Future Shock: Position... (08/29)
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August 30, 2007 Schrodinger's BatTilting the Playing Field
"It is the best game because the players look like us. They are not seven feet tall, they don’t weigh 350 pounds, and they don’t bench-press 650. We can relate to them. We can see them—they’re not obscured by some hideous face mask, and they don’t play behind a wall of Plexiglas—we can touch them and we can feel them. I see Greg Maddux with his shirt off, with his concave chest and no discernible muscles, and I marvel: This is one of the six greatest pitchers in the history of the game? I see Tony Gwynn with his shirt off and I see a short, fat guy with the smallest hands I've ever seen on an athlete, and I wonder: 'This is the best hitter since Ted Williams?'...They are regular guys, at least most of them, who just happen to be really, really good at something that everyone else is not." This fan certainly agrees with Mr. Kurkjian that baseball is indeed the best game. Where opinions start to diverge is in the related claim that because players "look like folks," there is little difference between the players of, say, 60 years ago and today. If we could bring players from the past back to life and suit them up, so the argument goes, Ted Williams would still be walking down the street hearing people call him the greatest hitter who ever lived and Babe Ruth would still be, well, Ruthian. The perception that this view is on the money is fueled not only by the accessibility and appearance of many players, but by the statistics that we use to record their performances on the field. Unlike in swimming or sprinting, accomplishments in baseball are recorded in a relativistic manner, with the credits of hitters perfectly balancing with the debits of pitchers and defenders, as in an accountant's ledger book. In addition, the powers that be have ensured that the balance between offense and defense has never swayed too far from a historical norm; with some exceptions, individual performance data can be reasonably compared across eras by the average fan. As a result, similar stat lines from different eras can mask underlying differences in the skills and abilities of players that would be otherwise evident if they played side by side. As I discussed in a column last January titled "The Myth of the Golden Age", the same processes that drive improvements in other systems and sports are at work in baseball. Chief among these are that complex systems improve when the best performers play by the same rules for an extended period of time, permitting the system to reach equilibrium and allow various strategies and techniques to be discovered, selected, and optimized. In baseball, this manifests itself in everything from defensive positioning and technique to batting stances and pitching mechanics that have improved over time through a process of trial and error. Secondly, as in all sports, today's athletes are superior to those of the past in size, speed, and strength, as evidenced by contests where an absolute--rather than a relative--measuring stick is used (as in track and field). When combined with the advantages of modern medical care, nutrition, and training regimes, this improvement has pushed the average major leaguer closer to the absolute right wall of human ability. These processes have had the consequence of decreasing the variation between players. In short, the greats of the past were outliers who could take advantage of the sub-optimal play among populations characterized by a lower general level of ability. But in addition, baseball has also benefited from an ever-increasing population pool from which to draw--first via African-American integration, and later through the influx of Latin and, more recently, Asian players. More players to choose from will ensure that the quality of those players is higher. And this was on the heels of a minor league and scouting system that has been developing since Branch Rickey increased the efficiency of discovering and cultivating talent. All of this adds up to an increasing excellence in play on the field. In the previous article we discussed several attempts to detect the magnitude of that increase using various lines of evidence; before closing my off-season ruminations in late February, I promised readers that we'd have one more installment related to this topic. And so for those who have been on pins and needles since before the snow melted and the games began, this is your lucky day. Today we'll take one of those techniques and apply it to position players in order to tilt the stat lines away from the forces that have conspired to level the playing field. A Lack of Selection Pressure As discussed in the previous column, we'll use the offensive production of pitchers relative to position players as a measure of the increasing level of play over time. As the game evolved from where pitching was throwing underhand with a straight arm (as in "pitching" horseshoes) in the 1850s, to a variety of submarine and sidearm deliveries in the 1860s and 70s, and finally to the full overhand delivery after 1883 in the National League (NL) and 1884 in the American Association (AA), pitchers were selected primarily for their pitching and not their hitting ability. In an evolutionary sense, batting skills of pitchers did not undergo the same selection pressure as their pitching skills. The consequence of substantially lowering or removing this selection pressure is that the actual or true hitting ability of pitchers should have remained relatively constant throughout the history of baseball. By comparing the offensive production of pitchers to position players who do face the rigors of selection, we should be able to measure the increase in the level of play. This is the case since the factors mentioned previously are all constantly contributing to subtly raising the talent level of the environment in which pitchers as batters find themselves less and less able to successfully compete. Ironically, their frustration as a group is in large part a consequence of their own ever-increasing ability to execute their craft. As I showed in the previous column, the results from making this comparison do indeed show a decrease in offensive output for pitchers over time. Unlike in the previous column, however, the following graph breaks down park-adjusted normalized OPS for pitchers relative to hitters by league.
