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A New Generation of Stars

May 17, 2017
 2017-25

 

A New Generation of Stars

 

              Recently I have heard commentary to the effect that we are entering a new generation of stars in baseball; we are definitely entering a new generation of stars in baseball, etc.   How would we know if this was true or was not?

              Suppose that we

              1) generated a list of the best players in baseball each season, and

              2) compared the list for one year to the list for the next. 

              This leads to two questions:

              1)  How do we generate a list of the best players in baseball in each season?, and

              2)  How do we mathematically compare one list to the next?

              We can generate lists of the best players each year by the established value of Season Scores.   I have explained established values here before; I have explained Season Scores, so that’s an adequate Step One explanation of how we get a list of the best players in baseball each season, I think.   How do we compare one list to the next?

              Suppose that we have two lists of the biggest movie stars of 1970:

 

1

Clint Eastwood

 

1

Paul Newman

2

Paul Newman

 

2

Robert Redford

3

Barbra Streisand

 

3

Raquel Welch

4

Jack Nicholson

 

4

Clint Eastwood

5

Faye Dunaway

 

5

Barbra Streisand

6

James Caan

 

6

Jack Nicholson

 

              Obviously these two lists are somewhat the same, and somewhat different, but how do we measure to what extent they are the same, and to what extent they are different?

              Suppose that we say that being first on a six-person list is worth 6 points, being second is worth 5, etc., so that if an actor is first on one list but left off of the other one, that is a larger discrepancy than if an actor is last on one list and left off the other one:

1

Clint Eastwood

6

 

1

Paul Newman

6

2

Paul Newman

5

 

2

Robert Redford

5

3

Barbra Streisand

4

 

3

Raquel Welch

4

4

Jack Nicholson

3

 

4

Clint Eastwood

3

5

Faye Dunaway

2

 

5

Barbra Streisand

2

6

James Caan

1

 

6

Jack Nicholson

1

 

              Then we multiply the values for actors who are both lists.   Eastwood has 6 and 3, so that’s 18 points.   Newman has 5 and 6, so that’s 30.   Streisand has 4 and 2, so that’s 8.   Nicholson has 3 and 1, so that’s 3.   Adding together, that’s 59 points (18 + 30 + 8 + 3).  

              If the two lists were perfectly aligned, this would produce a total of 91 (36 + 25 + 16 + 9 + 4 + 1).   It produces a total of 59, so the two lists are 65% the same—59, divided by 91.     These two lists, on the other hand, are only 7% the same:

 

1957 Ford

 

1953 Plymouth

1971 Chevy Impala

 

2009 Mercedes

2006 Hyundai

 

1972 Citroen

1961 Cadillac

 

1971 Chevy Bel Air

1936 Studebaker

 

1974 Lamborghini

1922 Oldsmobile

 

2006 Hyundai

1982 Honda Accord

 

1963 Buick

 

              A key question is how many players you regard as "stars", when you are looking at whether the major league baseball star list is changing rapidly.   I regarded two players per team as stars. . . not two on each team, but since there are 16 teams in 1960, I listed the top 32 players as stars, whereas, with 30 teams in 2016, I listed the top 60 players are stars.    Mike Trout, Josh Donaldson and Paul Goldschmidt are listed 1-2-3, while Eric Hosmer, Corey Seager and Adam Jones are 58-59-60.  

              It seems reasonably likely that we would get different results (as to the amount of turnover in the star population) if we listed 100 stars or 10 stars than if we list 60, although I don’t know what the difference would be.    With a list of six, the score of a perfect match is 91; with a list of seven, it is 140.   With a list of 60 players, a perfect score is 73,810.  

              In any case, when we compare the 2015 and 2016 lists, we get an 81% match—81.2%, actually.   This number is actually a little above the historic norm, which is 79.1%.  

              When people talk about this transition, they often speak of it in absolute terms; there is a changing of the guard, the old guard is leaving, a new generation of stars, etc.    In reality, of course, it is never an absolute.  There has never been a clean transition between generations of stars.    Mickey Mantle played ten years against Ted Williams, Harmon Killebrew played ten years against Mantle, Reggie Jackson played almost ten years against Killebrew, George Brett played ten years against Reggie, Rickey Henderson played more than ten years against George Brett, Ken Griffey Jr. played more than ten years against Rickey and then moved to the National League and played about ten years against Albert Pujols.   Pujols has now in his sixth season as a teammate of Mike Trout.   There has never been a quick transition; there are always multiple generations of stars on the field.

