Friday, July 22, 2011

Ichiro Suzuki and the Leaderboard Score

As the season passes the halfway point and the calendar creeps ever closer to fall, many baseball fans begin to turn their attention to another favorite pastime: leaderboard watching.  AL fans getting a jump on the race for this year’s batting leader will notice a glaring omission from the list in Ichiro Suzuki.  Since coming over from Japan in 2001 Ichiro has won two batting titles, batted under .310 only once and has finished over .350 a mind-blowing four times.  Year after year, the names atop the batting leaderboard change, mostly containing players in the midst of career years; Ichiro’s name is seemingly the only constant, finishing out of the top 10 only once in his career (12th).  Currently batting just .260, Ichiro is having a career-worst season but the fact that he possesses an elite ability to hit for average is undeniable.  This begs the question: how does Ichiro compare to other historic players in this ability to hit for average?

There are many statistics intended to reduce a player's total value to a single number.  Wins Above Replacement (WAR) does a great job of measuring a player’s total value and there are many choices for measuring a player’s batting or pitching production.  These stats do a great job of allowing the comparison between players of different eras and different playing styles but this general comparison tends to let the specifics of a player’s game get lost in history.  Discovering that Kenny Lofton and Mark McGwire had similar career values (65.3 WAR and 63.1 WAR, respectively) is extremely insightful but misses all of the ways they’re different.

One way to examine the shape of a player’s game is to look at their raw statistics in a single statistical category, but this method is obviously flawed in that it completely ignores the differences between eras.  Even comparing career stats of players in the same era is flawed because counting stats (hits, home runs, etc.) will be skewed toward players with longer careers and rate stats (batting average, etc.) will be skewed toward players with shorter careers whose average missed the opportunity to decline alongside their waning skill.  After his age-30 season (2000), Ken Griffey Jr. had collected 438 home runs and hit at a .296/.380/568 clip.  In 10 additional seasons of an all-too-familiar arc, he increased his home run total to 630 but lowered his rate stats to .284/.370/.538.  His final ten years of average-to-bad performance somewhat overshadow his early-career brilliance.

This article introduces a method which seeks to fill this statistical void by comparing players from different eras not against each other but against their peers.  Rather than looking at a player’s entire career and allowing non-peak seasons to bias player comparisons, only a player’s elite seasons will be taken into account.  Every player who has picked up a glove or swung a bat since 1871 will be given a Leaderboard Score in every major statistical category and compared against each other to determine the greatest players of all-time at every measureable skill.

The basics of this method are:
-        A leaderboard of every major stat is created for every season of every league since 1871.
-        The top players on this leaderboard are given a score according to the order they finished. #1 gets 10 points, #2 gets a little less, #3 less still, etc.  Only the very best players in each league receive a score.
-        A small bonus is added to reward consecutive seasons of greatness.
-        The scores from each season a player plays in are added together in each statistical category to come up with a Leaderboard Score for that player in each category.
-        Players are ranked by their Leaderboard Score to find the #10 all-time players in each category.

For those not interested in the nitty-gritty how of this method, feel free to skip the following section to see the results.

The Method

The basic idea of this method is to look at the leaderboard for each statistical category to determine which players are “elite” in that season of play.  The biggest benefit of this method is that since players are only compared against those in the same season, it fairly compares all players against all eras.  The biggest weakness is that without any ballpark effects factored in, a pitcher in a pitchers’ park has an unfair advantage over one in a hitters’ park.  Additionally, by awarding the same score to a player that barely ranks #1 in a given season versus one who is a clear-cut #1 (think Babe Ruth in home runs) seems unfair.  Even so - while imperfect - this method should serve as a good starting point in accomplishing the goal of picking those players who dominated a given statistical category for a long time.

