average and multiplied by 100. The "plus" method is a good way to pull out year-to-year differences in the observations. ERA is the normal standard by which most fans judge pitcher performance. I admit I could have used the DIPS ERA, but I did not want to calculate it going back to 1980. I think when you look at performance over time there is not that much of a need to make the correction, so I will not expend the effort. Instead I will use another good metric of pitching performance, the strikeout-to-walk ratio. As Skip discussed the other day, in 1974 Gerald Scully first noticed this metric to be an important measure of pitcher quality, and Bill James agrees. X is a vector of coefficients for different degrees of polynomials of Age (Age, Age^2, Age^3, etc.). V is a vector for individual player constants to factor out any individual player characteristics not included in the model (i.e. this is a fixed-effects model). The two control variables I include are the previous year's performance in ERA+ or K/BB+ to proxy pitcher quality and # of batters faced by pitchers in a given season to proxy for injury.

For a sample I use individual players by season from 1980-2003. Data is from the Lahman Database. I include only pitchers who start at least 10 games in any season of observation. I tried using a wider sample of pitchers initially, but the inclusion of relief pitchers seems to make estimating the model very difficult. This is probably a good thing since starting pitchers and relief pitchers have almost completely distinct roles. It is also important to note that the league averages I use to calculate ERA+ and K/BB+ are the average of all players starting 10 games or more in that particular season. I estimate the model using the xtregar command in Stata, which basically estimates the coefficients using OLS but corrects for serial correlation.

Here are the fitted plots on three samples of pitchers for both measures of pitching performance: the entire sample of pitchers, those pitchers with below 100+ careers , and those with above 100+ careers.

The best fit for ERA+ is quartic, or adding the polynomials from Age to Age ^4 ; thereforefore, the minimums I report are rough visual estimates. Many thanks to an altruistic reader who tried to help me minimize the function by hand, but it was too much of a pain (we need Mathematica). Pitcher ERA+ is minimized at about 28-29 for the good (below 100) pitchers, 26-27 for the entire sample, and seems to be ever rising for the not-so-good (above 100) pitchers.



The best fit for K/BB+ was quadratic, and therefore easy to maximize. Pitcher K/BB+ is maximized at 29.67 for the good (above 100) pitchers, 28.58 for the entire sample, and 25.66 for the not-so-good (below 100) pitchers.



From this, I think it is safe to say that the best estimate of peak pitching performance is a little more than 28. It is a little higher for good pitchers, and a little earlier for lower quality pitchers. This is not surprising since high-quality pitchers will have more opportunities to pitch as they get older than low-quality pitchers. Below I include the regression tables for those who are interested. I do not report the standard errors. All of the statistics are statistically significant at the 1% level in the K/BB+ model. For ERA+ the coefficients are statistically significant for the entire sample model at the 5% level or less; however, when I break the sample up, some of the coefficients on the higher-orders of age are not statistically significant. I am still working on this a bit, but I just want to post what I have. Sorry about the spacing problem, but it is a defect in the Blogger design. Please feel free to lend me your thoughts or suggestions.










Variable ALL ERA+ < 100 ERA+ > 100
Age 24.22148 22.96265 32.37705
Age^2 -1.369466 -1.25484 -2.218376
Age^3 0.0315969 0.0275669 0.0604417
Age^4 -0.0002519 -0.0002059 -0.0005627
Lag(ERA+) -0.2734865 -0.2851918 -0.280756
BFP -0.0430742 -0.0340235 -0.0566215
R-sq. 0.28 0.24 0.37
Obs. 1911 1251 660
Players 448 234 214
Peak Age 26-27 28-29 early 20s









Variable ALL K/BB+ > 100 K/BB+ < 100
Age 7.265849 8.569231 5.124458
Age^2 -0.127119 -0.1444294 -0.0998337
Lag(K/BB+) -0.1721541 -0.1464887 -0.2262057
BFP 0.041634 0.0500489 0.0318835
R-sq. 0.13 0.12 0.18
Obs. 1911 987 924
Players 448 144 264
Peak Age 28.58 29.67 25.66


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Sewanee and Gomorrah 

Shonk points to some criticism that The Sewanee Purple (our student newspaper) is receiving from Virtuosity -- a site that claims to be "the voice for Global Orthodox Anglicanism." It seems the most recent issue of The Purple had a few articles with sexual content in them, which, according to Virtuosity readers, is not appropriate for a school owned by several diocese of the Episcopal Church. Oooo...scandal. But what is most interesting is the lack of complaint about a visit to Sewanee by Christopher Hitchens. Hitchens gave a talk entitled The Moral Necessity of Atheism on February 23. Though I did not attend -- I found the speaker/subject combo to be too weird. Why do I care what Hitchens thinks about religion? -- but I heard from a few sources that he basically called believers of all religions irrational idiots. There are two articles in The Purple on his visit, yet no one at Virtuosity seems to care. They are more concerned about the moral ramifications of a condom-covered banana than they are about a widely publicized talk advocating atheism.

