Explaining a Team's W-L Record

According to Baseball-Reference.com:

The Pythagorean Theorem of Baseball is a creation of Bill James which relates the number of runs a team has scored and surrendered to its actual winning percentage, based on the idea that runs scored/runs allowed is a better indicator of a team's (future) performance than a team's actual winning percentage. This results in a formula which is referred to as Pythagorean Winning Percentage....

There are two ways of calculating Pythagorean Winning Percentage (W%). The more commonly used, and simpler version uses an exponent of 2 in the formula.

W%=[(Runs Scored)^2]/[(Runs Scored)^2 + (Runs Allowed)^2]

More accurate versions of the formula use 1.81 or 1.83 as the exponent.

W%=[(Runs Scored)^1.81]/[(Runs Scored)^1.81 + (Runs Allowed)^1.81]

Expected W-L can then be obtained by multiplying W% by the team's total number of games played, then rounding off....

The rationale behind Pythagorean Winning Percentage is that, while winning as many games as possible is still the ultimate goal of a baseball team, a team's run differential (once a sufficient number of games have been played) provides a better idea of how well a team is actually playing. Therefore, barring personnel issues (injuries, trades), a team's actual W-L record will approach the Pythagorean Expected W-L record over time, not the other way around. Expected W-L is almost always within 3 games of actual W-L at the end of a season (although a recent exception is the 2005 and 2007 Arizona Diamondbacks, who both beat their expected W-L by 11 games). Deviations from expected W-L are often attributed to the quality of a team's bullpen, or more dubiously, "clutch play"; many sabermetrics advocates believe the deviations are the result of luck and random chance.

I agree with those who say that deviations reflect the quality of a team's bullpen. A more precise formula can be obtained by regressing winning percentage on two explanatory variables: RFA (runs scored/[runs scored + runs allowed]) and saves recorded by a team's bullpen. The result for the American League in 2008:

W-L percentage (expressed as a decimal fraction) = -0.44595 + 1.66556 x RFA + 0.002747 x saves

Adjusted R-squared: 0.899; standard error: 0.022 (i.e., 2.2 percentage points); t-statistics on the intercept and coefficients: -4.246, 7.319, 3.763 (all significant above the 0.99 level).

That is, the average American League team (RFA = .506, saves = 41) compiled a W-L percentage of .510. (The AL beat the NL in interleague play, thus enabling the AL as a whole to compile a better-than-.500 average.)

According to the Pythagorean formula, the LA Angels were the lucky recipients of 11 extra wins in 2008; that is, the formula underestimates the Angels' 2008 wins by 11. The regression equation, on the other hand, underestimates the Angels' 2008 wins by only 2. Generally, the regression equation (indicated by blue) gives much better results than the Pythagorean formula (indicated by black):


"Luck" is a catch-all term for unexplained variance. It shouldn't be thrown around as if it has real meaning. In this case, the evidence suggests that a decisive factor in a team's W-L record is the quality of its bullpen -- especially the quality of its closers.

Checking In

UPDATED, 07/06/09

About three years ago (at Liberty Corner) I drew on the archives of Dead or Alive? to list a number of erstwhile celebrities who were then alive at the age of 90 or older. Here's how the list looks today:

Charles Lane 102, George Kennan 101, George Beverly Shea 100, Max Schmeling 99, Eddie Albert 99, Michael DeBakey 99, Luise Rainer 99, Gloria Stuart 99, Dale Messick 98, John Wooden 98, Mitch Miller 98, John Kenneth Galbraith 97, Ernest Gallo 97, John Mills 97, Estée Lauder 97, Al Lopez 97, Karl Malden 97, Fay Wray 96, Kitty Carlisle 96, Jane Wyatt 96, Art Linkletter 96, Risë Stevens 96, Henri Cartier-Bresson 95, Peter Rodino, Jr. 95, Joseph Barbera 95, Tony Martin 95, Kevin McCarthy 95, Byron Nelson 94, Constance Cummings 94, Lady Bird Johnson 94, Robert Mondavi 94, Sammy Baugh 94, Irwin Corey 94, Jack LaLanne 94, Harry Morgan 94, Herman Wouk 94, Les Paul 94, Artie Shaw 93, Frankie Laine 93, Ruth Hussey 93, Richard Widmark 93, Robert McNamara 93, Sargent Shriver 93, Eli Wallach 93, Oleg Cassini 92, Ralph Edwards 92, William Westmoreland 91, Frances Langford 91, John Profumo 91, Geraldine Fitzgerald 91, Archibald Cox 91, Julia Child 91, Jane Wyman 90.