              When we get into measurement of the transition, we need to understand that the numbers don’t go to zero and a hundred.    While one can identify a few "transition points" in major league history

              (a) it is just a few, and  

              (b) those aren’t one-year transitions.   Those transitions between generations of stars that you can identify occur over a period of three to five years. 

              (c)  You can’t really identify a transition point between the stars of the 1950s (Mantle, Mays, Berra, Ford, Spahn, Robin Roberts, Banks) and those of the 1960s (Gibson, Koufax, Yastrzemski, Killebrew, Oliva, McCovey, Cepeda).   The stars who bridge the gap between these two (Aaron, Frank Robinson, Drysdale, Kaline, Clemente) are just as strong or stronger than the stars who can be placed one place or the other, so there’s no transition point.

              (d)  For that matter, you can’t really identify a transition point between the stars of the 1940s (Musial, DiMaggio, Ted Williams, Feller, Kiner, Jackie) and the stars of the fifties, either, nor can you really identify a transition point between the stars of the 1960s and those of the 1970s.   The reality is that they are all braided together into one uninterrupted history.

              Anyway, let me angle toward the conclusion.   There has in fact been a transition between generations of stars in recent years, in the years 2011 to 2015.   Whether that transition is still going on, or whether we are now down to ordinary rates of turnover, is one of those things that only the passage of a little bit of time will make clear; however, I am skeptical.   I would tend to suspect we are more accurately described as early in the current generation of stars, with new stars still emerging, rather than as still being in the transition.  

              Let’s look first at the one-year transition rates, from 1900 to the present:

 

From

To

Pct

 

From

To

Pct

 

From

To

Pct

1900

1901

.769

 

1940

1941

.828

 

1980

1981

.872

1901

1902

.703

 

1941

1942

.779

 

1981

1982

.721

1902

1903

.712

 

1942

1943

.569

 

1982

1983

.785

1903

1904

.780

 

1943

1944

.574

 

1983

1984

.791

1904

1905

.713

 

1944

1945

.656

 

1984

1985

.851

1905

1906

.796

 

1945

1946

.403

 

1985

1986

.845

1906

1907

.707

 

1946

1947

.772

 

1986

1987

.836

1907

1908

.885

 

1947

1948

.743

 

1987

1988

.826

1908

1909

.847

 

1948

1949

.806

 

1988

1989

.782

1909

1910

.672

 

1949

1950

.777

 

1989

1990

.758

1910

1911

.817

 

1950

1951

.801

 

1990

1991

.800

1911

1912

.821

 

1951

1952

.681

 

1991

1992

.803

1912

1913

.818

 

1952

1953

.765

 

1992

1993

.695

1913

1914

.693

 

1953

1954

.832

 

1993

1994

.775

1914

1915

.685

 

1954

1955

.814

 

1994

1995

.758

1915

1916

.716

 

1955

1956

.907

 

1995

1996

.727

1916

1917

.693

 

1956

1957

.851

 

1996

1997

.883

1917

1918

.768

 

1957

1958

.874

 

1997

1998

.896

1918

1919

.797

 

1958

1959

.800

 

1998

1999

.836

1919

1920

.813

 

1959

1960

.830

 

1999

2000

.838

1920

1921

.643

 

1960

1961

.792

 

2000

2001

.833

1921

1922

.810

 

1961

1962

.861

 

2001

2002

.916

1922

1923

.722

 

1962

1963

.793

 

2002

2003

.885

1923

1924

.823

 

1963

1964

.830

 

2003

2004

.801

1924

1925

.857

 

1964

1965

.809

 

2004

2005

.807

1925

1926

.727

 

1965

1966

.841

 

2005

2006

.809

1926

1927

.820

 

1966

1967

.799

 

2006

2007

.836

1927

1928

.854

 

1967

1968

.697

 

2007

2008

.879

1928

1929

.792

 

1968

1969

.791

 

2008

2009

.808

1929

1930

.893

 

1969

1970

.868

 

2009

2010

.743

1930

1931

.910

 

1970

1971

.837

 

2010

2011

.729

1931

1932

.911

 

1971

1972

.785

 

2011

2012

.779

1932

1933

.912

 

1972

1973

.855

 

2012

2013

.751

1933

1934

.764

 

1973

1974

.827

 

2013

2014

.743

1934

1935

.887

 

1974

1975

.779

 

2014

2015

.741

1935

1936

.810

 

1975

1976

.839

 