After a good amount of thought and tinkering, the following specifics were settled on:
-        A leaderboard of the best players in every major statistic in each league between 1871 and 2010 is generated.  Since the number of teams has grown over the years and it’s easier to be a top player in an 8-team league than a 16-team league, looking at the top 10 of each league is insufficient.  To solve this problem, the number of players on the leaderboard is tied to the number of teams in each league.  The number of “elite” players in each league is defined as being the top [# Teams in League]*.75 players.  In the current alignment of 14 AL and 16 NL teams, the AL leaderboard has 11 players and the NL leaderboard has 12.  In the 1921 alignment of 8 AL & 8 NL, the leaderboards contain the top 6 in each league.
-        The top player in each league is always awarded 10 points - regardless of league size - while the rest of the rankings are scaled to award points on a 0-10 range.  In an 8-team league, the scoring goes: 2nd Place: 8.3; 3rd Place: 6.7; 4th Place: 5; 5th Place: 3.3; 6th Place: 1.7.  In a 16-team league, the scoring goes: 2nd Place: 9.17; 3rd Place: 8.3; ...; 12th place: 0.83.  This method attempts to keep the scale of scores the same across eras while taking into account that it's easier to appear on the leaderboard of a smaller league.
-        To filter out small sample sizes and ensure proper treatment of rate stats, eligibility requirements are implemented in order for a season to qualify for the leaderboard:
o   Batting Stats: Same as traditional requirements to qualify for batting title:
      • 1957-Current: 3.1 plate appearances per team game
      • 1945-1956: 2.6 at bats per team game.
      • 1938-1955, NL: At least 100 games
      • 1938-1955, AL: At least 400 at bats
      • 1920-1937: At least 100 games
      • 1871-1919: Played in at least 60% of team games
    • Pitching Stats: 1 inning pitched per team game.
    • Baserunning Stats:
      • SB, SB %, CS: At least 1 steal attempt per 10 team games.
    • Fielding:
      • In field for 4.5 innings per team game. (In other words: at least half of the possible defensive innings).
Once a score is calculated for every eligible statistical category in every season a player has played, a small bonus is awarded for back-to-back seasons of greatness.  This bonus is calculated as half of the smaller of back-to-back seasons.  So if a player in the modern-day NL were to place #8 (4.17 pts) in 2008, #3 (8.33 pts) in 2009 and #1 (10 pts) in 2010 in a certain category, their bonus would be: [4.17/2] = 2.09 for 2008/2009 and [8.33/2] = 4.17 for 2009/2010.

The base score and bonus are added together and rounded to an integer to come up with a player's Leaderboard Score for every statistical category.  All players’ Leaderboard Scores are then compared to come up with the most dominant players of all-time in every major statistical category.  A score is also computed to come up with the worst in every category, so not only can we see who was the most dominant base stealer in terms of SB% (Joe Morgan, ranking 1st four times, 2nd two times, 3rd three times) but also who was the worst (Minnie Minoso, ranking 2nd-worst four times and 3rd-worst three times).  The best part of this "least dominant" list is that Minoso had to attempt at least 15 steals per year to even quality to be on the list; it takes a prolonged career of repeated failure to really make a mark on the least dominant list.

In addition to determining which players are the most dominant in each category, by comparing the Leaderboard Score of the leaders across statistical categories we can get an idea of how repeatable eliteness is for each particular skill.  As an example, one of the most dominant scores across all statistics is Rickey Henderson in stolen bases, scoring 239 points by ranking 1st an impressive 12 times.  One of the least dominant leaders among pitchers is in home runs allowed where Greg Maddux scores 106 points by ranking 1st three times and 2nd one time.  While the raw numbers 106 and 239 don't mean anything by themselves, by comparing the leaders between categories we can see that Rickey Henderson dominated the category of stolen bases far and away more than Greg Maddux dominated the category of home runs allowed.  Even though Maddux was the most dominant player of all-time at preventing home runs, he was not nearly as dominant as Henderson was at stealing bases.  This tells us something about Henderson’s feat as well as giving insight into how difficult it is to repeatedly allow a small number of home runs.  The worst pitcher at giving up home runs was Ferguson Jenkins who ranked dead last an (un)impressive seven times and score 137 points.  It is, apparently, easier to repeatedly serve up home runs than to prevent them.

Note: After writing this entry, I learned of a somewhat similar study that uses a much more advanced method which can be found here.  I have a few thoughts on the differences between methods that I’ll comment on in my next post.

The Results: Batting Average

Eventually this idea will be developed a bit more and some of the more interesting occurrences on the leaderboard will be found and listed.  For the time being, the 10 all-time most dominant players in the category of batting average are listed below.  In addition to the top 10, the list is expanded so that at least one player of the last 50 years from every current team is listed so that no one is disappointed when scanning the list looking for their favorite team.  Otherwise we’d never know that Ichiro – while the greatest Mariner of all time - doesn’t even come close to cracking the top 10 at #25.  Nor would we discover that the best (Devil) Rays batter is Jason Bartlett, coming in at a not-so-dominant #600 by ranking 7th exactly once.  The top player shouldn’t be a surprise to anyone: Ty Cobb’s 11 batting championships give him the win in a landslide.  Cobb out-scored 2nd-place Stan Musial by 35 points: the equivalent of more than three batting championships.