Here are some newcomers to the list since my last posting on the subject: Olivia de Havilland 93, Ernest Borgnine 92, Zsa Zsa Gabor 92, Vera Lynn 92, Lena Horne 92, Herbert Lom 91, Ernie Harwell 91, Patti Andrews 91, Bob Feller 90, Billy Graham 90, Monte Irvin 90.

For many, many more names, go to "People Alive Over 85" at Dead or Alive?

Baseball in the Nation's Capital, Revisited

Way back in September 2004, before the Montreal Expos became the Washington Nationals, I wrote:

To succeed financially, the new Washington team must draw well from the Maryland and Virginia suburbs. Attendance will be high for a few years, because the closeness of major-league baseball will be a novelty to fans who've had to trek to Baltimore to see the increasingly hapless Orioles. But suburbanites' allegiance to the new Washington team won't survive more than a few losing seasons -- and more than a few seem likely, given the Expos' track record. As the crowds wane, suburbanites will become increasingly reluctant to journey into the city. And, so, the taxpayers of D.C. (and perhaps the taxpayers of the nation) are likely to be stuck with an expensive memento of false civic pride.

I'm not sure about this year's attendance, but the trend is almost certain to be downward, given the Nats steady dive toward the bottom of the National League. Here are the Nats' W-L records from 2005 through yesterday:

2005 - .500 (5th of 5 in their division; tied for 9th in their 16-team league)

2006 - .438 (5th of 5 in their division; 14th in the league)

2007 - .451 (4th of 5 in their division; tied for 11th in the league)

2008 - .366 (5th of 5 in their division; last in the league)

2009. - .345 (5th of 5 in their division; last in the league)

As I've said before, D.C. isn't a baseball town. The teams are jinxed by their non-fans.

Timely Trivia Question

One person administered the presidential oath of office nine times (a record). Who was that person, and to which presidents did he administer the oath? Scroll down for the answer.



















John Marshall, Chief Justice of the United States from 1801 to 1835, administered the oath to Thomas Jefferson in 1801 and 1805, James Madison in 1809 and 1813, James Monroe in 1817 and 1821, John Quincy Adams in 1825, and Andrew Jackson in 1829 and 1833.

Roger B. Taney, Marshall's successor as Chief Justice (1836 to 1864), administered the oath of office seven times. Warren E. Burger (Chief Justice from 1969 to 1986) administered the oath six times.

For more trivia about inauguration day, go here.

Math Puzzler

Here is the problem (from Misha Lemeshko, via Eugene Volokh):

8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0

2581 = ?

I found the general and specific solutions to the problem after pondering it for about 15 minutes. Can you do it?

If you've given up, or want to check your answers against mine, scroll down.



















Specific solution: 2581 = 2, because...

General solution: The value of a string of numbers comprising the integers 0, 1, 2, 3, 5, 6, 7, 8, 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed curves contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 0000 = 4 because each integer in the string has 1 closed curve; that is, 1 + 1 + 1 + 1 = 4.

Note that the preceding general solution omits the integer 4. Why? There is no way of determining the value of 4 because it doesn't occur in Lemeshko's list of strings. If, however, the value of 4 were known to be 0 (e.g., 8884 = 6, 1114 = 0), the general solution would be as follows: The value of a string of numbers comprising the integers 0 through 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed curves contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 4 = 0, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 4444 = 0 (0 + 0 + 0 + 0 = 0) because 4 (in standard typography) contains a closed area but not a closed curve.