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Sewanee Weblogs 

Selling Waves has just posted the most extensive catalog of Sewanee blogs to date. Good work Shonk. I have links to a few Sewanee blogs over on the left sidebar that I post only with permission of the blog owner. I am always open to add more.

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Thursday, March 18, 2004

Academics and Incentives 

From an email I received earlier from a Florida Atlantic University professor of marketing regarding a new Jeb Bush initiative to use standardized testing to determine part of state university budgets:

Florida's university faculty are blasting a proposal to tie student achievement to how much state aid universities receive. A new law requires the state Board of Governors to come up with a way to measure student achievement. The results could determine whether a university receives 10 percent of its state funding.

University faculty disagree with having yet another standardized test and punishing or rewarding universities based on the results.


Unbelievable! It is unacceptable and insulting to me that Jeb Bush would even consider measuring my productivity. His proposal to tie university funds or heaven forbid faculty salaries to such measures of productivity clearly shows he is more evil than Hitler. I am already smothered by oversight and rules as a college professor, and I am pretty sure that if I stopped coming to class, in less than 3 weeks somebody would have the nerve to complain and make trouble. Crude and idiotic people like Jeb Bush will never understand what sort of magic is done by the creative and special intellectuals who teach in Florida’s public universities. His sort will never comprehend the personal growth and magic that happens in the classroom, and will only unreasonably focus on crude and irrelevant things like whether college graduates can read and do math at a 9th grade level.

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Super Worldwide Exclusive  

Today I received a phone call from a top secret contact in the Kerry campaign who told me some very interesting and exclusive new information. According to my source, not only do many powerful, but anonymous world leaders support John Kerry, but they also read “Old Fishinghat” everyday, not just for entertainment, but to help them make important and difficult policy choices. The same is true for many very powerful businessmen and Hollywood celebrities, who naturally must remain anonymous. In addition, what is perhaps most surprising is that a very well known baseball executive from California, who would only agree to be identified as “bb” gave this review of our humble website “Hey, I like baseball and regressions as much, if not more, than most people, but good God, not every single day!”

Remember this is a worldwide press exclusive that must be credited to this website.

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Wednesday, March 17, 2004

Amazing Evidence of Monopoly Power! 

Stephen Moore of the Club for Growth on the Wednesday, March 17, 2004 episode of Dennis Miller on CNBC:

Iraq should not rejoin OPEC, which is the one monopoly in the global economy. If oil were actually selling at the market price today rather than under a monopoly system, oil would actually cost you 40 or 50 cents a gallon at the pump, not $2.29 a gallon.

Wow! That is some real monopoly power, especially since OPEC only controls 40% of the world’s oil production. If you believe that OPEC is a powerful monopoly, you might check out this graph that shows that how little power OPEC has had over real oil prices since its 1960 creation. Current nominal gasoline prices are high, but nowhere close to the high real prices of the 50s, as pointed out in this essay by some guy named Stephen Moore of the Cato Institute. I wonder if the two Stephen Moores are related?

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Spring Break! 

Enjoy your spring break, but don't let this happen to you.




Or you could end up like this.



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More Site Maintenance 

I have made some more changes to the CSS of the site, thanks to some friendly advice from Shonk. IE 6 can handle it, but lower versions are not perfect. However, the new layout should work better for Mozilla and some others. Since, the IE 6 update is free, I am going to leave it as is, but if anyone is having any serious problems viewing the site, please post in the comments section. Be sure to include your browser.

Note: If this is causing any problems, blame me. I took some liberties with Shonk's suggestions that may be causing the problem. In summary, direct praise to Shonk, blame to JC. :-)

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Tuesday, March 16, 2004

Bonds and McGwire versus the Rest 

A reader has asked me to produce some graphs for Bonds and McGwire compared to a baseline of other players. The baseline I chose is all players with a career OPS+ > 120. The lines are quadratic fits of their OPS+ by age.



Interesting.
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More on Age and Batting Performance 

Since my last posts (here and here) I have received several excellent suggestions on how to modify the model. First, I want to break down the player/age effect by different types of players. Though I discussed this below, the age-performance curves make it clear that there is not much difference in aging patterns across differently-abled players. The three classifications of players with career OPS+s of <90, >90 & <110, and >110.



Second, Skip suggested that I incorporate some higher polynomials in the estimates. While the quadratic is certainly preferred to the linear estimate, other polynomials may provide even better estimates. And he was right, because adding the cubed or third degree of age to the regression model has an interesting effect. While the R-sq. did not change much (.0086) the cubed term was statistically significant, and the estimated peak age shifted from 29 to about 27.



As you can see, adding the cube of age looks very different. (Note, adding the 4th and 5th powers did not help). I am less concerned about the different peaks and the rate of decline among the two estimates. From about 28 on, the estimates are very similar. The interesting part is the early career. In the cubed model players start just below their peak before declining, while in the squared model players improve quite a bit before they decline. I would also like to point out that this fitted prediction includes controls for the number of ABs in a season, to attempt to control for injury problems.

So which model do you like? Wade Boggs or Chipper Jones?





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Monday, March 15, 2004

New Baseball Webpage 

Aaron Gleeman & Co. have started a new webpage which contains much sabermetric- inclined commentary. Visit The Hard Times to see for yourself.