2015

2016

.812

1936

1937

.829

 

1976

1977

.753

       

1937

1938

.897

 

1977

1978

.832

       

1938

1939

.830

 

1978

1979

.706

       

1939

1940

.849

 

1979

1980

.763

       

 

              Too many numbers there to make sense of, I know, but we’ll work on it.   A high number means relatively little transition between stars, and a low number indicates a high transition of stars.    Between 2015 and 2016 there was a 19% transition in the list of stars.   These are the highest numbers of all time:

 

From

To

Pct

2001

2002

.916

1932

1933

.912

1931

1932

.911

1930

1931

.910

1955

1956

.907

1937

1938

.897

1997

1998

.896

1929

1930

.893

1934

1935

.887

1907

1908

.885

 

              And these are the lowest:

From

To

Pct

1945

1946

.403

1942

1943

.569

1943

1944

.574

1920

1921

.643

1944

1945

.656

1909

1910

.672

1951

1952

.681

1914

1915

.685

1916

1917

.693

1913

1914

.693

 

              The most year-to-year turnover in stars ever was at the end of World War II, which is what you would expect, while the least year-to-year turnover ever was in the heart of the steroid era; don’t know if that was connected to the steroid use, or if it just happened then.  

              To help make sense of this, suppose that we color code the high numbers as red, and the low numbers as blue, and then run the chart above:

 

From

To

Pct

 

From

To

Pct

 

From

To

Pct

1900

1901

.769

 

1940

1941

.828

 

1980

1981

.872

1901

1902

.703

 

1941

1942

.779

 

1981

1982

.721

1902

1903

.712

 

1942

1943

.569

 

1982

1983

.785

1903

1904

.780

 

1943

1944

.574

 

1983

1984

.791

1904

1905

.713

 

1944

1945

.656

 

1984

1985

.851

1905

1906

.796

 

1945

1946

.403

 

1985

1986

.845

1906

1907

.707

 

1946

1947

.772

 

1986

1987

.836

1907

1908

.885

 

1947

1948

.743

 

1987

1988

.826

1908

1909

.847

 

1948

1949

.806

 

1988

1989

.782

1909

1910

.672

 

1949

1950

.777

 

1989

1990

.758

1910

1911

.817

 

1950

1951

.801

 

1990

1991

.800

1911

1912

.821

 

1951

1952

.681

 

1991

1992

.803

1912

1913

.818

 

1952

1953

.765

 

1992

1993

.695

1913

1914

.693

 

1953

1954

.832

 

1993

1994

.775

1914

1915

.685

 

1954

1955

.814

 

1994

1995

.758

1915

1916

.716

 

1955

1956

.907

 

1995

1996

.727

1916

1917

.693

 

1956

1957

.851

 

1996

1997

.883

1917

1918

.768

 

1957

1958

.874

 

1997

1998

.896

1918

1919

.797

 

1958

1959

.800

 

1998

1999

.836

1919

1920

.813

 

1959

1960

.830

 

1999

2000

.838

1920

1921

.643

 

1960

1961

.792

 

2000

2001

.833

1921

1922

.810

 

1961

1962

.861

 

2001

2002

.916

1922

1923

.722

 

1962

1963

.793

 

2002

2003

.885

1923

1924

.823

 

1963

1964

.830

 

2003

2004

.801

1924

1925

.857

 

1964

1965

.809

 

2004

2005

.807

1925

1926

.727

 

1965

1966

.841

 

2005

2006

.809

1926

1927

.820

 

1966

1967

.799

 

2006

2007

.836

1927

1928

.854

 

1967

1968

.697

 

2007

2008

.879

1928

1929

.792

 

1968

1969

.791

 

2008

2009

.808

1929

1930

.893

 

1969

1970

.868

 

2009

2010

.743

1930

1931

.910

 

1970

1971

.837

 

2010

2011

.729

1931

1932

.911

 

1971

1972

.785

 

2011

2012

.779

1932

1933

.912

 

1972

1973

.855

 

2012

2013

.751

1933

1934

.764

 

1973

1974

.827

 

2013

2014

.743

1934

1935

.887

 

1974

1975

.779

 

2014

2015

.741

1935

1936

.810

 

1975

1976

.839

 

2015

2016

.812

1936

1937

.829

 

1976

1977

.753

       

1937

1938

.897

 

1977

1978

.832

       

1938

1939

.830

 

1978

1979

.706

       

1939

1940

.849

 

1979

1980

.763

       

 

 

              We can see, then, that

              1)  In the Dead Ball era (1901 to 1909) there was more year-to-year turnover in stars than there has been generally since 1920, although the rates were not dramatically different.