If, however, the value of 4 were known to be 1 (e.g., 8884 = 7, or 1114 =1), the general solution would be as follows: The value of a string of numbers comprising the integers 0 through 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed areas contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 4 = 1, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 4444 = 4 because each integer in the string has 1 closed area; that is, 1 + 1 + 1 + 1 = 4.

A Logical Fallacy

The sub-hed of an article at City Journal asks "If human beings are naturally risk-averse, then what the heck happened on Wall Street?" The question can be expressed in the following syllogism:

Major premise: All humans are risk-averse.

Minor premise: Humans work on Wall Street (i.e., financial markets).

Conclusion: The humans who work on Wall Street are risk-averse.

It should be obvious to the casual observer that both the major premise and conclusion are false.

The article, by the way, is spot-on. Don't be deceived by its flawed sub-hed.

The Fed and Business Cycles

Given the recent (official) announcement that the U.S. has been in recession since December 2007, I decided to look at the record of business cycles compiled by the National Bureau of Economic Research. The following graphs depict the length of expansions and contractions (and the trends in both), before and since the creation of the Federal Reserve System in 1913.

Source: "Business Cycle Expansions and Contractions," National Bureau of Economic Research.

It seems that the creation of the Fed might have had a stabilizing effect on business cycles. (How much of an effect is impossible to tell, given the many other variables at work.)

But...the graphs don't depict the relative severity of the various contractions. It is worth noting that the worst of them all -- the Great Depression -- occurred after the creation of the Fed and, in part, because of actions taken by the Fed. (A note to the history-challenged: The Great Depression began in September 1929 and ended only because of America's entry into World War II.)

In any event, the long-run cost of economic stability has been high. (See this and this, for example.)

By Their Musical Preferences Ye Shall Know Them

Marginal Revolution has become an increasingly "marginal" blog because its dominant contributor, Tyler Cowen, has become increasingly incoherent. It turns out that Cowen is a fan of Elliott Carter, who writes incoherent "music," of which many samples can be heard here.

Neither sound economics nor good music is consistent with incoherence. Therefore, I have scratched Marginal Revolution from my reading list, just as years ago I scratched my copy of a chamber-music LP to eradicate an unlistenable piece by Elliott Carter.

Maddux to the Hall?

Greg Maddux, who is about to announce his retirement from baseball, is a cinch for election to the Hall of Fame: 355 wins, .610 winning average, ERA+ of 132. But Maddux, like recently-retired Mike Mussina, shouldn't be ranked with the "immortals" -- the 16 Hall of Fame pitchers whose excellence, in my view, ranks them above their peers. (See this post and this post for relevant background.)

Maddux had only two 20-win seasons, which is why he isn't an "immortal" pitcher, in my book. Roger Clemens, Maddux's contemporary, had six 20-win seasons (in addition to his 354 wins, .658 winning average, ERA+ of 143), which would make him an "immortal" but for the strong suspicion that his career totals were inflated by steroids and HGH. (It is, by the way, a strong suspicion that cannot be confirmed by statistical evidence.)

P.S. (12/08/08) The election of Joe Gordon to the Hall of Fame is a joke, by my reckoning.

My Crystal Ball

From a post at my old blog, dated January 16, 2008:

On November 14, 2007, I wrote:

Is it possible that the current bull market reached a temporary peak in May of this year, and is now descending toward a secondary bottom that it will not reach for a few years?

This was my tentative answer, then:

A reversal that lasts a year or two seems entirely possible to me.

My less tentative answer, now, is that the stock market (as measured by the Dow Jones Wilshire 5000 Composite Index) has crossed into "bear country." That is, it has met the two conditions which indicate a "correction" or bear market that will last for months or years:

• the index has dropped below its 250-trading-day average, and

• the 250-day average is moving downward (if imperceptibly)....

P.S. [added March 12, 2008] By my reckoning, every downturn in the 250-day average since 1970 has signaled every recession since 1970.