Let's hope this Hard Times isn't dedicated to Thomas Carlyle. ;-)
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Saturday, March 13, 2004

Age and Batting Performance Continued 

Since my earlier post, I have had some more time to analyze the data and examine a few other studies on aging in baseball. The literature tends to support the conventional wisdom that players peak around 27. Here are some links to studies and their predictions of peak age. Keep in mind that this is a brief summary on my part and my reporting does not reflect the caveats of the authors. I think all of these studies are good and anyone who is interested in the issue should read them.

Bill James (from the 1982 BJHA): 27 is the peak including all offense and defense. This is a must-read article if you can get your hands on it. Luckily, I have a friend who loaned me his tattered copy.
David Luciani: 24-26
Don Malcolm: Doesn't really take a stand on this issue, but it is an interesting study on age and performance by hitting components.
Tangotiger: 27
Keith Woolner: 25-28, but probably a little less than 27.

Given my earlier results, I was a bit concerned. My model seems to produce different conclusions, but I have quite a bit of confidence in my empirical approach. So, I decided to break out the numbers in several different ways. The two most logical ways to parse the data are by player quality and career length. Recall, I only include player seasons where the batter has more the 300 ABs. The first table reports the results for players with career OPS+s of <80, <90, <100, >100, >110, and >120.









Variable All Players <90 <100 >100 >110 >120
Age 8.876 7.792 8.737 9.109 9.953 10.275
Age^2 -0.152 -0.135 -0.149 -0.156 -0.170 -0.162
Lag(OPS+) -0.261 -0.253 -0.303 -0.242 -0.226 -0.109
R-sq. 0.3 0.35 0.35 0.27 0.32 0.33
Obs. 2848 321 1203 1645 576 151
Players 621 103 332 289 79 21
Peak Age 29.21 28.88 29.37 29.2 29.28 31.62

The results indicate that players of different quality age the same, except for the superstars (>120). While most other players peak at age 29, the superstars peak between 31 and 32.

Now, I want to estimate the model on players with different career lengths. Maybe there is some bias from bad players leaving early and good players sticking around. In all of these samples I include players with at least two consecutive seasons with 300 ABs. The career seaons categories are 5 or less, 10 or less, 5 or more, 10 or more, and 15 or more.









Variable All Players 5- 10- 5+ 10+ 15+
Age 8.876 12.212 9.780 8.872 8.906 9.414
Age^2 -0.152 -0.238 -0.177 -0.152 -0.150 -0.155
Lag(OPS+) -0.261 -0.452 -0.299 -0.259 -0.228 -0.340
R-sq. 0.3 0.4 0.32 0.31 0.28 0.23
Obs. 2848 434 1755 2651 1307 252
Players 621 250 515 467 135 18
Peak Age 29.21 25.64 27.57 29.22 29.62 30.29

Players with shorter careers seem to peak earlier than players with longer careers. This is not surprising since these players are likely to be the weakest of the talent pool, plus they do not get the opportunity to improve since they are no longer in the league. But, that number 29 keeps popping up as the peak age for players, and this runs against the conventional wisdom.

I have three explanations for my difference. First, I use OPS as a measure of offense, and most of the studies discussed above use other measures. If you think OPS is a bad measure of offense, then my study probably doesn't mean that much to you. Second, I focus on a relatively modern sample, in which players are playing longer due to better nutrition, conditioning, and medical technology. Third, I may have made a data error somewhere in the mix. While I doubt this, I do plan to double-check my numbers to make sure I did not make a mistake in generating. I will update this if I find out this is the case. I plan to think more on the subject, and I hope others do as well. Please feel free to pass along any comments.

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Friday, March 12, 2004

Age and Batting Performance in MLB (updated) 

Well, I might as well give up on trying to make this site a news filter with commentary. I'm teaching econometrics this semester, which means I have Stata up on my computer a lot, and well...somehow whenever a question pops into my head I cannot resist the temptation to answer it. And it just so happens that I have been thinking a lot about baseball lately. Putting aside my apologies...

I was curious about the peak age of performance for baseball players. A Google search revealed a few studies, but they didn't handle the question the way I would. So I thought I would try it my way. I am not saying those studies are bad, I plan to read several over the weekend.

Using the Lahman database, I used a sample of every player in MLB that had 300 at-bats in a season from 1980-2003. If a player failed to get 300 ABs in a season, he was dropped from the analysis for that season and the season that followed (because I am using lags), but he was then returned when he had 300 ABs. I picked this time period because, I am not interested in aging patterns from the past at this moment. Using Stata I estimated the following equation using the xtregar command (this is basically an OLS estimate with a correction for first-order autocorrelation). The unit of observation is a player in a season.

OPS+ = B1 (Age) + B2 (Age^2) + B3 (Lag of OPS+) + B4 (League OPS for that year) + V (player constants) + e

OPS+ is simple the OPS of a player relative to the average OPS of the league in that year. This measure is NOT park-adjusted. V is a vector of fixed effects to control for individual player attributes. I'll spare presenting the numerical results for the moment, but I will tell you that the peak age of OPS + for the sample is about 29. Plugging in the average numbers for the Lag and League OPS variables the table below plots the estimated OPS+ by age.


