Challenging nostalgia and performance metrics in baseball Daniel J. Eck March 28, 2018 Abstract In this writeup, we show that the great old time players are overrated relative to the great players of recent time and we show that performance metrics used to compare players have substantial era biases. In showing that the old time players are overrated, no individual statistics or era adjusted metrics are used. Instead, we provide substantial evidence that the composition of the eras themselves are drastically different. In particular, there were significantly fewer eligible MLB players available in the older eras of baseball. As a consequence, we argue that ESPN’s greatest MLB players of all time list includes too many old time players in their top 25 and many performance metrics fail to adequately compare players across eras. 1 Introduction When one looks at the raw or advanced baseball statistics, one is often blown away by the accomplishments of old time baseball players. The greatest players from the old eras of major league baseball produced mind- boggling numbers. As examples, see Babe Ruth’s batting average and pitching numbers, Honus Wagner’s 1900 season, Tris Speaker’s 1916 season, Walter Johnson’s 1913 season, Ty Cobb’s 1911 season, Lou Gehrig’s 1931 season, Rogers Hornsby’s 1925 season, and many others. The accomplishments achieved by players during these seasons are far beyond what recent players produce and it seems, at first glance, that players from the old eras were vastly superior to the players that play in more modern eras. But, is this true? Are the old time ball players actually superior? In this paper, we investigate whether or not the old time baseball players are overrated and whether or not the recent baseball players are underrated. We define old time baseball players to be those that played in the MLB in the 1950 season or before. This year is chosen because it coincides with the decennial United States Census and is close to the year in which baseball became integrated. Recent baseball players are defined to be those that played in the MLB in the 1980 season or after. In this analysis, we do not compare baseball players via their statistical accomplishments or the awards they earned over their careers. Such measures often have era biases that are confounded with actual perfor- mance. The only statistics that are of interest are when a player played and the eligible MLB population at that time. The population data (in Section 2) is constructed and used to formally test (in Section 4) whether or not too many old time players are represented in ESPN’s top 25 list (ESPN, 2016). We do discover that there are far too many old time players included in ESPN’s top 25 list. The extent of our conclusions conflicts with many conventional baseball evaluation metrics as well as a sophisticated era-adjustment de- trending metric (Petersen, Penner, and Stanley, 2011). The reference Petersen, Penner, and Stanley (2011) will henceforth be called PPS due to repeated use. A detailed comparison and critique of the methodologies underlying the evaluation metrics and our initial analysis is then given. 1 2 Data The eligible MLB population is not over any particular time period. As a proxy, we say that the eligible MLB population is the decennial count of males aged 20-24. This demographic data for the United States eligible MLB population is obtained from the US Census (Census, 2016). The MLB started in 1 876 so our data collection begins with the 1880 Census. In 1947, the i ntegration of the MLB began. African American and Hispanic demographic data is added to our dataset starting in 1950. Prior to 1950, the US black and Hispanic populations are excluded from the tallies since baseball was not yet integrated. African American and Hispanic citizens were not the only group discriminated against by pre (and post) integration baseball. Players from Latin American countries were also discriminated against, and citizens from those countries are added to the eligible MLB player pool after 1950. The population data of Latin American countries is obtained from Brea (2003). It should be noted that Brazil and Argentina has been excluded from Latin America in this study since the Brazilians and Argentinians do not largely play baseball and their populations are large compared with Latin American countries where baseball is considered to be a dominant sport. In the 1990s the MLB and minors saw an influx of Asian baseball players from Japan, Korea, and Taiwan. The populations from these countries are added to the eligible MLB player talent pool for those years. The foreign Census data is not as precise so 5% of the total population data is added to our datasets corresponding to the estimate of the proportion of these counties’ populations which are males aged 20-24. The cumulative proportion means that at each era, the population of the previous eras is also included. The population dataset is seen below. As an example of how to interpret this dataset, consider the year 1930. There were an 4.8 million males aged 18-24 in 1930. The proportion of the eligible MLB population throughout all eras that was available to play baseball in 1930 or before is 0.113. year pop pop prop 1 1880 2.200 0.012 2 1890 2.700 0.026 3 1900 3.200 0.043 4 1910 4.100 0.065 5 1920 4.000 0.087 6 1930 4.800 0.113 7 1940 5.100 0.140 8 1950 5.000 0.167 9 1960 11.515 0.228 10 1970 16.140 0.315 11 1980 21.270 0.429 12 1990 32.385 0.602 13 2000 35.100 0.790 14 2010 39.100 1.000 Table 1: Eligible MLB population throughout the years 3 The Greats The population data is the essential part of our argument that the great old time baseball players are over- rated. At a quick glance of this population dataset, one can see how small the proportion of the pre-1950 2 eligible MLB population actually is. We now list the top 25 MLB players, along with the years they played, according to ESPN. This list is displayed in Table 2 (ESPN, 2016). Using our definition of old time and recent players, we see that Table 2 has 6 old time players and 1 recent player in the top 10 and this list has 10 old time players and 7 recent players in the top 25. When the eligible MLB population is considered, it appears that old time players are over represented in this top 25 list. In the next Section, we formally test whether or not this is so. rank name years played 1 Babe Ruth 1914-1935 2 Willie Mays 1951-1973 3 Hank Aaron 1954-1976 4 Ted Williams 1939-1960 5 Barry Bonds 1986-2007 6 Mickey Mantle 1951-1968 7 Lou Gehrig 1923-1939 8 Ty Cobb 1905-1928 9 Walter Johnson 1907-1927 10 Stan Musial 1941-1963 11 Pedro Martinez 1992-2009 12 Greg Maddux 1986-2008 13 Honus Wagner 1897-1917 14 Ken Griffey Jr. 1989-2008 15 Joe Dimaggio 1936-1951 16 Sandy Koufax 1955-1966 17 Cy Young 1890-1911 18 Roberto Clemente 1955-1972 19 Roger Clemens 1984-2007 20 Bob Gibson 1959-1975 21 Alex Rodriguez 1994-2016 22 Rickey Henderson 1979-2003 23 Randy Johnson 1988-2009 24 Frank Robinson 1956-1976 25 Rogers Hornsby 1915-1937 Table 2: ESPN’s list of the top 25 greatest baseball players to ever play in the MLB. 4 Testing We now test whether or not there are too many old time players or too few recent players included in the top 10 and top 25 lists. It should be noted that these two tests are not independent of one another. If there are too many old time players included, then it is likely that there are too few recent players included simply because there were too many old time players included. One should pick a perspective of interest. However, we will present tests from both perspectives. In order to conduct these statistical tests, we make two assumptions: • First, we assume that innate talent is uniformly distributed over the eligible MLB population over the different eras. 3 • Second, we assume that the outside competition to the MLB available by other sports leagues is offset by the increased salary incentives received by more recent players. We now have enough information and assumptions to conduct our tests. We start out testing whether or not ESPN has included too many old time players in their list. The hypotheses that we are interested in testing are of the form: H1 : The ESPN list in Table 1 is correct. H2 : There are too many old time players included in the ESPN list. This testing format means that we assume that the ESPN list of the top 10 or top 25 greatest players is correct and we require strong evidence against this assumption to conclude otherwise. We now test whether or not 6 old time players in the top 10 is too many. Based on the population statistics and our two assumptions, the chances that an MLB eligible person from 1950 or before belongs in the top 10 is 0.167. The chances of observing at least 6 such people in the top 10 is calculated using the binomial distribution with n = 10 and p = 0:1667. This chance is found to be 0:0024. This says that the chances of randomly distributed talent producing 6 or more players in the top 10 is 0:24%.