It's been obvious for months that we're in a bear market. It's now also obvious (to the National Bureau of Economic Research) that we're in a recession and have been since January of this year (a "peak" in economic activity having occurred in December 2007).

Macroeconomics and Microeconomics: Part I

Macroeconomics (the study of aggregate economic activity), in most expositions of it that I have seen, fails on two counts. First, macroeconomics usually ignores or accounts inadequately for microeconomic behavior, that is, the behavior of individual persons and firms. Second, it aggregates that which cannot be aggregated, namely, disparate forms of economic activity performed by disparate actors.

Regarding the first point, macro without micro is meaningless. Macroeconomic aggregates have no independent existence.

Secondly, an aggregate is meaningless if it represents disparate phenomena. A foot (measure of distance) is a meaningful measure only if it represents a collection of inches (or fractions thereof); a pound (measure of weight) is meaningful only if it represents a collection of ounces (or fractions thereof); and so on. But a foot is a foot, and a pound is a pound; the two cannot be aggregated because they measure different things. (Yes, there is in physics a measure of force known as the foot-pound, which "is the amount of energy expended when a force of one pound acts through a distance of one foot along the direction of the force." But "foot-pound" is something distinct from "foot" and "pound"; it is a measure of force, not a way of making length and weight commensurate.)

This post illustrates both points. Consider A and B, who have discovered, through trial and error, that each can have more clothing and more food if they specialize: A in the manufacture of clothing, B in the production of food.

Our primitive pair also has discovered a "just right" balance in the amount and allocation of clothing and food that they make and consume. Through voluntary exchange (bargaining), they have found a jointly satisfactory balance of production and consumption. A makes "just enough" clothing so that he can cover himself adequately, keep some clothing on hand for emergencies, trade the balance to B for "just enough" food, and enjoy "just enough" leisure. B does likewise with food. Both A and B might like to have more clothing and/or food, but both are doing as well as they can do in a voluntary relationship.

A and B's respective decisions and actions are microeconomic; the sum of their decisions, macroeconomic. The microeconomic picture might look like this:

• A produces 10 units of clothing a week, 5 of which he trades to B for 5 units of food a week, 4 of which he uses each week, and 1 of which he saves for an emergency.

• B, like A, uses 4 units of clothing each week and saves 1 for an emergency.

• B produces 10 units of food a week, 5 of which she trades to A for 5 units of clothing a week, 4 of which she consumes each week, and 1 of which she saves for an emergency.

• A, like B, consumes 4 units of food each week and saves 1 for an emergency.

Given the microeconomic picture, it is trivial to depict the macroeconomic situation:

• Gross weekly output = 10 units of clothing and 10 units of food

• Weekly consumption = 8 units of clothing and 8 units of food

• Weekly saving = 2 units of clothing and 2 units of food

You will note that the macroeconomic metrics add no useful information; they merely summarize the salient facts of A and B's economic lives -- though not the essential facts of their lives, which include (but are far from limited to) the degree of satisfaction that A and B derive from their economic activities.

The customary way of getting around the aggregation problem is to sum the dollar value of microeconomic activity. But this method simply masks the aggregation problem by assuming that it is possible to add the marginal valuations (i.e., prices) of disparate products and services being bought and sold at disparate moments in time by disparate individuals and firms for disparate purposes. One might as well add two bananas to two apples and call the result four bapples. The essential problem is that A, B, and everyone else will derive different types and levels of enjoyment from clothing and food (both of which come in many forms), not to mention the vast array of other kinds of goods and services that are bought and sold. (For a long disquisition on this point, go here.)

In sum, macroeconomic concepts (e.g., aggregate demand) are not exogenous entities that exist independently of microeconomic activity. At best, they are ambiguous, qualitative proxies for a host of disparate microeconomic activities.

In future installments I will cover such topics as recession and fiscal policy.

Putting Risks in Perspective

According to the Centers for Disease Control, about eight-tenths of one percent of Americans died in 2005 (the most recent year for which CDC has published death rates). That's about 800 persons (825.9 to be precise) out of every 100,000.