Interesting. The general wisdom on this stuff is that the peak age is closer to 27. I will have to think more on it.

Update: Here are the coefficient estimates. All are statistically significant at the 1% level except League OPS, which is significant at just about the 5% level. I also report a second specification with League OPS dropped.








Variable Coefficient Coefficient
Age 8.051103 8.876295
Age^2 -0.1400366 -0.1519125
Lag(OPS+) -0.2633548 -0.2610575
League OPS 18.8625
R-sq. 0.31 0.3
Obs. 2848 2848
Players 621 621
Peak Age 28.75 29.21


There is still more to come. Sorry if the spacing if off. I'm trying a better table format, and I am having trouble turning off the line-breaks temporarily.
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Thursday, March 11, 2004

MLB, Monopoly, and the Anti-Trust Exemption 

All of the steroids talk has stimulated a discussion on baseball's anti-trust exemption over at Baseball Musings. A reader comments,

Look, the MLB exists only because Congress is willing to grant it an exception from anti-trust laws.

David responds,

If anything, Major League Baseball would be stronger without the antitrust exemption. It would have to compete against independent minor leagues.

While this discussion focuses on the effect of MLB's monopoly power on the steroid issue, I want to disagree with both of the above statements on the importance of the anti-trust exemption. I believe the anti-trust exemption has virtually no effect on the structure of MLB as we see it today. If anything, the anti-trust exemption may make baseball better than the other major sports leagues, because less effort is wasted on frivolous anti-trust lawsuits that rarely solve anything. Now, I don't wish to defend my second point at this time, so feel free to disregard. I just wanted to add my opinin on this. Sorry to drop this bomb and run, but this is a huge argument for another day. I think the important issue is that the anti-trust exemption does nothing to give MLB any protection from outside competition. Here is why:

1) The anti-trust exemption does not prevent other leagues from rising up to compete with MLB. In fact, any league that attempted to compete with MLB would receive the same anti-trust exemption. I think there is a public misperception that the exemption is a barrier to entry by rival leagues. For example, the Continental League was prepared to open for play in the early 1960s before it reached agreement with the MLB to expand. Other barriers to entry may exist, such as a natural monopoly cost structure (which I don't buy either), but the exemption is not such a barrier.

2) When compared to the other major sports leagues in the US, MLB acts no more like a monopolist than the other leagues. A simple monopolist will restrict output, thereby raising the price. -- I am ignoring the possibility of a price-discriminating monopolist here, but a price-discriminating monopolist does not produce near the harm of a single-price monopolist. -- If the anti-trust exemption gives more market power to baseball its output should be less and its price higher. The following table lists the number of teams, regular season games, the average ticket price per game, and the average ticket price adjusted for the percent of the regular season viewed per game.

League Teams Games Price Adj. Price
NBA* 30 82 $43.60 $35.75
NFL 32 16 $50.02 $8.00
NHL 30 82 $41.56 $34.08
MLB 30 162 $18.30 $29.65
Ave. 30.5 85.25 $38.37 $26.87

(*Including my hometown Charlotte Bobcats. All other data from the 2002-2003 season available from Rodney Fort.)

If anything, MLB seems to be producing more output at a lower price than the other leagues; all of which lack the anti-trust exemption.

A few things to rap this up. This does not mean that MLB does not act like a monopolist. In fact, all of the sports leagues may be acting like monopolists. However, I don't think there is any evidence that the anti-trust exemption affects MLB's monopoly behavior. I also realize that some sports economists disagree with this (Fort, Quirk, Zimbalist), but others feel that the exemption is not important (Scully and Shughart). Also, I acknowledge that there are some problems comparing leagues with differing cost and demand structures, but I don't think the difference are enough to simply throw out these numbers.

Fire away! Now, on to steroids...(to be continued).

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Tuesday, March 09, 2004

Skewness Revisited 

When reexamining my data on ERA skewness I realized that the data I used to generate the histograms was not my ideal choice. I prefer the data, which I report below, that limits the observations to pitchers facing more than 50 batters in a season. I just grabbed the wrong dataset; however, the skew looks pretty similar to the data reported below. I'll report it numerically by percentiles this time for ease of interpretation.

Year 2000 2003
% Cutoff Cutoff
1% 1.99 1.2
5% 2.64 2.13
10% 3.17 2.69
25% 3.905 3.51
50% 4.815 4.5
75% 5.96 5.63
90% 7.62 6.83
95% 8.84 8.31
99% 12.54 11.94

Obs 532 551
Mean 5.16 4.72
SD 1.97 1.94
Var. 3.88 3.75
C.V. 0.38 0.41
Skew 1.62 1.40
Kurt. 7.47 7.17


Also, when you look at the stem plot, it is clear that pitcher ERA is improving across the talent spectrum. Unfortunately, posting stem plots in Blogger presents a real challenge. Thanks to all of you who have sent me comments publicly and in private. I hope this answers your questions. I am now convinced that pitchers are gaining on hitters. This could soon change, but who knows.

