Mike Piazza announced his retirement. Mike is my favorite baseball player; I was there at Chavez Ravine the first time he batted third. It was the third home game of 1993; Darryl and Eric Davis had been benched after stinking up the first two games. He set a lot of records for the Dodgers until they traded him shortly before his free agency, to the Marlins, who flipped him to the Mets a week later, and he played the bulk of his career for them, before playing out two final years in San Diego and Oakland. His two best years were his rookie year, in 1993, and his penultimate year with the Dodgers, in 1998 at age 28. That year, he was worth 12.3 wins, a peak season for the ages. Bench had a 13.3, but defense put him over; his offense never came close to Mike. 31 is my third-favorite number (behind 47 and 42).

When he was traded from the Dodgers, I made up this chart and used a push-pin to mark my progress, and regress, through the five stages of grieving. Then I became a sort-of Mets fan, as long as they weren't playing the Dodgers, a secondary loyalty made easier when they ended up with Pedro, among other former Dodgers.)

Here's a sportswriter:

He made the act of squatting behind a plate for three hours cool for the first time since a man named Johnny Bench did it in the '70s.

... He was the best hitting catcher of all time.

He was a Florida Marlin for five glorious games.

He pulled off a mullet [and a silly moustache] for most of the '90s.

Yes, Mike Piazza had a hell of a career.

—Kevin Kaduk

The New York Times has a habit of supporting the Yankees in print, regularly featuring Yankees stories on the front page of the sports section while the Mets are buried in the back. The lede on the nytimes.com website takes things to a new level of boosterdom:

The dreadlocks are part of his body. Thus, if he is hit by a pitch, he would be awarded the base, unless he failed to make an effort to avoid the pitch or was struck by the pitch in the strike zone--in other words, were his hair to intrude upon the strike zone in trying to get out of the way, hanging over the strike zone or such. Also, if tagged out on the bases via a tag or on the hair, he would be out. If he were to be struck on the hair by a batted ball, he would also be ruled out. — Mike Port, baseball's vice president of umpires, on Manny Ramirez.

A few ignorant gems from the New York Times' special baseball supplement today:

George Vecsey writes, "... baseball players come off as average people, although obviously their hand-eye coordination is anything but typical. (The bulked-up physiques seem to be returning toward normal dimensions, for some mysterious reason.)" That's the sort of cheap shot that I guess you can get away with when you aren't held to journalistic standards. If you look at a chart of player height/weight over the last hundred and thirty-plus years, you see a very clear trend of annual increases in height and weight, back to 1871 when ballplayers averaged about 155 pounds and five foot eight and a half. The 2006 average was about 200 pounds and almost six foot two. Not normal dimensions. Further, most of the steroid users caught in the last two years of testing have been using drugs to rehabilitate injuries, not grow to hulk-like proportions.

Next, a classic "back in my day..." story, "Of Rocks and Apples and the Disappearance of 20-Game Winners." Murray Chass investigates the mystery of the first-ever full-length baseball season without any twenty-game-winning pitchers, with penetrating analysis like, "Gone are the days, as recently as in the mid-1970s, when pitchers worked 300 innings a season, started every fourth day, and often finished what they started." Note the moral judgment implied in that wording—what kind of man doesn't finish what he starts?

Which expert does he quote in depth? Third-base coach Rich Donnelly, who relates, "I was raised in an alley. They would deliver coal for the furnaces, and waste would come out and there would be a clinker, a rock. We had rock fights all the time. These guys never had an apple fight or a rock fight in their life. I'll bet all the no-parking signs in their neighborhoods are clean." Chass adds, "And they don't win 20 games."

Donnelly also says, "It used to be if you're tired, you're coming out. Now you get around 100 [pitches], you're coming out ... I think everybody is overprotective." Sadly, Donnelly and his ignorance coach for the Dodgers. At least he's not a pitching coach, though. Yankee pitching coach and former star pitcher Ron Guidry: "I don't know if there are as many quality guys as you used to have ...." (Guidry was a very good pitcher, with one great season at age 27, and a sharp decline in his last three seasons, retiring at age 37 in 1988. I guess he ran out of quality.)

Stephen Jay Gould wrote the book on this argument, Full House. He convincingly argues that the decline of statistical high outliers in the major league baseball population proves that the quality of competition is increasing, not decreasing: as everybody gets better, it's harder and harder to stand out. In the book he talks about .400 hitters, of which there haven't been any since 1941, but the argument applies as well to 20-game winners. One more bit of actual data for you: a chart of the best baseball pitchers in history, with currently active pitchers in bold. You will notice that two of the four best pitchers in history are still pitching (probably).

On the bright side, the same article quotes Curt Schilling, who seems to be one of the smartest guys in baseball: "I think there's a lot more good pitching in the game now." And the same section does have a fact-based article, No Reason to Use a Designated Hitter Who Doesn't Hit, which includes quotes such as "Had [the Mariners] instead acquired Branyan ... they probably would have added enough offense to win two or three more games this season, and saved $6.5 million." If only the Times baseball writers would read their own paper. Or be expected to base their opinions in reality. (Of course, David Brooks and many other Times opinion writes fail that standard as well....)

Baseball fans focus on championships, but the best way to judge a team's management is by its economic efficiency: how well did it turn payroll into wins? Prompted by the announcement that Joe Girardi won the NL Manager of the Year award for the Florida Marlins, who finished with a losing record but had by far the lowest payroll and an almost all-rookie lineup, I've graphed some data. Here is a chart showing number of wins in the 2006 regular season against opening day payroll:

In general more payroll does mean more wins. You can see a few outliers - the Yankees, the Red Sox, the Cubs, and the Marlins in particular. Teams above the line are overpaying for wins; below the line, getting a bargain.

But to get to the real meat, you need serious analysis. Baseball Prospetus modifies the wins and payroll down to account for the "Marginal" concept - the idea that there is an effectively unlimited pool of low-quality talent at minimum cost (where minimum = $327,000/season). Now you can really see which teams made the most and least of their money:

All data is from Baseball Prospectus.