To put that number in perspective, imagine a dozen dozen eggs (i.e., a gross of eggs, for those who still know the numeric meaning of "gross"). Only about one of those eggs is broken in the span of a year, in spite of all of the hazards to which the eggs are exposed.

Remember that analogy the next time you read or hear about the "threats" posed by heart disease, cancer, Alzheimer's, motor-vehicle accidents, firearms, etc., etc., etc. The combined effect of all such "threats" is close to nil; more than 99 percent of Americans survive every year, and more than 70 percent of those who don't survive are old (age 65 and older). But that's not the kind of "news" of that sells advertising.

(For much more about mortality in the United States, go here.)

November 22, 1963

I have said all that I wish to say about November 22, 1963, as a political event, and about JFK's performance as president. My purpose here is simply to mark what ranks as the third-most shocking day of my lifetime. The most shocking, because I remember it all too well, is September 11, 2001. The second-most shocking, which I remember not at all (because I was so young), is December 7, 1941.

JFK's assassination was a mighty shock for two reasons:

• It had been 62 years since the assassination of a president (William McKinley, 1901).

• There was, in the early 1960s, less of the intense political polarization that would now render a president's assassination almost unsurprising.

Why Settle for a Theoretical Estimate...

...of the Laffer Curve, when you can have the real thing? The author of the first-linked item suggests that the amount of income remaining in private hands is maximized at an overall tax rate of 25 percent. My empirically-based estimate (second link) puts the private-income maximizing tax rate at 15 percent. The latter figure is a practical minimum:

The normal peacetime burden of government spending between the end of the Civil War and the eve of the Great Depression ranged from 5 to 10 percent of GDP,¹ enough to maintain law and order and to provide minimal "social services." To that I would add 5 to 10 percent for the kind of defense that we need in these parlous times. (See this post, for example.)

You can't have a vibrant economy without law, order, and defense from foreign enemies.

Mussina to the Hall?

I once opined that a

Hall of Fame [starting] pitcher will have

• at least 300 wins

• or, at least 250 wins and an ERA+ of 120 or higher. (Go here and scroll down for the definition of ERA+.)

• or, at least 200 wins and a W-L average of .600 or better and an ERA+ of 120 or higher.

I opined, further, that an " 'immortal' pitcher will have at least 250 wins, a winning average of at least .600, and an ERA+ of at least 120."

Well, it turns out that, by my definition, Mike Mussina qualifies as an "immortal": 270 wins, a winning average of .638, and an ERA+ of 123. Not so fast.

Mussina, who has just announced his retirement, deserves to be in the Hall of Fame; I have no quibble with his qualifications on that score. But Mussina doesn't strike me as an "immortal," which is an honor that I would reserve for these starting pitchers:

Pete Alexander
John Clarkson
Bob Feller
Lefty Grove
Carl Hubbell
Walter Johnson
Tim Keefe
Christy Mathewson
Kid Nichols
Jim Palmer
Eddie Plank
Charley Radbourn
Tom Seaver
Cy Young

Accordingly, I must add another criterion for "immortality" among starting pitchers: at least five seasons with 20 or more wins. Mussina had only one such season: his last.

If -- in this era of the relief pitcher -- there is never another "immortal" starting pitcher, so be it. Tom Seaver will then have the honor of being the last of the breed.

Musical Memories

The six songs I remember from an early age:

"I've Got Spurs That Jingle Jangle Jingle" (probably sung by Gene Autry)

"You Are My Sunshine" (probably sung by Jimmie Davis, who wrote it)

"Cool Water" (sung by the Sons of the Pioneers)

"Always" (sung by Dinah Shore)

"Mairzy Doats" (probably sung by the Andrews Sisters)

"Let It Snow"

Presidential Heights

I once remarked on the longevity of presidents:

The [following] graph highlights trends (such as they are) in the age at which presidents have died (or to which they have survived if still living), the age at which they were elected or succeeded to the presidency, and the number of years by which they survived (or have thus far survived) election or succession. (I have omitted assassinated presidents from the data for age of death and number of years surviving, thus the gaps in the first and third series.)