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Monday, March 08, 2004

ERA Skewness 

Last Friday I commented that despite the recent fall in ERAs in MLB since 2000, the variance relative to the mean ERA has risen. Using an assumption from Stephen Jay Gould I assumed that this increased variance in pitching performance indicated an influx of some very bad pitching into the league. However, Skip was a little more skeptical.

Time for a skewness check! If Kurjian & Bagwell are right, the skewness should show up in the right tail of the distribution. If right skewness has increased in recent years, coincident with your increase in std deviation, then they are right. In which case we won't be seeing those 50 home run years of the recent past. I like Gould, but think Kurkjian is on to something an give him the edge here.

Great idea! While I am no skewness expert, I did run a few tests. The histograms seems to be quite informative. Here are frequency distributions for ERAs in 2000 and 2003.





Skip is right. The skewness indicates that pitchers seem to be improving. While some very bad pitchers still play in the big leagues, overall most pitchers seem to be getting better.

Also, see the post that started it all on The Sports Economist.

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Abandoning Science and Reason on "The Living Wage" 

Johnny Shoaf posts some excellent commentary on a recent speech given at Sewanee by Dr. Stephanie Luce. Luce is the coauthor of Living Wage, which I discussed in December as a simply awful book. For example, the law of demand -- oh, excuse me Dr. Luce -- the "law of demand" applies when the workforce increases with welfare reform, but it does not exist when "living wage" laws go into affect. Fortunately, I was too busy to attend. I am glad Johnny was there to confirm my fears about her arguments.

He writes:
In addition to declaring research unnecessary, Dr. Luce found the economic theory relating to wages incorrect and useless as well. So, we had someone talking to us who denied that academic theory and empirical evidence are useful aids for evaluating policy. Yikes!

Yikes is right.

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The New Setup 

I have been wanting a three-column layout for some time, but Blogger doesn't offer it. Finally, I bit the bullet and learned a little CSS to turn my two-column Blogger template into a three-column setup. It was harder than you think, especially when one-handed typing with my 6-month-old daughter in the other arm. I would like to thank Glish.com for the information needed to convert my template. Once I found this site, it was easy. But wading through the other sites I visited taught me much more about CSS. Another great CSS site is CSS Style-Sheets.com. I plan to use the third column to index some of the quick studies I have done here. I will add them as I have time.

Please, let me know if you are having a problem viewing the new setup IN THE COMMENTS SECTION, and let me know what browser you use. That way if someone is having a problem with Netscape 6, other people with the same browser can confirm or deny a problem.

I'd also like to thank the readers of this site for checking in. If you have any thoughts or suggestions, feel free to pass them along. Over the next few days I will probably post some bureaucratic material on policies for e-mail and commenting. Now, that a "sufficient" number of people are stopping by, I want to make some things official to keep trolls out of my life. I want everyone to know that the problems have been minor and no regular reader has done anything to piss me off. I just don't want any reader to think that I am pointing a finger at him/her.

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Friday, March 05, 2004

Comparing Bonds to Caminiti 

I thought of another interesting way to look at stats to see how steroids affect performance. Luckily, we have one player whom we know took steroids, and when he started. Ken Caminiti's 1996 performance for the San Diego Padres was his best season, and it won him the MVP. And two years ago he revealed that during this season he also took steroids. And though he continued to use steroids after this year, he claims that his use was nothing like 1996. So, what happened to Caminiti's OBP and Iso-Power during this season in comparison to what he had been doing? How does this compare to Bonds?

K.Cam. OBP Iso-Power
1996 0.408 0.295
1993-95 0.351 0.184
Change 0.057 0.111
%Change 16.2% 60.6%

B.Bonds
2000-03 0.517 0.439
1987-99 0.413 0.280
Change 0.104 0.159
%Change 25.2% 56.8%

Yikes! The percentage changes are a little too similar to my liking. Certainly, this means very little, but it is interesting. I am being a bit unfair to Bonds by selecting his whole career, while only picking out a few years for Caminiti. I did this because there careers were very different. Caminiti was never close to the player Bonds was (note Caminiti's one big year was about the same as Bonds's pre-2000 career) so I tried to pick out a slice that was more comparable to Bonds. One other important note is that Caminiti says steroids destroyed his body, causing him to leave the game; Bonds is still going strong. However, Bonds was never arrested for using crack cocaine either.

Thanks to Baseball-Reference for the stats.

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Are Pitchers Getting Better than Hitters?  

Skip links to an interesting article by Tim Kurkjian at ESPN on the improvement of pitchers in MLB. What caught my eye first was the quote by Jeff Bagwell.

"Pitching is so much better today,'' says Astros first baseman Jeff Bagwell. "When I came up (1991), 91 (mph) is about as hard as anyone threw except for like (Rob) Dibble who threw 94. Now, almost everyone throws 94, and most of them are starting pitchers. Look at Juan Cruz (of the Cubs). He throws 97 (mph) and he can't make their rotation.''