Girardi, by the way, was rewarded for his efforts (note, though, that the actual credit should be shared between Girardi, the general manager who actually negotiates contracts and makes trades, and the Marlins scouts who selected the rookies) with a big "you're fired" sandwich. Moral of the story: results matter less than sucking up to the boss.

Sportswriter Lee Jenkins writes in Friday's Times:

How the A’s keep shedding million-dollar salaries and collecting division titles remains baseball’s ultimate mystery. —New York Times

Well, I guess that if you never read Moneyball, the detailed account by Michael Lewis of how the A's, under general manager Billy Beane and his protégés, have sought undervalued talent by using statistics and critical thinking to measure players more accurately than traditional baseball techniques, which rely on appearances, rules of thumb, and "the way it's always been done", then yes, that would remain an ultimate mystery.

Moneyball was published in 2003, and both it and the backlash against it has been one of, probably, the top five stories in baseball since then. The biggest baseball story since 2003 was the Red Sox winning the World Series in 2004 (for the first time in 86 years), and their general manager was Theo Epstein, who worked for Beane in Oakland, was the source of some of Beane's unconventional strategies, and was mentioned repeatedly in the book.

So it's unlikely Jenkins has never heard of Moneyball, sabermetrics, on-base-percentage, or other new-fangled notions. The obvious conclusion is that he read Moneyball (or a summary of it), rejected its contents out of hand, and will remain mystified until the end of his days. Very sad, but deliberate, willful ignorance does seem to be a prerequisite for sportswriters.

Two thirds of the way into the season, each of the five teams in the NL West (baseball) has been in both first place and last place. With 106 games played, the total distance between first and last is 4.5 games. Last year the Padres won the division with a record of 82 and 80, the worst winning record for any team in the history of baseball. This year, maybe the whole division can finish three or four games over .500, in a five-way tie. Then we can go to goal differential to determine the winner.

"We're all trying to get on the same page ... Well, I guess we've been on the same page. We've all been sucking. We want to get on a different page."

—Royals outfielder Emil Brown, on the team's struggles (Kansas City Star)

My theory of baseball and life:
*Life consists, in large part, of random or semi-random events
*Humans are very bad at understanding randomness, and so frequently misunderstand life
*Baseball consists, in large part, of random or semi-random events in a controlled environment
*Understanding baseball is thus a useful step towards understanding life

As you know, part of why I adore baseball is its intersection of statistics, random variation, and human interest give us a mirror to see how humans think. Greg Maddux's good start to the 2006 season is the latest textbook example. Maddux is the second-best pitcher of the last fifty years, behind only Roger Clemens, who himself is behind only 1910s pitcher Walter Johnson for the title of best pitcher ever. However, Maddux is forty, and has been in decline for several years. This season, without any appreciable change in his methodology, his results have been outstanding. So far this season he's the second best pitcher[1], up from roughly average last year.

Naturally, any notable fact requires an explanation. While us Maddux fans—and pretty much every nerd is a Maddux fan, since Maddux is a himself a slightly built thrower without great velocity, who has dominated with pinpoint accuracy and the ability to deceive and outthink most hitters rather than through raw power—would love to hear that he's back to full effect, the nerds have looked at the data. And the data says that Maddux is merely repeating last year's league-average performance, in terms of preventing hitters from hitting the ball, but fewer of the balls put in play have resulted in hits. That's generally not something under the pitcher's control. In other words, Maddux has simply been lucky.[2]

And Maddux himself agrees with this analysis:

... somehow -- and Maddux will swear he doesn't know how -- he's turned the losses of last season into wins.

"If he tells you that [he doesn't know], you gotta believe it. I believe whatever he tells me," Cubs manager Dusty Baker said last weekend in St. Louis. ... And from Maddux himself: "I wish I could explain it. Personally, I'm just getting ready to pitch like I always have. I'm just catching a lot of breaks. Sometimes you catch a lot of breaks in this game, and right now I feel like am."

But that's not satisfactory for baseball writers:

The real truth, or at least a major part of it, is simple: Maddux is in better shape than he's been in years. Maybe ever. After failing to win 15 games in 2005 for the first time since '87, Maddux approached Keith Kleven, a physical therapist in Las Vegas, and asked for help.

Kleven started Maddux on a new workout last November, a couple of months before he normally begins his offseason regimen. The results are speaking for themselves. (Jim Donovan, SI.com)

Random variation is often the best explanation for surprises, but humans seem to have a real problem accepting that. And explanations that include hard work and merit and cause and effect are always comforting. But "shit happens" is far closer to universal truth then you might want to believe.

Notes:

1. Maddux is second in both VORP and RA. VORP means the number of runs he has prevented compared to an average minimum-wage pitcher throwing the same number of innings. RA is simply the number of runs allowed per nine innings pitched. VORP is a cumulative statistic and RA is a rate statistic. The nerds prefer RA to the more familiar "ERA" for esoteric reasons.
2. "He’s benefitting from a very low batting average on balls in play (.192, fifth in MLB among pitchers with at least 15 IP). His peripheral stats don’t support a league-leading anything, and his groundball-to-flyball ratio is the lowest of his career, which is contributing to that BABIP. That he’s given up just one home run and three doubles on 18 fly balls is an accident, and can’t be expected to continue." —In Praise of Maddux, Joe Sheehan, 24 April 2006, Baseballprospectus.com

A great article on ESPN.com about Barry Bonds, baseball, and what it means historically and culturally:

... the past five years have been an especially depressing stretch to be an American ... it's the Era of Predictable Disillusionment: a half-decade in which many long-standing fears about how America works (and what America has come to represent) were gradually—and then suddenly—hammered into the collective consciousness of just about everyone, including all the people who hadn't been paying attention to begin with.

This will not be lost on future historians. In 50 or 100 years, they will search for events within the popular culture that supposedly embodied the zeitgeist of the time. Some of these people will use sports, not unlike the way contemporary historians might use Muhammad Ali as a means to define the 1960s. As these future historians try to explain what was wrong with the world in the early 21st century, I suspect they will use Barry Bonds.

[...]