 Pitchers as a group were pretty similar to position players in terms of offensive output in the 1870s, often producing in the range of 80 to 95 percent. That started to change relatively quickly in the 1880s; by 1901 pitchers would see their last season at 75 percent or above as recorded in the nascent American League (AL). The ratio fell from around 70 percent in the first decade of the twentieth century to under 50 percent most recently, as illustrated in the following table (AL and NL only), with only a small bump in the 1970s:
Pitcher Production Relative to Hitters
Decade Ratio
----------------
1900s .694
1910s .662
1920s .653
1930s .612
1940s .606
1950s .574
1960s .510
1970s .526
1980s .494
1990s .478
2000s .465
The trend by decade shows a fairly steep decrease from the 1900s through the 1920s, a leveling off in the 1930s and 40s, and then another steep decline in the 1950s and 1960s before the increase in the 1970s followed by smaller declines in the 1980s, 90s, and first decade of this century. In one sense this is what we might expect. For example, we could easily imagine that this tracks with the following five-era chronology:
The other interesting aspect of this graph that may be unexpected is that it shows pretty clearly the differences in the leagues themselves. For example:
Where things appear less clear, the data indicates that from 1914 through 1926 the leagues appeared fairly evenly matched, but then the tide turned back to the NL again through the early 1930s. Beginning around 1934 the balance again returned and stayed through the end of World War II. Upside Down and Backwards So if we're correct in our assumption that pitcher hitting records the rate at which the level of play has increased, we can use that data to construct an index of level of play over time. However, since the data from the plot above has a lot of noise in it and slopes in the wrong direction, we'll apply a couple of transformations. By combining both the NL and AL, applying a moving average, inverting the ratios from the above plot, and finally normalizing each year relative to 2006, we can smooth out the rough edges and come up with the following graph, which shows the "Level Index," or LI, for each year beginning in 1876:
 You'll notice that this graph follows the trends noted earlier, in addition to picking up the effects of both World Wars, which interrupted the upward march temporarily. Readers somewhat familiar with this discussion will note that earlier this summer David Gassko wrote a three part series of articles where he used a different technique to develop a similar index, and compare that to the methods used in both Dick Cramer's original 1977 study and by Clay Davenport's Baseball Between The Numbers essay. That methodology relies on direct comparisons of player performance from year to year, and is somewhat more difficult to sort out, given there are conflating factors at work. Gassko's version of that technique--after a critique by our own Nate Silver--accounts for regression to the mean using a player's predicted career performance based on plate appearances, as well as neutralizing the affects of aging by using only 26 to 29 year olds (who show no overall performance change during that time span). In his addendum on the subject, Gassko produces a graph that depicts his final attempt along with Davenport's method, and which looks similar to the graph above. A quick side-by-side comparison reveals that the LI line we've drawn here has a slightly larger slope, thereby somewhat splitting the difference between Davenport and Gassko, although ending up much closer to Gassko. If you click on the link and review his graph, you'll also notice that the dip during World War II in all the lines shown by Gassko is more pronounced than shown here. The reason is that we've used a moving average, which tends to smooth out the data. While that's good for most of the graph, it underestimates the magnitude of the talent loss during the war. There is now one final adjustment to make. If we're going to tilt the playing field, we'll also need to adjust for the differences between leagues. As mentioned previously, the chart of pitcher versus position player hitting provides us with some data to use to create separate LIs for the AL and NL. The way this was done was to note that relative percentage difference between the leagues, again using a moving average, and then to calculate how that difference would be reflected if it were applied to the previous graph. The result is the graph below, where the AL is depicted in red and the NL in blue:
 Based as it is on the relative performance of pitcher hitting, it includes the same differences noted earlier, namely the strength of the NL in the 1900s, and again in the post-integration era. The weakness of his approach is that since pitcher hitting data dries up after 1972, we need to estimate the league differences after that time. I've done this by showing a slight advantage for the NL through the 1970s, introducing parity in the mid-80s, and then giving the AL a slight advantage through the present. Surely this isn't a perfect system; in simply eyeballing the results, it probably overestimates the difference between the leagues in the late 40s and early 50s. Tilt! Finally, we're able to use the previous graph to tilt the playing field. To take this final step we'll use Keith Woolner's Win Expectancy (WX) framework and the derivative WX1 that I discussed in a column last year. In short, the WX framework allows for the aggregation of all events that a batter was responsible for, and debits or credits the player corresponding to how much that event pushed his team either towards winning or losing. It does not include defense or baserunning. The derivative WX1 relies on the same concept, although instead of being calculated using individual plays complete with their base, out, inning, and run environment attributes, it uses general coefficients for each offensive event based on the run environment of the league and the player's home park. This provides an overall picture of the win contribution of a player. Basically, WX1 is a shorthand way of getting to WX when you don't have play by play records available, as we don't prior to 1959. When we calculate WX1 for all AL and NL seasons going back to 1876, we find that the top and bottom 15 seasons are as follows:
Year Name PA WX1 ---------------------------------------- 2001 Barry Bonds 655 11.3 2002 Barry Bonds 603 10.6 1923 Babe Ruth 695 9.7 1921 Babe Ruth 689 9.5 1920 Babe Ruth 612 9.4 1927 Babe Ruth 691 9.2 1926 Babe Ruth 649 9.1 1927 Lou Gehrig 714 9.0 1946 Ted Williams 670 8.9 1941 Ted Williams 603 8.9 1957 Mickey Mantle 623 8.7 1917 Ty Cobb 665 8.6 2004 Barry Bonds 608 8.5 1924 Rogers Hornsby 638 8.4 1942 Ted Williams 667 8.4 ---------------------------------------- 1891 Lou Bierbauer 528 -4.7 1890 Germany Smith 523 -4.8 1884 Jim Lillie 476 -4.8 1891 Germany Smith 550 -4.8 1892 Joe Quinn 567 -4.8 2002 Neifi Perez 585 -5.0 1885 Joe Gerhardt 423 -5.1 1894 Chippy McGarr 551 -5.2 1895 Jack Boyle 620 -5.2 1890 Bob Gilks 576 -5.2 1894 John Ward 574 -5.3 1893 Joe Quinn 580 -5.5 1886 Jim Lillie 427 -5.5 1933 Jim Levey 564 -5.9 1894 Jiggs Parrott 533 -6.1 Bonds, Ruth, and Williams dominate the list, taking eleven of the top fifteen spots, with Gehrig, Mantle, Cobb, and Hornsby each grabbing a spot. Bonds is the only player to amass 10 wins, doing so in both 2001 and 2002. On the other end of the spectrum, the only players not from the nineteenth century include Neifi the Terrible and Jim Levey; the latter played shortstop for the 1933 St. Louis Browns in what would be, at age 26, his final year in the big leagues. That season he hit .195/.237/.240 in those 564 plate appearances and was 20 runs below average on defense for good measure. Because the bottom of the list is dominated by nineteenth century players, we'll re-run the bottom fifteen starting at 1901, thereby allowing Neifi to sneak in there one more time, along with the immortal Rob Picciolo of the 1977 A's.