This puzzled me. Was he serious? If you look at the stats there is no doubt that hitters are doing much better than pitchers today when compared to 1991 with these NL stats.

Year - HR/Team - SLG - Ave.
1991 - 119 - .373 - .250
2003 - 169 - .417 - .262

But as Skip points out, Tim K. is not out to defend Bagwell's grumpy old man syndrome. There is no doubt that pitchers now have less of an advantage over hitters than they did 15 years ago, but the recent offensive surge may be waning. I'm not so sure, and this table explains the reason for my skepticism.


Year AveERA C.V.ERA
1990 4.12 0.381
1991 4.21 0.395
1992 4.04 0.392
1993 4.45 0.341
1994 4.87 0.360
1995 4.81 0.396
1996 5.00 0.372
1997 4.89 0.393
1998 4.76 0.395
1999 5.02 0.381
2000 5.16 0.382
2001 4.68 0.368
2002 4.64 0.409
2003 4.72 0.410

Mean 4.67 0.38
Median 4.74 0.39
SD 0.344 0.019


This table lists the average ERA and the Coefficient of Variation of ERA for MLB pitchers facing more than 50 batters in a season. The C.V. ERA is simply the SD/Mean, which superior to simple SD which is biased by the Mean. The C.V. is important because it tells the dispersion of quality among all pitchers in the league. Because athletic performance hits a wall on the right side of the talent distribution, increased dispersion normally means an increase in lower-quality players. More lower-quality pitchers means more opportunities for very good players to take advantage of the bad players. This leads to more records being broken. (If this idea interests you, read Stephen Jay Gould's "Death of the .400 Hitter." in Full House.) With dispersion on the rise, I would not be surprised if some very good batters have some career years this year.

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Thursday, March 04, 2004

Why Globalization is a Good Thing 

Life Expectancy
Women's Well-Being

From the Foreign Policy Globalization Index. See more from Tyler.

I wonder if I could make a huge puppet of these diagrams and take them to the next World Bank protest. If there is one thing I know, it's that World Bank protesters like puppets.
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Why College and Athletics Need to be Separated 

UGA has released a copy of the final exam from Jim Harrick, Jr.'s "Coaching Principles and Strategies of Basketball" class. Here are my favorite questions from the 20 question exam.

1. How many goals are on a basketball court? a. 1 b. 2 c. 3 d. 4

2. How many players are allowed to play at one time on any one team in a regulation game? a. 2 b. 3 c. 4 d. 5

5. How many halves are in a college basketball game? a. 1 b. 2 c. 3 d. 4

6. How many quarters are in a high school basketball game? a. 1 b. 2 c. 3 d. 4

7. How many points does one field goal account for in a Basketball Game? a. 1 b. 2 c. 3 d. 4

8. How many points does a 3-point field goal account for in a Basketball Game? a. 1 b. 2 c. 3 d. 4

11. What is the name of the exam which all high school seniors in the State of Georgia must pass? a. Eye Exam b. How Do The Grits Taste Exam c. Bug Control Exam d. Georgia Exit Exam


The sad part is that I think this is the norm for big-time college athletics. But even worse, if this guy is supposed to be teaching the students to be better basketball players, shouldn't he want to quiz them on fundamental strategies in basketball? How do you beat a double team? When should you foul an opposing player? Not only does this prove what a joke of a class this was, but it also reveals what a terrible coach Harrick was. Read more on Volokh.
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Does Power Cause Walks? Test 2: Bonds 2001 

As promised in the update from yesterday's post here are the results from the test of hitting power on walks for 2001. The format is close to the same as before, with only a few modifications. First, the coefficients I report result from regressions without the control variables. I did this because I want show you the strongest support I can find for power preceding walks (recall that I have been biased in the opposite direction). I included the controls last time, because they led to the strongest results. It is important to note that the controls change very little about the result so I think they are likely unimportant. The second change is that I was able to pull intentional walks (IBBs) out of the analysis with this data. I could not do that for the 2002 analysis. As you will see, the results do change some when looking only at non-intentional walks.

Here are the coefficient estimates when IBBs are included in the walk-rate.

Var. Coef. T-stat Elasticity
SLG 0.413 1.92 1.28
Iso-P 0.573 1.7 1.14
HR 0.052 0.64 0.10

SLG is not-quite statistically significant at the 5% level. Iso-Power is significant at only the 10% level. The marginal impact of power on walks is much larger in 2001 than in 2002 for SLG and Iso-Power. 2001 is the year that Bonds really, I mean REALLY, stepped it up. I remember watching that Braves series in May when he hit 6 HRs in 3 games. I am sure many pitchers took note of such power jumps (although HRs alone don't seem to explain pitcher behavior). By 2002, Bonds's reputation was at a whole new level, which is why the effect may not be so pronounced. In 2002 Bonds, pitchers percieved Bonds to be dangerous at all times.

But, how much did pitchers respond by simply giving Bonds a free pass, and how much of it was pitching around Bonds? That is, when pitchers pitched to Bonds, did they nibble or go after him based on his recnt history of hitting power. In this table I look at the walk-rate excluding all intentional walks.