A mound of evidence suggests that Bonds has been less than honest about steroids. But it seems like he's been honest about a lot of other things. "The last time I played baseball was in college," he said in his grand jury testimony during the BALCO case. He said almost the exact same thing to The New York Times Magazine in 2002: "The last game I played was in college. Ever since then, it's been a business. This is a business."

[...]

Early in "Game of Shadows," authors Mark Fainaru-Wada and Lance Williams try to illustrate what motivated Bonds to inject chemicals into his rump, and they suggest that his actions were driven by jealousy and, to a lesser extent, race. "They're just letting him do it because he's a white boy," Bonds supposedly said of McGwire's steroid-fueled run at the single-season home run mark. This statement makes Bonds seem as paranoid as Richard Nixon. How, one wonders, could unseen puppet masters be pulling the strings behind the home run race? It all seems crazy.

But, then again, nobody ever wrote a takedown book on Mark McGwire. I'm not sure anyone even considered it.

Nixon wasn't always wrong.

[...]

For all practical—and statistical—purposes, Ruth wasn't a real person. In 1927 he hit 60 home runs, exactly twice as many as NL co-champs Hack Wilson and Cy Williams hit; when Ruth retired in 1935, he had hit 714 homers, more than twice as many as Lou Gehrig, the man in second place. In 1925, he got a tummy ache, and it was one of the biggest stories of the year. He revolutionized the game, captivated radio audiences, built houses, inspired candy bars and was used as an epithet by Japanese soldiers during the war. Ruth has been dead for 57 years, and he is still substantially more famous than Barry Bonds.

But Bonds is going to pass him, and no one knows how to feel. Ruth was a troubling person, but he's a wonderful idea; Bonds is a troubling person who's an empty idea.

This is the kind of news I like to wake up to:

The Dodgers win big and Cardinals fans get their hearts broken.

Remember, it's not enough to win. The other guy has to lose, too.

There's been a mini-revolution in baseball the last decade, which can be oversimplified to Traditionalists vs Statheads. Essentially the Statheads showed up and said, a lot of what you think is true about baseball is demonstrably wrong. The Traditionalists said, go to hell. The poster child of the Stathead movement is the Oakland A's general manager, Billy Beane. Despite a small payroll, Oakland has won its division or placed second for many years in a row, and has easily the best win per dollar ratio of any time since Beane started.

Two of Beane's staff have gone to other teams. One, Theo Epstein, led the Red Sox to their first World Series victory in 86 years. The other, Paul DePodesta, was hired as general manager of the Dodgers. (In baseball, general managers are responsible for signing and trading players, and managers are responsible for day-to-day oversight of players and tactics during games.) The Dodgers did well in 2004, his first year, and did poorly in 2005, when they lost $36 million in payroll (about a third) to injuries. DePodesta had never gotten along especially well with the Dodgers' well-respected Traditionalist manager, Jim Tracy. DePodesta effectively fired Tracy after the 2005 season. The owner of the Dodgers, Frank McCourt, a highly leveraged East Coast real estate magnate, fired DePodesta two weeks later. Given that both DePodesta and Tracy are both very good, and between the two of them exemplify the two different philosophies currently in play, letting both of them go is evidence that McCourt is incompetent.

Jim Tracy landed a job managing the Pirates, who have been lousy for over a decade. Today the Pirates played the Dodgers, and lost. Tracy's commentary is priceless:

"One-and-7 obviously isn't the way you want to start," Tracy said. "But the (Dodgers) team I managed last year started 12-2 and we won 71 games. So it's not a large enough sample size of games. It doesn't mean this is the kind of team we're going to be for the next six months."

Jim Tracy using the phrase "sample size". Awesome.

King Kaufman says of Barry Bonds' reality TV show, "It's impressive in a way that Bonds would approve of a show that leaves him, in the end, looking like a giant prick ... It would be more impressive if I could believe that Bonds realizes the show makes him look like a giant prick. I'm not sure he does." New York Times reviewer Charles McGrath similarly exposes himself as a giant prick. Although he acknowledges that one of Bonds' legitimate woes is "his daily barrage of ugly, racist hate mail," he still ends his review of Barry's show with, "... you realize that Bonds's greatest tragedy is that he was born too late. He would have been a hero back in the day when all players had to do was play, not give interviews."

Um. I guess McGrath forgot that black players weren't allowed in Major League baseball "back in the day."

I saw Barry last night here in San Diego. Hit by pitch, reached on an error, and walked. He also turned a single into a double, but it was a single by Adrian Gonzalez of the Padres, which Barry's steady jog was unable to cut off before it rolled to the wall. Bonds was pulled after the sixth for defensive replacement Steve Finley. (At 41, Finley is almost a year younger than Bonds, but has two healthy knees.) Personally, I'm cheering for Barry. He very probably used, but so have a lot of people; if Babe Ruth and his contemporaries wasn't taking steroids, it was only because they weren't available yet. Meanwhile they found plenty of other ways to cheat; Kevin Gross didn't invent sandpaper and Pete Rose didn't invent gambling. Until and unless Barry Bonds' records are proven to violate the rules in effect when he played, they shoud stand.

I also got to see my favorite player, Mike Piazza, in person for the first time in many years. He grounded out twice, lined out to center, and flied out. He's looking good, though, aside from the new goatee.

The New York Times features an interview with Elden Auker, a 95-year-old former major league pitcher. His proferred wisdom includes such gems as "The legs are not in condition today, and that's why these fellas have sore arms," and "I never had a sore arm or sore leg in my life," and "we never had four or five trainers who had us rolling around on the ground and touching our toes. We ran sprints," and "The idea of a pitcher wearing out is ridiculous. He weakens because he's not in condition. I was never taken out of a game because I was weak. I was taken out because I was getting hit."