It seems to me that the early presidents were generally "healthy and wise" (and wealthy, by the standards of their time). That is, they were of superior genetic stock, relative to the average person. Their successors have tended to be of less-superior stock, and it shows in the downward trends after 1836.

The general rise in life expectancies since 1900 masks the relative inferiority of twentieth century presidents. The rising age of accession to the presidency after 1932 and the rise in years of survivorship after 1924 (both with wide variations around the trend) should not be taken to indicate that presidents of the twentieth century are on a par, genetically, with the early presidents. They are not.

These observations are consistent with the following graph of presidents' heights (here including only those men who were elected to the presidency):

Source: "Heights of United States presidents and presidential candidates" at Wikipedia.

With the notable exception of Lincoln, presidential heights generally diminished from the late 1700s to the late 1800s. The upward trend since 1900 attests to the general health and vigor of the population; it says nothing about the relative robustness of the men who have been elected to the presidency in the 20th and 21st centuries.

Popular-Vote Margins in Presidential Elections

I present the following graph as a matter of historical interest; no political commentary is intended or implied.

Draw your own conclusions, if there are any to be drawn.

Random Thoughts

Why is "gunite" pronounced gun-ite, whereas "granite" is pronounced gran-it?

If, in 1950, Harry Truman had said "four score and seven years ago," he would have been referring to 1863, the year in which Abraham Lincoln uttered that famous phrase.

In the computer industry, "email" is preferred to "e-mail." But it seems to me that "e-mail" better represents the phrase "electronic mail." The meaning of "e-mail" is immediately obvious to me; "email," at first glance, looks like a typo.

If the dismal northern weather of early April and late October -- which delayed the start of the 2008 baseball season in some cities and then disrupted the World Series -- doesn't convince Major League Baseball to lop two weeks from each end of the regular season, nothing will.

One of the funniest movies I've seen is Harold Lloyd's Dr. Jack (1922). It starts slowly, but builds to a hilariously frantic finish. Lloyd's Safety Last! is better known -- and deservedly considered a comedy classic -- but it isn't half as funny as Dr. Jack.

Between novels, I have been slogging my way through Thomas K. McCraw's Prophet of Innovation: Joseph Schumpeter and Creative Destruction. There's too much armchair psychology in it, but it whets my appetite for Schumpeter's classic Capitalism, Socialism, and Democracy, which (I hate to admit) I haven't read. Schumpter's famous term for capitalism, "creative destruction," often is applied with an emphasis on "destruction"; the emphasis should be on "creative."

I must observe, relatedly, that my grandmother's lifetime (1880-1977) spanned the invention and adoption of far more new technology than is likely to emerge in my lifetime, even if I live as long as my grandmother did.

The Names, They Are A Changing

The popularity of the first names of my grandparents, in the years of their birth (all in the last three decades of the nineteenth century):

Joseph - 7th (all ranks from the Social Security index of popular baby names)
Delia - 126th
Ernest - 24th
Hazel - 26th

As of 2007:

Joseph - 13th
Delia - 989th
Ernest - not in the top 1000
Hazel - 361st

Whereas, in 2007,

Anthony was 7th among male names (103rd when Joseph was born);
Serenity was 126th among female names (not in top 1000 when Delia was born);
Nathan was 24th among male names (136th when Ernest was born); and
Kayla was 26th among female names (not in top 1000 when Hazel was born, probably not a name then).

In 1908, the five most popular female names were Mary, Helen, Margaret, Ruth, and Anna. In 2007, the five most popular female names were Emily, Isabella, Emma, Ava, and Madison. The top five male names in 1908 were John, William, James, George, and Robert; in 2007 the top five male names were Jacob, Michael, Ethan, Joshua, and Daniel -- an ironic turn toward the Old Testament in this secular age.

My own name -- which is associated mainly with an Apostle -- stood at or near 10th place from 1880 through the mid-1960s. It has slipped to 51st place.