              2)  In the era 1929 to 1932, there were extremely low levels of year to year transition in the star population.

              3)  During World War II, of course, there was extremely high year to year turnover.

              4)  Followed by a period of stability in the 1950s. 

              5)  After that, there wasn’t another major transition until the 1988-1995 era, when there was clear transition between generations. 

              6)  In the steroid era the numbers were extremely high—extremely little year-to-year transition, perhaps the highest numbers of all time.

              7)  Beginning in 2009, there is another transition era. 

 

              As a technical detail, I didn’t adjust the number of players considered stars for the 1914-1915 era, when there was a third league, the Federal League.   Since we take a multi-year look at performance, a "star" is defined by what a player has done over a period of several years.   It’s not clear what we should do with the Federal League, and none of the answers seems to be right, so I just stayed with 32 players, interpreting the "number of teams" to not include teams with a very short history.   It was a long time ago, and I don’t figure it matters a lot.

              Anyway, to this point in the article I have been dwelling on one-year transitions.   One year transitions are actually NOT the best way to look at the issue; it is just the easiest to explain.   You can compare lists from consecutive years; you can compare lists from two years apart, three years, four years, five years, whatever.   I ran the data for one, two, three, four, five and ten years.    

              In one year, the "match" between the lists is 79.1%, so the turnover in stars is 20.9%.   In a two-year test, the match between the lists 63.8%, so the turnover in stars is 36.2%.   In a three-year test, the match between the lists is 52%, so the turnover is 48%.   Basically, half of the star population turns over in a three-year period, and half of it stays the same.  

              In a four-year match—that is, comparing the lists of 1916 to 1920, or 1960 to 1964, or 1987 to 1991, whatever—there is a 42% match between the lists, so there is a 58% turnover.   Comparing lists of stars five years apart, there is a 33.8% match, meaning there is a 66.2% turnover.  

              Comparing lists ten years apart, there is a 9.6% match between the lists, meaning that in an average ten-year span, there is a 90% turnover in the population of baseball’s stars.   Interestingly, the one-year percentage is .79149, and the ten-year percentage is .0962.   .79149 to the tenth power is .0965. 

              I didn’t compare lists 6, 7, 8 or 9 years apart, but given the stability of the data, we can estimate with a very high degree of accuracy what the data would be.   The six-year percentage would be .263 (73.7% turnover.)   The seven-year percentage would be .205 (79.5% turnover.)   The eight-year percentage would be .159 (84.1% turnover), and the nine-year percentage would be .124 (87.6% turnover.)

              For the two-year comparisons, these are the most similar lists:

 

First

Last

Pct

1930

1932

.844

1931

1933

.812

2001

2003

.812

1929

1931

.793

1934

1936

.791

1955

1957

.773

2006

2008

.770

1996

1998

.765

1969

1971

.764

1956

1958

.759

2000

2002

.757

 

              You can see that there is a period in there (1998 to 2003) when there was very little turnover in the star population.    But the best measurement appears to be the three-year comp.    There are all the three-year comps from 1900 to the present, color-coded.  

 

 