Of course it's human nature to say things were better back then—spirits were brave, the stakes were high, men were real men, women were real women and small furry creatures from Alpha Centuari were real small furry creatures from Alpha Centauri. And so I don't want to pick on Auker, who has pitched 1933 and a third more major league innings than I ever will, and clearly is doing something right with his health if he's 95. But I do think that the NY Times sports writer is a fair target, and quotes Auker sympathetically and chimes in with disapproving clucks of his own: "Auker's views are not original; throwing and running were, once upon a time, routine. But in recent decades, the practice has changed. Today, baseball pampers pitchers and teaches them that too much throwing can be hazardous to their health."

Uh, yeah. That must be it. I'm not surprised that Chass leaves out the most common reasons for increased pressure on modern pitchers: hitters who train year-round, video-tape analysis, hitting charts, and multi-million-dollar contracts. But I am surprised to learn that the "things were better back then" storyline can beat out even the "steroids have ruined everything" storyline. Just remember that, however manly men were back in Auker's day, he himself only pitched until he was 31. (His last season was 1942, so he may have joined the army, but if so, why did he pitch in 1942, and why does the war have only two mentions in his autobiography?) And take this as another piece of evidence in the pile showing that sports writers are not entertainers, not journalists.

Baseball has a tradition of rule continuity, and there have not been many substantive changes in the last hundred years. Some of the rules are a bit complicated, like the infield fly rule, and the rulebook isn't particularly well written, but it's pretty straightforward. It's the rules outside the white lines that are tricky:

If a player with at least five years of major-league service is traded in the middle of a multi-year contract, he has the right to demand a trade after the season. If the player so chooses, he can also identify as many as six teams to which he will not accept a trade. Notice of the trade demand must be given within the 15-day period beginning on October 15 (or the day following the last game of the World Series, whichever is later). ...

The player's club has until March 15 to trade him, and if they fail to do so, the remaining years on the player's multi-year contract are voided and he becomes a free agent. Any club signing such a player does so without regard to either the compensation requirement of the CBA (which requires draft pick compensation to clubs that lose Type A, B or C free agents) or the quota provisions (which limits the number of Type A and B free-agent signings allowed to each club in years with few free agents)....

I guess labor negotiations can have that effect.

Analyzing a game like last night's really gives me a sense of the outer boundaries of performance analysis. We can look at players' performance records and approximate their talent levels and get a sense of what to expect over a given time frame. On a single night in October, though, the analysis breaks down and you're left with 50 guys playing a game of baseball. There's no tool in our box that's going to tell you what will happen.

... [Was] I was surprised that Roy Oswalt was so ineffective last night ... The answer is, "no." I know, and the people who do this kind of analysis know, that players aren't "stat-generating robots," .... Just because Oswalt had an ERA of 2.94 doesn't mean he'll allow two runs in 6 2/3 innings each time out. Just because he'd been very good in his last three starts doesn't mean he'll be good in his next one. Player performances oscillate around a mean, that mean being their performance record, and some nights are going to be much worse than others.

What is grating is for people like me to know this, and for Phil Garner to act as if he doesn't. Oswalt scuffled from the start last night, lacking the movement on his fastball and the location on his breaking ball that he'd shown in three previous postseason starts. That he didn't allow any runs in the first four innings was misleading at best, dangerous at worst; Garner may have been lulled into a false sense of confidence based on the zeroes on the scoreboard--the stats--rather than what was obvious to anyone with two eyes.

So when the White Sox started beating Oswalt like a pinata in the fifth, Garner should have been prepared. [...] Instead, he let the Sox pile up six hits, a walk, a hit batsman and five runs without ever making a switch.

Then Oswalt went back out for the sixth, and I officially gave up on Phil Garner. Forget that Oswalt got through the inning unscathed; Garner didn't do his job last night, which is to give his team the best chance to win the game. In the fifth, Oswalt wasn't the best pitcher available, and Garner needed to recognize that and make a move. A label of "ace" doesn't actually get guys out, and Oswalt doesn't get to throw his strikeout rate and groundball/flyball ratio at hitters. Garner was looking for a stat line last night, and what he got was a human being.

[...]

The one guy I would hope doesn't come in for too much criticism is Ezequiel Astacio, who officially took the loss. I submit that using him in the 14th inning of a tied World Series game violates his warranty pretty thoroughly, given that his career consists of 81 innings with a 5.67 ERA and 23 home runs allowed. —Joe Sheehan, Baseball Prospectus

But what I really want to know is: Why is it always three strikes and you're out? Why isn't it ever two or four? Does it really make sense to base a whole law-enforcement philosophy on the rules of an athletic contest?

In 1887 baseball experimented with requiring four strikes for a strikeout. What if that had stuck? First of all, that song would be harder to sing -- "for it's one, two-three, four strikes you're out ..."

But more important, would law-and-order types be a third more lenient toward repeat offenders? Would our national sense of the proper blend of punishment and second chances be governed by the saying "four strikes and you're out"?

What if track were the national pastime? Would states be passing "two false starts and you're disqualified" laws that locked up second offenders for life? Or if football had developed earlier and become the American game a century before it did, would legislatures have debated "four downs and you're punted" bills?—King Kaufman, Salon

After Dodger rookie D.J. Houlton kept pace with Roger Clemens for seven innings, I was inspired to a frenzy of data analysis and some wrestling with the OpenOffice graphing system. I now have some pictures to show, which should clear things up.

Comparing pitchers directly is very difficult. Numbers like wins and losses are very easily shown to have little intrinsic value, since they are strongly dependent on how a pitcher's team performs. Earned Run Average is more useful, but favors pitchers with short, excellent careers, and also varies somewhat year to year, most notably in the 1960s when pitchers became so dominant that the height of pitchers' mounds was dropped from 15" to 10" to restore balance. For my comparison I used one of the newfangled nerd stats, WARP-3. It measures how many wins a particular player is responsible for based on their performance, compared to a hypothetical "replacement-level" player, taking into consideration the quality of opponents and the bias of the home and away parks, balanced over all seasons since 1890 including adjustments for different season lengths, and quite possibly incorporating the phases of the moon and ladies' skirt lengths.

