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:

              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:

              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:

              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:

              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:

              And these are the lowest:

              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:

              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:

              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.  

              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.