I hope you enjoy the list.  If you have any other specific categories that interest you, let me know.  Otherwise I’ll post them as I find time.





1. Ty Cobb (DET Tigers, PHI Athletics). Leaderboard Score: 215
"The Georgia Peach". 6' 1", 175 lbs. Bats Left. Throws Right. HOF Player. Triple Crown (1909), MVP (1911).
Peak Years: 1906-1927
Rankings: 6 (.316), 1 (.350), 1 (.324), 1 (.377), 2 (.383), 1 (.420), 1 (.409), 1 (.390), 1 (.368), 1 (.369), 2 (.371), 1 (.383), 1 (.382), 1 (.384), 10 (.334), 2 (.389), 2 (.401), 8 (.340), 11 (.338), 4 (.378), -, 5 (.357)

2. Stan Musial (STL Cardinals). Leaderboard Score: 180
"Stan the Man". 6' 0", 175 lbs. Bats Left. Throws Left. 20-Time All-Star (Started 14). HOF Player. MVP (1943, 1946, 1948).
Peak Years: 1942-1962
Rankings: 3 (.315), 1 (.357), 2 (.347), -, 1 (.365), 5 (.312), 1 (.376), 2 (.338), 1 (.346), 1 (.355), 1 (.336), 3 (.337), 4 (.330), 3 (.319), 4 (.310), 1 (.351), 3 (.337), -, -, -, 3 (.330)

3. Tony Gwynn (SD Padres). Leaderboard Score: 154
"Mr. Padre,Captain Video". 5' 11", 185 lbs. Bats Left. Throws Left. 15-Time All-Star (Started 10). HOF Player. Gold Glove (1986 - 1987, 1989 - 1991).
Peak Years: 1984-1998
Rankings: 1 (.351), 4 (.317), 3 (.329), 1 (.370), 1 (.313), 1 (.336), 7 (.309), 3 (.317), 5 (.317), 2 (.358), 1 (.394), 1 (.368), -, 1 (.372), 9 (.321)

4. Rogers Hornsby (STL Cardinals, NY Giants, BOS Braves, CHI Cubs). Leaderboard Score: 146
"Rajah". 5' 11", 175 lbs. Bats Right. Throws Right. HOF Player. Triple Crown (1922, 1925), MVP (1925, 1929).
Peak Years: 1916-1930
Rankings: 4 (.313), 2 (.327), 16 (.281), 2 (.318), 1 (.370), 1 (.397), 1 (.401), 1 (.384), 1 (.424), 1 (.403), 17 (.317), 2 (.361), 1 (.387), 3 (.380), -

5. Rod Carew (MIN Twins, CAL Angels). Leaderboard Score: 145
6' 0", 170 lbs. Bats Left. Throws Right. 18-Time All-Star (Started 15). HOF Player. MVP (1977).
Peak Years: 1967-1984
Rankings: 6 (.292), -, 1 (.332), -, 5 (.307), 1 (.318), 1 (.350), 1 (.364), 1 (.359), 3 (.331), 1 (.388), 1 (.333), -, 5 (.331), 11 (.305), 3 (.319), 2 (.339), -

6. Honus Wagner (PIT Pirates). Leaderboard Score: 143
"The Flying Dutchman". 5' 11", 200 lbs. Bats Right. Throws Right. HOF Player.
Peak Years: 1899-1913
Rankings: 12 (.336), 1 (.381), 4 (.353), 4 (.330), 1 (.355), 1 (.349), 2 (.363), 1 (.339), 1 (.350), 1 (.354), 1 (.339), 5 (.320), 1 (.334), 6 (.324), 10 (.300)

7. Wade Boggs (BOS Red Sox, NY Yankees). Leaderboard Score: 127
6' 2", 190 lbs. Bats Left. Throws Right. 12-Time All-Star (Started 11). HOF Player. Gold Glove (1994 - 1995).
Peak Years: 1983-1996
Rankings: 1 (.361), 3 (.325), 1 (.368), 1 (.357), 1 (.363), 1 (.366), 3 (.330), 6 (.302), 2 (.332), 49 (.259), 16 (.302), 5 (.342), 5 (.324), 17 (.311)