This all means that WARP-3, or "wins" as I'll call it, has many nice properties. It's directly comparable across different decades or centuries; it's cumulative, so that a pitcher with 15 wins is better than one with 10. It's relative to a baseline, so that a pitcher hanging on past their prime will accumulate fewer and fewer wins even in full seasons, and can actually lose points if they perform badly enough. And it has a clear intrinsic meaning: if pitcher X had a WARP-3 of 10 this year, then his team won 10 more games than it would have with a generic replacement (eg, a journeyman or unremarkable rookie who is barely able to compete at the major league level).

With all that in mind, let's look at the first chart. It shows the career performances of the best currently active pitchers in baseball, Roger Clemens, Greg Maddux, Randy Johnson, Pedro Martinez, and Curt Schilling. I added the best major league pitcher ever, Walter Johnson, for comparison. (The "Big Train" pitched for the Washington Senators from 1907 to 1927 and is consistently considered one of the top five pitchers ever. By WARP-3, he's the best.)

First, we can see that Clemens is on the verge of overtaking Walter Johnson as the best pitcher ever. Second, we can that Maddux and Clemens have traded the lead a few times (Clemens is a few years older than Maddux; this chart lines them up by age, so Maddux is shown four years behind Clemens even though both are still pitching), but Maddux has been falling behind for several years. Maddux last had the lead at age 35; Maddux's 2002 season brought his total to 144.2 wins, Clemens was 35 in 1999 and his total was then 143.6. Since then, Clemens has rebounded while Maddux has declined.

Meanwhile, Pedro Martinez is only slightly behind either of them at age 33, but he'll have to maintain his current plateau for another six or eight years to reach their level. The Big Unit (Randy Johnson) and Curt Schilling are well behind by age, but Johnson has been able to log good years up through age 42, whereas Schilling has already lost most of 2005 to injury and is unlikely to catch Johnson, much less the others. Still, everyone but Schilling is certainly headed for the Hall of Fame, and Schilling is knocking on the door.

How do they look in the context of the best pitchers in history?

Clemens is in second place for all time. Maddux is in fourth, but unlikely to move up. Martinez will have to stay healthy and motivated for years to break into the top 20. Walter Johnson really stands out. Bob Feller had an even better start, but that flat line from age 23 to 26 (when he was serving in World War II) cuts him down brutally. He roared back in 1946 with the fourth-best season ever, but was ineffective by age 33. Randy Johnson's late bloom is the only thing keeping him in the second tier. Nolan Ryan, many people's pick for best, was good but not great for a very long time, but still doesn't break into the top ten. Phil Niekro started later than anybody else but played until age 48.

One name commonly found in this company but missing on this chart is Sandy Koufax. Although he was utterly dominant for four years, his peak coincided with Dodger Stadium (which strongly benefits pitchers) and with the pitcher-dominant 1960s. His career was short, and his peak, though anecdotally awesome, was less impressive in context. By WARP-3, Walter Johnson's 1912-1915 stands above all others, with Pedro's 1997-2000 and Maddux's 1992-1995 tied for distant second. (Looking at relative ERA, gives similar results.)

And that Dodger game where the Dodgers' rookie pitcher matched Clemens for seven innings? The Astros won 3-2 in the ninth. The National League Western Division is the weakest in the majors, and the Dodgers are sinking towards last in it. The Dodgers disabled list has claimed their entire starting outfield, half of the starting infield, the closer, and a big fraction of the rotation. If they could field the DL instead of the healthy players, they could easily win the division. Or at least tie with Barry Bonds solo.

Sports journalism is traditionaly the weakest branch of journalism in the US, and it's not like the average journalist is a genius, but this article features some of the dumbest writing I've ever seen. Sports Illustrated writer John Donovan:

No regular starter in baseball over the past 17 years has been as consistently successful ... as Greg Maddux. ... Maddux -- there's no sugarcoating this -- is getting hit these days, maybe harder than he ever has in his career.

...

His ERA, the mark that once set him apart, climbed to a galling 5.02.

The dart-throwers out there will insist that the 39-year-old Maddux is finished, that his stuff has stopped moving, that hitters are finally on to him ... The problem with that assessment is that, despite getting hit on occasion, Maddux still wins. Sometimes it's hard to figure out how he does it. But he does.

Maddux (who, before Tuesday's game, enjoyed the fifth-best run support in the National League at more than six runs a start) is clearly no longer the pitcher who won four straight Cy Young awards (1992-95). Still, he is the only pitcher in history to win 15 or more games in 17 straight seasons (1988-2004). During that run, he boasted a 2.83 ERA.

He is 7-6 -- that's more wins than anyone on that decimated Cubs' staff, and more losses, too -- even with his embarrassingly large 5.02 ERA. ... But even with that ballooning ERA, Maddux has proven his worth. ...Somehow, still, he keeps baffling.

Let me get this straight, John. Maddux is giving up an average of five runs per game, which is much worse than his career average of about three. But because he has a seven win, six loss record this season, he isn't actually a worse pitcher; he just has a mysterious ability to keep winning. Oh, and paranthetically, he's had the good fortune that his team is scoring, on average, over six runs each time he starts.

I know that serious mathematical analysis of baseball is only slowly penetrating the inside circles of baseball, but I feel confident that even my readers without any knowledge of baseball will be able to uncover the mystery of Maddux's winning record.

I went to an afternoon baseball game Thursday. The temperature was 72 degrees and the sky was cloudless. But despite looking like a giant mall from the outside, the ballpark has surprisingly few entrances so there's a lot of walking in crowds to get in. I suppose it's not much worse than Dodger Stadium, but since that's built into a hillside it's less obvious there. Once I got inside, the sightlines were lousy because the seat angle is too shallow. You have to crane to see the plate, and the staircase railings are intrusive (although they do use glass to minimize it, that's a bandaid after the fact).

So I was grumpy, despite all the suntan lotion seeping into my pores, and the only Dodger paraphanalia I had was my pencil, which needed sharpening. I was pretty much in a funk from the third inning to about the eighth inning, when my mood, very surprisingly, lifted considerably, and from then on I had a lovely time. (Correlating this information with the box score is left as an exercise to the reader.)

How did the new scorecard do? See for yourself: Front side, back.