From

To

Pct

1900

1903

.347

1901

1904

.404

1902

1905

.447

1903

1906

.546

1904

1907

.465

1905

1908

.504

1906

1909

.509

1907

1910

.520

1908

1911

.440

1909

1912

.417

1910

1913

.505

1911

1914

.539

1912

1915

.391

1913

1916

.453

1914

1917

.477

1915

1918

.338

1916

1919

.458

1917

1920

.711

1918

1921

.536

1919

1922

.305

1920

1923

.280

1921

1924

.621

1922

1925

.637

1923

1926

.501

1924

1927

.499

1925

1928

.535

1926

1929

.600

1927

1930

.599

1928

1931

.617

1929

1932

.740

1930

1933

.721

1931

1934

.592

1932

1935

.528

1933

1936

.588

1934

1937

.640

1935

1938

.672

1936

1939

.545

1937

1940

.604

1938

1941

.570

1939

1942

.505

1940

1943

.273

1941

1944

.212

1942

1945

.163

1943

1946

.280

1944

1947

.333

1945

1948

.190

1946

1949

.480

1947

1950

.425

1948

1951

.478

1949

1952

.428

1950

1953

.478

1951

1954

.521

1952

1955

.460

1953

1956

.538

1954

1957

.606

1955

1958

.647

1956

1959

.658

1957

1960

.641

1958

1961

.641

1959

1962

.722

1960

1963

.606

1961

1964

.583

1962

1965

.519

1963

1966

.581

1964

1967

.649

1966

1969

.542

1967

1970

.607

1968

1971

.575

1969

1972

.544

1970

1973

.486

1971

1974

.474

1972

1975

.553

1973

1976

.552

1974

1977

.445

1975

1978

.549

1976

1979

.401

1977

1980

.473

1978

1981

.480

1979

1982

.506

1980

1983

.578

1981

1984

.451

1982

1985

.515

1983

1986

.550

1984

1987

.591

1985

1988

.615

1986

1989

.515

1987

1990

.486

1988

1991

.518

1989

1992

.411

1990

1993

.347

1991

1994

.506

1992

1995

.465

1993

1996

.466

1994

1997

.611

1995

1998

.704

1996

1999

.732

1997

2000

.606

1998

2001

.552

1999

2002

.646

2000

2003

.711

2001

2004

.674

2002

2005

.587

2003

2006

.535

2004

2007

.558

2005

2008

.572

2006

2009

.610

2007

2010

.555

2008

2011

.449

2009

2012

.410

2010

2013

.528

2011

2014

.464

2012

2015

.504

2013

2016

.551

 

 

              The three-year data makes more coherent patterns than any of the other data, which you can see easily in the color coding:

              1)  From 1900 to 1920 the numbers are generally low.

              2)  From 1921 to 1937 they are quite high.

              3)  From 1940 to 1952 they were low again.

              4)  From 1954 to 1968 they were high.

              5)  In the 1970s they were mid-range, neither high nor low.

              6)  In the early 1980s there was a brief up period.

              7)  From 1989 to 1993 there was a clear transition between generations of players, as George Brett, Robin Yount, Dale Murphy, Don Mattingly, Dwight Evans, Jim Rice, Kirk Gibson, Andre Dawson, Dave Winfield, Alan Trammell, Mike Scott, Mike Schmidt and others either disappeared from the game or dropped off the list of stars, while Ken Griffey Jr., Barry Bonds, Frank Thomas, Greg Maddux, Juan Gonzalez, Roberto Alomar, Mike Piazza, Gary Sheffield, Derek Jeter, Mariano Rivera and others emerged as stars.  

              8)  From 1994 to 2006 the numbers were high, as this generation of players dominated the game, with relatively little in and out rotation.

              9)  From 2008 to 2014, at least, there was in fact a period of transition to a new generation of stars.   It is possible that this transition is still occurring, although I think it is unlikely.

 

              The 1940s data is different; that is more of a massive disruption than an actual transition.  Many of most of the stars of pre-World War II baseball (Musial, DiMaggio, Ted Williams, Bob Feller, Enos Slaughter, Johnny Mize, Phil Rizzuto) were actually young men early in their careers when the war started, and returned to baseball after the war was over.    

              Other than that, there are really three pretty clear transitions in baseball history. 

              One, which is sort of hidden in this data that I have given you but which shows up brightly in some of the other data, is about 1923-1925, when Lou Gehrig, Charlie Gehringer, Lefty Grove, Bill Terry, Gabby Hartnett, Hack Wilson, Pie Traynor, Mickey Cochrane, Earle Combs, Goose Goslin, Kiki Cuyler and others emerged, and most of the stars of the Dead Ball era faded into the background.     

              The second transition, which I described before, occurred in the late 1980s, early 1990s.

              The third transition was the recent one, beginning about 2008.    The 2009 and 2012 lists are only 41% the same, which was the lowest figure since the early 1990s, and the third-lowest figure since World War II.     In that period Bobby Abreu, Jason Bay, Lance Berkman, Carl Crawford, Johnny Damon, Jermaine Dye, Adam Dunn, Roy Halladay, Todd Helton, Ryan Howard, Raul Ibanez, Chipper Jones, Derek Lee, Tim Lincecum, Alex Rodriguez, Grady Sizemore, Kevin Youkilis and others disappeared as stars or declined substantially, while Jose Bautista, Matt Cain, Edwin Encarnacion, Carlos Gonzalez, Alex Gordon, Adam Jones, Clayton Kershaw, Craig Kimbrel, Andrew McCutchen, Buster Posey, David Price, Giancarlo Stanton and Mike Trout emerged as stars.  