Var. Coef. T-stat Elasticity
SLG 0.300 1.48 1.10
Iso-P 0.420 1.32 0.99
HR 0.046 0.6 0.10

All of the coefficients shrink some, and the results are no longer statistically significant. Thus, it seems that while there may have been some pitching around, pitchers were responding to Bonds's power surges with IBBs. Here is a link to the 2001 game-log data. Thanks again to Doug and Alec for pointing me to it.

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Wednesday, March 03, 2004

Does Power Cause Walks? Test 1: Bonds 2002 

In a previous post I proposed that Bonds's increased walks must be independent of power. Since that time I have come to believe that power might affect walks by causing pitchers to avoid pitching to Bonds. So, I decided to test it.

Thanks to a thoughtful reader I was able to acquire game-by-game stats for the 2002 season on ESPN.com. Unfortunately, I cannot find the game logs for 2001 anywhere online. I have tried hard, too.

To see if power precedes walks I examined the following model:

Walk-Rate = Constant + B (Power in the past 10 games) + V(Controls) + e

I used three measures of power in the previous 10 games: Slugging, Iso-Power, and HR.
The Controls were score differential, total score, and a dummy if the Giants won.

The results for coefficient estimates power are as follows:

Var. Coef T-stat Elasticity
SLG 0.099 0.9 0.28
Iso-P 0.128 0.93 0.21
HR 0.07 0.6 0.11


Although all of the estimates are positive, none are statistically significant. I corrected for heteroskedasticity and tested for autocorrelation (none found and correcting does not affect the results). If you don't know how to interpret the elasticity estimates, a 1% change in SLG is associated with a 0.28% change in the walk-rate, at the average. As best I can tell, there is no evidence that pitchers were shying away from Bonds when he was hot; however, Bonds was pretty hot over the entire season. I would prefer to see the estimates for 2001.

Other notes: The R-squared is about .04 for all estimates. The sample included 149 games. I tried several possible controls, these were the best and the power estimates were never statistically significant. I also tried some non-OLS estimates such as multinomial logit and poisson, but found the results were similar to OLS. I am not as familiar with these techniques so it is possible I fouled them up.

UPDATE: I just got the 2001 numbers. I have run them, and there is a difference from 2002. SLG does seem to lead the walk-rate by a larger amount, and it is statistically significant. Iso-Power is also larger and borderline significant. HRs do not seem to matter. Unfortunately, I will not be able to post until tomorrow. Thanks to Doug and Alec for the data.
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More on Bonds 

Here is a lesson for newbie bloggers. If you have a brain fart over the weekend, don't post it the day before a story breaks contradicting your hypothesis.

Thanks to all of you who have sent me comments. It is clear to me now that looking at Bonds's walk rate you cannot show his hitting improvement is a result of his hitting discipline steroid-free. However, proving he is on the juice from the stats is equally as daunting. I would like to propose a test of whether Bonds's walk explosion preceded his hitting explosion during the 2001 season. The only problem is that I do not have the data. I need game-by-game data in a simple spreadsheet format (not a box score). I just need to know Bonds's hits, walks, power, and the score for every Giants game that year. Then I can run a simple regression to see if walks lead power or if power leads walks. If you have this data or know of where to get this data, please e-mail me. Or if you know of someone who has run a similar test, please let me know (I know of MNP's analysis on Baseball Primer, but even he has backed off his claim).

I'd also like to point you to a few other links on the subject that I think are quite good.
Redbird Nation
Off Wing
Transition Game (several posts)

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Tuesday, March 02, 2004

Bush v. Kerry 

So the Presidential race is set. I have one thought: Bush in a landslide. I have said it before, but tonight my thoughts were confirmed. In front of his first national audience as the de facto Democratic nominee, who does Kerry have introduce him? Senator Ted Kennedy. How is this even remotely a good political move? Hey John, Dean is gone; stop moving left if you want to win.

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More on Steroids in MLB 

Given the recent news on steroids in MLB I thought I would dig up some stuff I have already written on the subject.

See here and here.

The general feeling among commentators on this issue is that owners want drug tests, but players do not. And both sides seem to mirror this feeling. But this is odd! Steroid use by one player gives him an advantage over non-steroid users. This converts scrubs to starters, and starters into stars. Naturally talented starters and scrubs want to prevent the lower tier of players from competing with them for salaries, thereby inducing all players to take the drugs. Everyone ends up taking the drugs and no one is any better than anyone else, so no salary bump. An individual player may go from 20 to 30 home runs, but that is no big deal if the stars are now hitting 40 dingers. Players don't gain anything in terms of relative performance, and the player face long run health effects. If anything, owners may gain from an overall increase in the quality of the game without having to increase salaries. It seems to me the two sides ought to be reversed. What am I missing?

Well, my sentiments seem to be more on target given this Allen Barra interview with Marvin Miller, which The Sports Economist excerpts.