Success

• The light background lines work really well. They are visible as guides but still keep the pencil marks most prominent.
• The pitch count area is a good graphical representation; the difference between pitchers is very obvious. Lawrence was on cruise control into the 8th inning, and was pulled at 83 pitches and 7+ IP only because the manager got nervous. (By rule of thumb, 100 pitches is when you start to think about pulling a pitcher, and 120+ is a danger zone for injury. For fragile pitchers, such as Pedro Martinez, the numbers are 80 and 100, but fragile, excellent pitchers can throw 9 innings in under a hundred pitches, so that doesn't reduce Pedro's value much.) Dessens was the opposite, throwing 93 pitches! in four innings. Dessens is a righty, the Padres lineup was heavy with lefties, and he appears afraid to throw inside to them. So he kept aiming for a magical spot six inches off the plate where nobody could possibly hit the ball, but only Tom Glavine gets strikes called there, so it was pretty brutal to watch. I'm stunned that Dessens only gave out four walks, and only had a single full count in twenty batters.
• The out counts in shaded, unbordered discs are nicer than the previous little circles with black borders.

Failure

• My previous scorecards had player # after player name, and position in a little box. For some reason I reversed it, and it screwed me up. I will change it back.
• Since I've stopped trying to mimic newspaper box scores, the only purpose of the player stats columns on the right is to show, at a glance, who had a good night. Having five columns, two of which are derivative, isn't helping that. I could replace OBP and SLG with OPS, but then I have to figure out an easy way to calculate that.
• I started by keeping the pitch counts on the same side as the pitchers' teams, but that's the opposite side as the batters, so after two innings I switched to the other way, which is much easier since you can just count on top and draw lines on the bottom. I think I'm going to put the pitcher stats on the same page, which means that each page will show one team's batting and the other team's pitching. But I guess that makes sense.
• The pitch count boxes can be much smaller. I went with four boxes across because I wanted to use shading to show at a glance whether or not the pitcher is staying at the magic ~12 pitches an inning for a complete game. You can see that pretty well in the first seven innings of the front side. But I ended up with a checkerboard pattern and a lot of base-twelve math. It should be easy just by looking at the lines to see the pitch count. I think I'll make it five or maybe 10 pitches across, add counters, and shade in a stairstep pattern.

I also found this site with lots of baseball scorecards. Some are intended for youth games or other participatory stuff like coaching, and I did pick up the cool idea of putting everything on one side of one (extra-large) sheet of paper. But the real problem with all of them is that they are ugly. They would all benefit from a hefty sprinkling of Tufte; specifically, they have terrible data-ink ratios. That is, they have a lot of heavy black lines and grids for a small amount of writing, especially given that the writing may be in pencil. The Mk 2 Scorecard was also guilty of this, but I believe I have corrected the problem with the Mk 3 and, after I add the refinements outlined above, will try submitting it to the aforementioned site.

After many mistakes and dead ends, I have finally completed the newest version of the baseball scorecard. I made a serious error in my approach which led to many problems: I mistook a high-quality picture on screen for my end product, which was actually a high-quality printout. I had a nice SVG file to look at six weeks ago, but getting it on paper was a great trial. First I tried using the Adobe SVG plug-in in Windows, but that produced a cut-off, distorted page. Then I tried converting it to a bitmap using the batik java tools, but Kinko's choked on the large 600dpi .tif files.

Next I bought a new Samsung Scx-4100 laser printer, which is pleasingly less-than-catastrophic linux support. However, linux printing remains nightmarish to the point where I consider any successful print job, even of a spreadsheet or web page, a blessed event, and the idea (or reality) of printing high-resolution bitmap graphics from linux would require entirely too many dark rituals.

So, I rebooted my laptop to Windows and plugged in the printer. First I tried printing the SVG directly, but the Adobe plugin and two other SVG tools each producing charmingly different, charmingly wrong output. One changed the fonts, one ignored the circles and diamonds, one just shrunk everything. Next, I tried printing the high-quality, 10mb bitmap from Paint, to no avail. Finally I found a free graphics viewer/printer called Brava! which could load and print 600dpi pages acceptably well.

So the process to create my scorecard is:

1. Edit the source SVG files in emacs and preview with batik squiggle.
2. Run this batch script to change them to tif files:

   #!/bin/sh
   for file in baseball_scorecard baseball_scorecard_back
     do
     java -Xmx800m -jar /usr/local/batik-1.6/batik-rasterizer.jar -dpi 600 -m image
   /tiff $file.svg
     convert -compress rle $file.tif $file.tif
   done
   

3. Transfer files to windows
4. Load files in Brava!
5. Print one side
6. Reload the paper upside-down and backwards
7. Print the other side

As a result of this, I had to use the mark 2 scorecard to record Rickey Henderson's debut with the independent Class A San Diego Surf Dawgs (sic). At age 46, Ricky didn't get invited to any major-league training camps this spring, probably because of a batting average barely above the Mendoza line. Thanks to his ability to walk, his on-base percentage is still a perfectly competitive .320 to .360, so I think he's not as washed up as traditional stats make him appear, but he's certainly not a player for the future. Still, he sold out the (San Diego State University) ballpark, drew a walk, hit a towering double to deep center, and stole a base, so no complaints from me.

Now that I have the new model, I'm eager to get to another game and try it out. But probably not a Dawgs' game.