              There is an alternative that I didn’t choose that I suppose I should discuss briefly before I close.   I considered a player to have left the star population when he was no longer a top player, rather than when he retired.   There is usually about a five-year lag time between a players’ losing his edge and his leaving the game; not too many David Ortizes who go out on top.   There is usually a Ryan Howard/David Wright/Albert Pujols/Mark Teixeira phase in there.  

              One COULD say that a star player, established as a star, is a star player as long as he is active, and that the transition occurs when he leaves the game, not when he loses his edge.   If you figured it that way, then the 2008-2012 transition phase that we have established here is moved back a few years—perhaps moved back as long as five years.

              That’s not IMPOSSIBLE math; it is just different math.   You COULD identify the biggest stars in the game based on some combination of recent seasons and career numbers.  

              As the system is designed, it is difficult for a rookie to make the star list—difficult, but not impossible.   Corey Seager made the star list after the 2016 season, but it’s not easy; it takes a big rookie season to make it.   If you factor in career accomplishments to keep Mark Teixeira on the list as long as he is active player, then you push younger players off the list on the other end—unless you go to three players per team or something.    Not saying it can’t be done; I just chose to look at the problem in a different way.

 

              I’ll open this up for comments tomorrow.  

 

 

             

 

 

 

 

 

 
 

COMMENTS (11 Comments, most recent shown first)

trn6229
Hi Bill, Nice article. My earliest baseball memory is the 1971 All Star Game, you had Mays, Aaron, Clemente, McCovey, Kaline, Frank and Brooks Robinson, Killebrew, Aparicio. Bench was a young superstar and Vide Blue was a super star in 1971, then not so great in 1972, but a 20 game winner in 1973. Reggie Jackson hit a cannon shot off Dock Ellis when he pinch hit for Blue. He was an injury replacement for Tony Oliva.

What about young players such as Gary Sanchez and Aaron Judge of the Yankees? Mookie Betts and Andrew Benintendi and Xander Bogaerts of the Red Sox.

I watched the MLB Draft yesterday. How many of those players will be All Stars of MVP or Cy Young candidates? I was surprised to see a few high school pitchers taken. We know from history that high school pitchers are a higher risk. Sometimes you get Dwight Gooden and other times you get Brien Taylor or Ron Walden.

Take Care,
Tom Nahigian
8:34 PM Jun 13th
 
lidsky
I'm curious if you had did a smaller number, say to 12 or so, whether the result would be similar or show differing trends. Focusing more on the elite as I think that is what more influences the feeling of the top stars.

I think of "star" as somebody most fans would know and be excited to see when they come to town. I don't feel that is 2 per team - even on average.
3:13 AM May 22nd
 
frisco
It's subjective but I think McQueen was fantastic. Could give you more with a glance than most actors could in three pages of dialogue.
9:33 PM May 20th
 
337
Brutal actor though. I just re-watched THE GETAWAY with him and Ali MacGraw, and they were competing for Dullest Acting Job ever in that film. Loved him in THE GREAT ESCAPE, where all he had to do was throw a hardball against the cooler wall and ride a motorcycle. He was good at physical stuff, acting not so much. He was ridiculous as Thomas Crown.
12:20 PM May 20th
 
ksclacktc
@frisco McQueen for sure! Very underrated.
6:00 PM May 19th
 
frisco
I think Steve McQueen has to be one of the biggest stars of 1970. :-)

Very good study, though.

My Best-Carey


12:30 PM May 19th
 
tangotiger
Bill, very interesting. We can basically say that the turnover rate is 20% year over year, and it's independent of the prior years. So, .8^yearsAgo fits your data as good as anything else.

10:07 AM May 19th
 
Robinsong
Fascinating analysis. Interesting to speculate on whether there are reasons for the patterns (other than chance and WWII). The pink and blue periods seem to correspond well to the "eras" that an earlier article by Bill analyzed. The steroid era pattern could be explained by the drugs themselves, which help prolong peak performance. The 50's/60's era stability may be explained in part by the breaking of the color line opening up the majors to a generation of young stars who did not have to displace older black stars.
9:45 AM May 19th
 
hotstatrat
Wonderful. And, I strongly agree that the hanging-on years of old stars are best left out of this study.​
9:42 AM May 19th
 
CharlesSaeger
Wait, I see Season Scores, and I take it some kind of weighting of last year higher, previous years lower, maybe with a regression.
7:52 AM May 19th
 
CharlesSaeger
How did you determine who were the star players?
7:47 AM May 19th
 
 
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