Well, we did work out a drug policy in 1984, or at least I thought we had one worked out. Peter Ueberroth, the commissioner of baseball at the time, obviously changed his mind after the fact. We agreed on a neutral panel of three doctors who were experts on the subjects of drugs and drug testing, and agreed on a policy of revolving examination.........And then, one day in 1985 Ueberroth astonished both Don Fehr [who succeeded Miller as head of the players union] and myself by going on television during a national telecast and announced that he was voiding the existing drug program because it didn't have mandatory testing. Don Fehr told him, in essence, to go to hell. Ueberroth was so arrogant he didn't seem to understand that he was undermining any possibility of instigating a drug program by tossing out the window what we had achieved through collective bargaining. Incredibly, in 1986, he tried again. Without even bothering to consult the union, he sent a letter to every major league player urging them to submit to voluntary drug tests.

Miller continues:
Ask yourself with the records being set and the tickets being sold, what incentive do the owners have for really wanting to end the use of anabolic steroids? Is it simply because they care what happens to the players after they retire? Let's just say I'm skeptical. I have to question whether the majority of owners really want to institute a system which might cause them to lose their star slugger just as, let's say, the playoffs begin.

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Ping Me 

Hey, guess what? Free Trackback!

Mitch Hedberg: "Dude, you've got to give me time to guess."

Thanks Haloscan!

So, I hope you get used to seeing "Trackback (0)."
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Economic Freedom in North America 

Tyler points to a Fraser Institute study on economic freedom across North American states and provinces. As with all studies of economic freedom, controlling for yadda yadda yadda, this freedom index is associated with greater income and income growth. I am all for more economic freedom, but I don't buy these intra-national comparisons of economic freedom in the way I buy the international studies. The difference between Delaware and West Virginia is not comparable even to differences between the US and UK. For one, if Delaware is so much better than WV you can move to Delaware. Free migration ought to restrict any policies that hinder economic well-being in any meaningful way. This is not the case across countries. I am not sure what this index is capturing, but I don't think it is the same thing in international economic freedom idices. I could be wrong, but this is my initial thinking on the subject.

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Bonds Update 

Well, the day after I open my big fat mouth about Bonds not using steroids I wake up to see the headline Bonds Got Steroids. The story cites one source stating that Bonds was given steroids by his trainer. I have to say that the story is poorly written, and I am not sure what to make of the article's quality. For example, the story claims Bonds was given steroids during his historic 73 HR season in 2001. But, later on it states Bonds's trainer gave steroids to "a baseball player" in November 2001 (after the season). Who knows? Bonds and other players deny the charges. I am withholding judgment. Read more on Primer.

I am also rethinking my logic of assuming walks are not a function of power. Pitchers might pitch around a more powerful hitter. I am not convinced on this (at least to the extreme that Bonds's walk-rate changed), but it is more information to consider.

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Monday, March 01, 2004

Defending Barry Bonds 

Update: My thoughts have changed somewhat since I first posted this. See here, here, and here; and direct your comments to these threads.

I am sick and tired of reading about how Barry Bonds's records, among others, are tainted due to steroids. Let's look at Bonds's success in his recent offensive boom. I'll exclude his first year in the league to limit some bias to these estimates. From 1987-1999 Bonds hit .292 with a SLG of .572. From 2000-2003 these numbers rose to .336 and .774. This change has two potential causes: 1) Bonds simply became better or 2) he used steroids to become better. "The media" is very fond of the latter explanation.

There is a simple way to determine which was the cause. Steroids ought to increase a hitter's ability to hit the ball harder. This will result in every ball he hits generating more power (i.e. outs become singles, singles become doubles, flyouts become HRs, etc.). This means both his batting average and SLG should go up with steroid use; although, I suspect the effect on batting average would be much less. But, one thing steroids should not change is Bonds's hitting discipline, as measured by his walk rate.

In the table below I list some of Bonds's statistics for three periods: career, 1987-1999, and 2003. The variables I use are On-Base-Percentage (OBP), OBP calculated with intentional walks excluded, non-intentional Walks per plate appearance, and Isolated Power (SLG-BA). The first three variables are good proxies for Bonds's plate discipline. The less willing he is to swing at pitches outside the strike zone, the more likely it is he will see pitches he can hit from pitchers. The fourth variable captures his hitting power only. Steroids can influence his power, but it should have no effect on his plate discipline. While hitting discipline can increase his power.


OBP OBP-IBB BB/PA Iso-Power
Career 0.431 0.407 0.144 0.310
1987-99 0.413 0.392 0.132 0.280
2000-03 0.517 0.477 0.185 0.439
StDev. 0.067 0.055 0.035 0.091


Clearly, Bonds is not just hitting the ball harder, he is improved his ability to wait for the right pitch. And interestingly enough, Bonds's improved power is consistant with his growth in OBP. Using an OLS regression, I estimated the effect of OBP on Iso-Power for all teams from 2000-2003. I found that every OBP point is worth about .86 Iso-Power points; hence, .86*(.517) = .445. That is pretty darn close to his actual Iso-Power average.

This leads me to conclude one of the following must be true.
1) Steroids increases hitting discipline as well as muscle mass.
2) Bonds's success is likely a product of becoming a better hitter, not using steroids.

My money is on the second. Thanks to Baseball-Reference for the stats.

Update: I'm bending a bit on this. See my post above.
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