In case you read the previous post about baseball scorecards and were eagerly awaiting the Mark 3, I am pleased to announce that it is ready to begin trials. In addition to recreating the basic form from the Mark 1 and Mark 2 in a more open file format, SVG, I have made several other changes, predicated on two ideas: implementing Tufte, and changing from traditional to modern measurement statistics:

• Eliminated some wasted space from the header
• moved the summary block down
• Changed the pitch count grid from an inning by inning count and total per pitcher to a grid. This is an experiment, and it's probably easier to print the scorecard, go to a game, fill it out, scan it, and upload it than to explain how it should work. The idea is that 1) the marks are the data; 2) it's easier to do totals inning to inning; 3) you can see at a glance how many pitches a pitcher is throwing per inning relative to a complete-game rate (12/inning).
• Changed some of the stats from traditional (At bats, hits, runs, strikeouts) to modern (On-base percentage, slugging, and what I think are the necessary raw ingredients - plate appearances, outs, and total bases). So when Jeff Kent (I still can't believe he's a Dodger. Or that he's hitting so well at 37.) draws three walks and makes two outs, his line OBP/SLG is .600/.000, which is more useful than his batting average, which would be 0-2 or .000. When J.D. Drew hits two singles, a double, and a homer, and grounds out to first, his line is .800/1.600, instead of just .800.
• Dropped the convention of recording RBIs, though this change is not visible on the blank scorecard
• Cosmetic changes to the at-bat box; removed the pitch count circle.
• Followed Tufte's ideas and made most of the lines gray, instead of black, so that data, which is recorded in pencil anyway, is more visible than the grid lines.

300dpi PNG, ready for printing: Mk3 Scorecard Front, Back.

Get the SVG source files.

I've made several custom baseball scorecards, since the ones that come in programs are quite inadequate. Unfortunately, I made them in Coreldraw and Visio, so I couldn't use them on my linux computer even if I hadn't misplaced the original files. I decided to use SVG (Scalable vector Graphics) to create version 3. This is a standard XML file format which allows you to "draw" shapes by describing them in text. Instead of using the mouse to lay out shapes, I can just type in the dimensions I want. It looks like this:

<rect x=".16" y=".16"
        width="0.18" height="0.18"
        transform="rotate(45 .25 .25)"
        fill="white"
        stroke="#cccccc"
        stroke-width="0.01"
        stroke-dasharray="0.02,0.02"/>

That code creates a diamond bordered with a gray dashed line.

I have run into two main problems with this project. The first is that the SVG specs on relative and absolute coordinates for reused components are clear as mud and devoid of helpful examples. This means in effect that I'm doing a lot of stuff the Wrong Way, using offsets and other tricks which just make it harder to move stuff around and correct mistakes. I got to a certain point where I probably should have backed up, created a simple trial document, and mastered viewport coordinate system, effect of the viewBox attribute on sibling attributes, Nested transformations, and the tangled relationship between patternUnits = "userSpaceOnUse | objectBoundingBox", patternContentUnits = "userSpaceOnUse | objectBoundingBox", and viewBox. Instead, I just bulled on ahead to finish the darn thing.

The second problem is that, although SVG has been around for a few years, support for it is mixed. I tried four different programs and got four different outputs, wrong on four different ways. GIMP's SVG module botches the text utterly, putting it in the wrong place and orders of magnitude too big. GIMP also gets most of the lines wrong, though that may only be an artifact of going to a print-ready resolution and then shrinking back down for display. KSVG in Konqueror looks much better, but the text is still destroyed: it seems to round all text block locations to the nearest inch or so, so that the headings for innings 1 and 2 are superposed, as are 3-4, etc. Sodipodi does the text fine and the lines look good, but the diamonds which are the most crucial element of the whole thing are not rotated. Finally, squiggle, a java program which is part of Batik, whatever that is, seems to get everything right except that the text seems to alternate being a pixel too high and a pixel too low. Still, if I can cajole print-quality raster files from squiggle, that will probably be the solution. But a one-afternoon project is now, stretching out into its fourth session of work. Bah.

As a result, I had to use fresh xeroxes of my old scorecard for the Dodgers-Padres game last week. The Padres' stadium, (commercial naming sponsor) Park, is reasonably nice. If you come on the trolley, you have to walk around most of the back side, which looks like a blank mall exterior, to get to a gate, but once inside it's pretty. The commercial signage is a notch past excessive, but at least the players don't wear any advertising (aside from little logos that are practically invisible). The game happened to fall on Military night, and the Padres were wearing camouflage jerseys—grounds for protest if ever there were any. Aside from lots of froo-frah before the game, there was a very very cool parachuting demonstration, with an eight-man Navy parachuting team jumping into the stadium. The first one put his foot down directly on the target in the outfield. Others did tricks with smoke, joined up in pairs, and/or did this thing where they plummet towards the ground at 60 mph until well below the tops of the nosebleed seats before pulling up and abruptly not dying. Useful when being shot at, no doubt, but I'd hate to practice that much. Most importantly, the Dodgers won, although it was the last victory of an improbable 8-game winning streak.

[Cubs shortstop] Nomar Garciaparra took two steps out of the batters' box, then collapsed in pain.

...

``I've strained my groin before but I've never felt anything like this before,'' Garciaparra said. ``It's kind of a freak thing.''

...

``It's not good, it's a bad groin,'' manager Dusty Baker said. — AP Sports

Gus adds, "What's really interesting is that the letters in the name Nomar Garciaparra can be rearranged to spell,"

ram... groin... crap... aaar!!

Baseball Prospectus breaks down the 47 free agent contracts signed over the 2004-2005 winter. The math is too complicated to explain without quoting most of the (subscription-only) article; basically they estimated how good the players in the free agent class of 2004-2005 were, and counted how much money they were paid, and then figured out which of those players were underpaid or overpaid, relative to the group. Other adjustments included discounting multi-year contracts by 5% per year and comparing the players to "replacement level" (the quality of player you can get by paying the minimum $316,000/yr salary) instead of to zero.

The three best deals:

1. Guzman, Cristian, signed a 4 yr/$15mil contract. Projected to win 14.7 games. By BP's estimates, underpaid by $17 million.
2. Drew, J.D., 5 years/$40 mil. Worth 29.1 wins, and underpaid by $14mil.
3. Eckstein, David, 3 years/$9 mil. Worth 10.2 wins, so underpaid by $13mil.

The worst deal:

1. Ordonez, Magglio, 5 years/$67 mil. Worth 16.4 wins; overpaid $32 mil.

Dodger fans will be interested to learn that Drew is projected to win more games than Beltre in the next five years, and at a substantial discount. (29.1 wins vs 28.2; $40mil vs $57mil). Overall, the Dodgers were the second most efficient spender in the market (Drew and Kent were both very good deals; Lowe and Perez were both mildly bad deals). The Mariners, Diamondbacks, and especially Tigers overpaid the worst.