Year Name PA WX1 ---------------------------------------- 1902 John Gochnauer 506.0 -4.1 1977 Rob Picciolo 445.0 -4.1 1901 John Ganzel 553.0 -4.1 1936 Skeeter Newsome 507.0 -4.3 1937 Jackie Hayes 629.0 -4.3 1901 Bill Hallman 521.0 -4.4 1999 Neifi Perez 731.0 -4.5 1909 Bill Bergen 372.0 -4.5 1931 Jim Levey 538.0 -4.5 1934 Ski Melillo 588.0 -4.5 1932 Ski Melillo 657.0 -4.5 1953 Billy Hunter 602.0 -4.6 1933 Art Scharein 521.0 -4.6 2002 Neifi Perez 585.0 -5.0 1933 Jim Levey 564.0 -5.9 Now, applying our Level Index, we'll run the top and bottom 15 seasons again, this time accounting for the difficulty of the league. Keep in mind that this adjustment treats every player as if they were transported to the 2006 AL with their hitting skills from the season in question intact.
Year Name PA WX1 --------------------------------------- 2001 Barry Bonds 655 11.0 2002 Barry Bonds 603 10.3 2004 Barry Bonds 608 8.2 1998 Mark McGwire 675 8.0 2001 Sammy Sosa 705 7.6 1993 Barry Bonds 672 7.1 2003 Albert Pujols 675 7.0 1992 Barry Bonds 607 7.0 1941 Ted Williams 603 6.9 2003 Barry Bonds 540 6.8 1957 Mickey Mantle 623 6.8 1923 Babe Ruth 695 6.6 2001 Jason Giambi 658 6.6 1961 Mickey Mantle 646 6.6 1942 Ted Williams 667 6.5 --------------------------------------- 1897 Germany Smith 449 -8.0 1894 Germany Smith 523 -8.0 1886 Joe Gerhardt 448 -8.1 1891 Germany Smith 550 -8.1 1892 Joe Quinn 567 -8.2 1879 Will White 300 -8.6 1890 Bob Gilks 576 -8.8 1884 Jim Lillie 476 -8.9 1895 Jack Boyle 620 -8.9 1894 Chippy McGarr 551 -9.0 1894 John Ward 574 -9.1 1885 Joe Gerhardt 423 -9.2 1893 Joe Quinn 580 -9.3 1886 Jim Lillie 427 -10.1 1894 Jiggs Parrott 533 -10.6 Not surprisingly, Bonds still dominates, this time adding his 2004, 1993, 1992, and 2003 campaigns to the list in capturing six of the top fifteen slots. Ruth is left with just his 1923 season (although he does claim two more spots in the top 20) making it the least recent, while Williams hangs on to two spots and Mantle actually adds his 1961 effort in the fifteenth slot. New to the list are recent stars McGwire, Sosa, Pujols, and Giambi. Derrek Lee's 2005 season also ranks 25th. To give you a feel for the magnitude of the adjustment, you'll notice that Ruth, Giambi, and Mantle are all tied at 6.6 wins and each separated by about 40 years. Their unadjusted batting lines for those three seasons are:
Year Name PA AVG/OBP/SLG HR BRAA EqA ------------------------------------------------- 1923 Ruth 695 .393/.545/.764 41 120 .405 1961 Mantle 646 .317/.448/.687 54 96 .379 2001 Giambi 658 .342/.477/.660 38 85 .369 Obviously the worst players from the remotest time period will do the most poorly, and now the entire list contains nineteenth century players. Poor Jiggs Parrott put up a .248/.274/.333 line playing for the Chicago Colts in the highest-scoring league (7.36 runs per game per team) in our data set. Next, we'll look at WX1 from the perspective of entire careers, with the unadjusted leaders and trailers in the following tables:
Name Start End PA WX1 -------------------------------------------------- Babe Ruth 1914 1935 10573 116.2 Barry Bonds 1986 2006 12026 108.6 Ty Cobb 1905 1928 12978 102.1 Ted Williams 1939 1960 9752 97.3 Hank Aaron 1954 1976 13908 89.3 Stan Musial 1941 1963 12659 86.0 Willie Mays 1951 1973 12449 83.8 Mickey Mantle 1951 1968 9896 81.8 Lou Gehrig 1923 1939 9615 78.1 Rogers Hornsby 1915 1937 9427 76.8 Tris Speaker 1907 1928 11885 73.9 Mel Ott 1926 1947 11273 70.2 Frank Robinson 1956 1976 11545 67.1 Eddie Collins 1906 1930 11960 62.4 Honus Wagner 1897 1917 11614 61.3 -------------------------------------------------- Davy Force 1876 1886 3081 -30.0 Fred Pfeffer 1882 1897 6544 -30.2 Herman Long 1890 1904 7798 -30.3 Ed Brinkman 1961 1975 6600 -30.8 Bones Ely 1884 1902 4991 -31.0 Ozzie Guillen 1985 2000 7126 -32.0 Malachi Kittridge 1890 1906 4438 -32.4 Bill Bergen 1901 1911 3228 -33.3 Kid Gleason 1888 1912 8160 -33.9 John Ward 1878 1894 7455 -34.6 Germany Smith 1884 1898 4638 -34.8 Alfredo Griffin 1976 1993 7305 -35.1 Bobby Lowe 1890 1907 7670 -35.9 Joe Quinn 1885 1901 6304 -39.5 Tommy Corcoran 1892 1907 8252 -41.8 Next, we'll make the adjustment by evaluating each season of their careers in the context of the 2006 AL:
Name Start End PA WX1 -------------------------------------------------- Barry Bonds 1986 2006 12026 104.6 Babe Ruth 1914 1935 10573 80.4 Hank Aaron 1954 1976 13908 78.9 Ted Williams 1939 1960 9752 73.7 Willie Mays 1951 1973 12449 73.4 Stan Musial 1941 1963 12659 69.3 Ty Cobb 1905 1928 12978 68.4 Mickey Mantle 1951 1968 9896 66.2 Frank Robinson 1956 1976 11545 59.2 Lou Gehrig 1923 1939 9615 55.9 Rogers Hornsby 1915 1937 9427 53.6 Rickey Henderson 1979 2003 13248 52.1 Mel Ott 1926 1947 11273 51.9 Frank Thomas 1990 2006 9084 51.8 Jeff Bagwell 1991 2005 9303 50.8 -------------------------------------------------- Jack Burdock 1876 1891 3747 -48.1 Tom Burns 1880 1892 5190 -48.7 Pud Galvin 1879 1892 2402 -48.7 Bill Bergen 1901 1911 3228 -48.7 Herman Long 1890 1904 7798 -50.5 Bones Ely 1884 1902 4991 -52.0 Malachi Kittridge 1890 1906 4438 -53.9 Fred Pfeffer 1882 1897 6544 -53.9 Kid Gleason 1888 1912 8160 -55.4 Davy Force 1876 1886 3081 -56.3 Bobby Lowe 1890 1907 7670 -59.4 Germany Smith 1884 1898 4638 -59.7 John Ward 1878 1894 7455 -62.8 Tommy Corcoran 1892 1907 8252 -67.9 Joe Quinn 1885 1901 6304 -68.0 Bonds takes over the top spot by a large margin, while Cobb falls from second to seventh. Ruth remains somewhat Ruthian, but is now coupled with Aaron. In the first list, the third through sixth spots were occupied by Williams, Aaron, Musial and Mays, while in the adjusted list the order is now Aaron, Williams, Mays, and Musial. Meanwhile, Gehrig only falls one spot, while Tris Speaker (now 16th), Eddie Collins (23rd), and Honus Wagner (24th) drop out of the top 15 altogether, with Rickey Henderson, Frank Thomas, and Jeff Bagwell taking their places. In addition, active players Gary Sheffield (18th), Manny Ramirez (27th), Chipper Jones (28th), and Mike Piazza (30th) all move up considerably. Once again, to get a feel for the adjustment, take a look at the career lines of Cobb and Musial, whose adjusted wins are very close at 68.4 and 69.3 respectively:
Name PA AVG/OBP/SLG HR BRAA EqA ----------------------------------------------- Cobb 12978 .366/.433/.512 117 1206 .335 Musial 12659 .331/.417/.559 475 1083 .332 In absolute terms, the adjustments cost Ruth the most (more than 35 wins), while also being hard on Cobb (34), Speaker (25), Williams (24), and Hornsby (23). Finally, let's take a look at the unadjusted leaders in WX1 per 600 plate appearances for those players with 2000 or more plate appearances in their careers:
Name Start End PA WX1Rate -------------------------------------------------- Babe Ruth 1914 1935 10573 6.6 Ted Williams 1939 1960 9752 6.0 Barry Bonds 1986 2006 12026 5.4 Albert Pujols 2001 2006 4014 5.0 Mickey Mantle 1951 1968 9896 5.0 Rogers Hornsby 1915 1937 9427 4.9 Lou Gehrig 1923 1939 9615 4.9 Ty Cobb 1905 1928 12978 4.7 Joe Jackson 1908 1920 5631 4.3 Stan Musial 1941 1963 12659 4.1 Willie Mays 1951 1973 12449 4.0 Hank Aaron 1954 1976 13908 3.9 Johnny Mize 1936 1953 7319 3.8 Mel Ott 1926 1947 11273 3.7 Tris Speaker 1907 1928 11885 3.7 Dick Allen 1963 1977 7298 3.7 Mark McGwire 1986 2001 7585 3.7 Joe DiMaggio 1936 1951 7625 3.6 Jimmie Foxx 1925 1945 9657 3.6 Frank Thomas 1990 2006 9084 3.5 Ruth and Williams are well ahead of the pack, although Pujols ties with Mantle for fourth place, while Frank Thomas slides in at number 20. This list also contains our first glimpses of Joe DiMaggio, Dick Allen, Jimmy Foxx, Johnny Mize, and Joe Jackson.
Name Start End PA WX1Rate -------------------------------------------------- Barry Bonds 1986 2006 12026 5.2 Albert Pujols 2001 2006 4014 4.9 Babe Ruth 1914 1935 10573 4.6 Ted Williams 1939 1960 9752 4.5 Mickey Mantle 1951 1968 9896 4.0 Willie Mays 1951 1973 12449 3.5 Mark McGwire 1986 2001 7585 3.5 Lou Gehrig 1923 1939 9615 3.5 Frank Thomas 1990 2006 9084 3.4 Rogers Hornsby 1915 1937 9427 3.4 Hank Aaron 1954 1976 13908 3.4 Dick Allen 1963 1977 7298 3.3 Lance Berkman 1999 2006 4414 3.3 Stan Musial 1941 1963 12659 3.3 Jeff Bagwell 1991 2005 9303 3.3 Travis Hafner 2002 2006 2065 3.2 Ty Cobb 1905 1928 12978 3.2 Chipper Jones 1993 2006 7528 3.1 Mike Piazza 1992 2006 7386 3.1 Frank Robinson 1956 1976 11545 3.1 As you would expect, several actives players jump into the list; perhaps most surprisingly, Lance Berkman coming in at 13th, and Travis Hafner at 16th. Wrapping Up So in the end, what does all of this tell us? I think it's important to note that while adjusting these statistics using the LI method certainly makes a difference, it does not wipe out the greatness of past stars by equating them to reserve players in today's game. Yes, they're knocked down a few pegs, but the adjusted lists are not populated only by active and recently-retired players. For example, Honus Wagner's fabulous 1908 Deadball Era season--in which he hit .354/.415/.542 with a .362 EqA--is adjusted to 5.5 wins, dropping it from the 28th--greatest offensive season of all time to the 62nd; it's still in the company of Sammy Sosa's 2000 campaign in which he hit .320 with 50 home runs, Ruth's 1928 season, and Frank Thomas's 1991 efforts. Wagner would still be a star, simply one that couldn't dominate so completely. Secondly, it should remind us that we have the privilege of watching players like Albert Pujols, who are among the most skilled hitters who have ever put on a uniform. But finally, while analyses like these are interesting, ultimately they're not a complete answer to the question, since they have nothing to say regarding some of the more interesting speculations. For example, how would Ruth have done with the aid of modern medicine, training programs, and especially nutrition? How would Pujols or Bonds perform without those aids and with inferior equipment, facilities, and the rigors of train travel? These are questions for which there can never be a complete answer; perhaps that's just fine, since it continues to leave us room for arguing about who was the greatest.
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