Also interesting is that this market put the value of a projected win at $2.14 million, which is double the current estimated value of a win. That is, looking at the revenue and records of the different baseball teams, BP statheads have determined that winning one extra baseball game is worth (other things being equal) a million dollars in gate revenue, TV contracts, etc. Therefore, paying a player up to a million dollars per projected win is good economics. By that measure, almost all of this years free agents were overpaid. Which is not unexpected; baseball players are indentured servents for the first six years of their major-league careers, during which period they are severely underpaid relative to the money they generate for their employers. By limiting free agency to veterans, the owners have ensured that free agents are almost always overpaid.

Beaming like a kid who just met his favorite sports star, Mayor Anthony A. Williams signed legislation Wednesday to bring major league baseball back to the nation's capital.

So Councilwoman Cropp's resistance to the billion dollar tax giveaway to baseball faded in the face of a non-binding promise to try to get private funding for some of it cost. But at least Mayor Williams is happy. Sign me up as one disgusted anti-corporate-subsidy baseball fan.

I'm a big fan of baseball, but I'm not a big fan of wealth transfer from tax payers to private corporations via subsidy. So naturally I'm deeply opposed to the deal between Major League Baseball (motto: "slightly less incompetent than the National Hockey League, but we make up for it with nastiness") and the city of Washington, D.C., in which DC would put up all of the money for a new stadium and the baseball team's owners would keep all of the profits. The fig leaf, that the money was coming from a new business tax, isn't worthy of being spit at. Are you telling me that businesses will submit to a tax for a stadium but not for schools?

I was pleased to hear a mainstream news source (NPR) finally mention on air what's been known for over a decade: that stadiums and arenas provide negligable or even negative economic benefits to their neighborhoods, and are therefore terrible ways for governments to spend money. But I'm even more pleased to find that the City Council has rallied behind dissident Councilmembers to defy MLB and their lapdog the mayor (motto: "Making you nostalgic for former mayor and crack addict Marion Barry") and demand at least 1/2 private financing. One half! The audacity. Let's hope this starts a trend of local governments standing up to extortion by sports teams and other companies demanding public funding in exchange for the pleasure of their company.

Roxie Campanella, widow of (Brooklyn!) Dodgers Hall of Fame catcher Roy, died last week at age 77. An excerpt from the LA Times article by Bill Plaschke:

Several years ago, while visiting with Roxie, I wondered whether there was any part of her that was relieved that Roy had left for a world where surely he could stand and run again.

She began crying.

"Of course not," she said. "I miss him. I miss him every day. He was never a burden, never once. How can someone you love ever be a burden?"

Soon, I, too, was crying, mourning my pathetic ignorance.

In 1900, a mathematician named David Hilbert addressed the International Congress of Mathematicians in Paris and delivered what was to become history's most influential speech about mathematics. Hilbert outlined 23 major problems to be studied in the coming century. In doing so he expressed optimism about the field, sharing his feeling that unsolved problems were a sign of vitality, encouraging more people to do more research.
...

By putting forth our own "Hilbert problems" for baseball analysts of the future, Baseball Prospectus is outlining our philosophy for how and why this kind of work ought to be done--our attempt to provide inspiration and guidance to the baseball community at large.

Hilbert Problem in Math	"Hilbert Problem" in baseball
3. The equality of two volumes of two tetrahedra of equal bases and equal altitudes. In two letters to Gerling, Gauss5 expresses his regret that certain theorems of solid geometry depend upon the method of exhaustion, i. e., in modern phraseology, upon the axiom of continuity (or upon the axiom of Archimedes). Gauss mentions in particular the theorem of Euclid, that triangular pyramids of equal altitudes are to each other as their bases. Now the analogous problem in the plane has been solved.6 Gerling also succeeded in proving the equality of volume of symmetrical polyhedra by dividing them into congruent parts. Nevertheless, it seems to me probable that a general proof of this kind for the theorem of Euclid just mentioned is impossible, and it should be our task to give a rigorous proof of its impossibility.	3) Measuring the catcher's role in run prevention. In Baseball Prospectus 1999, Keith Woolner presented a compelling case that catchers do not have a noticeable effect on a pitcher's performance. If there is no "game-calling" effect, what impact does a catcher have? Is it primarily controlling the running game? If so, how much of that is attributable to the pitching staff? Is it in preventing wild pitches and passed balls, thus giving the pitcher more confidence to keep the ball low? What about reading a pitcher's physical state and helping to keep his pitch count low?
10. Determination of the solvability of a diophantine equation Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: to devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.	10) Projecting minor league pitchers accurately. One of the holy grails of sabermetrics is creating useful projections of major league pitcher performance based on minor league performance. While strikeout-to-walk ratios and other means of assessment can give us rough guides to good and bad young pitchers, we're nowhere near the level of certainty we want to achieve. ...
17. Expression of definite forms by squares A rational integral function or form in any number of variables with real coefficient such that it becomes negative for no real values of these variables, is said to be definite. The system of all definite forms is invariant with respect to the operations of addition and multiplication, but the quotient of two definite forms—in case it should be an integral function of the variables—is also a definite form. The square of any form is evidently always a definite form. But since, as I have shown,37 not every definite form can be compounded by addition from squares of forms, the question arises—which I have answered affirmatively for ternary forms38—whether every definite form may not be expressed as a quotient of sums of squares of forms....	17) Determining the value of draft picks, Rule 5 picks, player-to-be-named-later arrangements, and other non-specific forms of compensation in transactions. The more esoteric forms of compensation in trades are usually ignored, but they must have some real value if teams continue to exchange talent for them. What does a team give up when it signs a Type A free agent? How much is that draft pick worth? Is a typical Rule 5 pick worth the $50,000 and the roster spot? Are teams taking full advantage of the Rule 5 draft? What kinds of PTBNL deals make sense for both teams?

Selected Hilbert problems from Mathematical Problems, Lecture delivered before the International Congress of Mathematicians at Paris in 1900. By Professor David Hilbert