8. Ted Williams (BOS Red Sox). Leaderboard Score: 118
"The Kid,Teddy Ballgame,Splendid Splinter,Thumper". 6' 3", 205 lbs. Bats Left. Throws Right. 17-Time All-Star (Started 12). HOF Player. Triple Crown (1942, 1947), MVP (1946, 1949).
Peak Years: 1939-1958
Rankings: 6 (.327), 3 (.344), 1 (.406), 1 (.356), -, -, -, 2 (.342), 1 (.343), 1 (.369), 2 (.343), -, 4 (.318), -, -, -, -, -, 1 (.388), 1 (.328)

9. Tris Speaker (BOS Red Sox, CLE Indians). Leaderboard Score: 113
"The Grey Eagle". 5' 11", 193 lbs. Bats Left. Throws Left. HOF Player. MVP (1912).
Peak Years: 1909-1926
Rankings: 6 (.309), 3 (.340), 9 (.334), 3 (.383), 3 (.363), 3 (.338), 4 (.322), 1 (.386), 3 (.352), 4 (.318), 22 (.296), 2 (.388), 5 (.362), 3 (.378), 3 (.380), 8 (.344), 2 (.389), 21 (.304)

10. Cap Anson (PHI Athletics, CHI White Stockings). Leaderboard Score: 109
"Pop". 6' 0", 227 lbs. Bats Right. Throws Right. HOF Player.
Peak Years: 1871-1895
Rankings: 18 (.325), 3 (.415), 2 (.398), 9 (.336), 7 (.325), 3 (.356), 5 (.337), 5 (.341), 8 (.317), 2 (.337), 1 (.399), 2 (.362), 11 (.308), 5 (.335), 7 (.310), 2 (.371), 2 (.347), 1 (.344), 10 (.311), 7 (.312), 9 (.291), 33 (.272), 21 (.314), 7 (.388), 25 (.335)

14. Roberto Clemente (PIT Pirates). Leaderboard Score: 100
"Arriba". 5' 11", 175 lbs. Bats Right. Throws Right. 12-Time All-Star (Started 5). HOF Player. Gold Glove (1961 - 1972), MVP (1966).
Peak Years: 1955-1971
Rankings: 36 (.255), 3 (.311), -, 14 (.289), -, 4 (.314), 1 (.351), 8 (.312), 2 (.320), 1 (.339), 1 (.329), 5 (.317), 1 (.357), 10 (.291), 2 (.345), -, 4 (.341)

18. Hank Aaron (MIL Braves, ATL Braves). Leaderboard Score: 92
"Hammer,Hammerin' Hank,Bad Henry". 6' 0", 180 lbs. Bats Right. Throws Right. 21-Time All-Star (Started 15). HOF Player. MVP (1957), Gold Glove (1958 - 1960).
Peak Years: 1954-1972
Rankings: 28 (.280), 5 (.314), 1 (.328), 4 (.322), 4 (.326), 1 (.355), 13 (.292), 5 (.327), 5 (.323), 3 (.319), 3 (.328), 2 (.318), 25 (.279), 8 (.307), 16 (.287), 12 (.300), 18 (.298), 5 (.327), 31 (.265)

19. Todd Helton (COL Rockies). Leaderboard Score: 90
"The Toddfather". 6' 2", 215 lbs. Bats Left. Throws Left. 5-Time All-Star (Started 3). Gold Glove (2001 - 2002, 2004).
Peak Years: 1998-2009
Rankings: 12 (.315), 9 (.320), 1 (.372), 2 (.336), 4 (.329), 2 (.358), 2 (.347), 4 (.320), 13 (.302), 9 (.320), -, 4 (.325)

20. Pete Rose (CIN Reds, PHI Phillies). Leaderboard Score: 89
"Charlie Hustle". 5' 11", 192 lbs. Switch Hitter. Throws Right. 17-Time All-Star (Started 8). Gold Glove (1969 - 1970), MVP (1973).
Peak Years: 1964-1982
Rankings: 29 (.269), 5 (.312), 8 (.313), 11 (.301), 1 (.335), 1 (.348), 8 (.316), 13 (.304), 8 (.307), 1 (.338), 26 (.284), 8 (.317), 4 (.323), 6 (.311), 8 (.302), 2 (.331), 22 (.282), 1 (.325), 40 (.271)

25. Ichiro Suzuki (SEA Mariners). Leaderboard Score: 78
5' 11", 170 lbs. Bats Left. Throws Right. 10-Time All-Star (Started 9). MVP (2001), Gold Glove (2001 - 2010).
Peak Years: 2001-2010
Rankings: 1 (.350), 4 (.321), 7 (.312), 1 (.372), 12 (.303), 6 (.322), 2 (.351), 7 (.310), 2 (.352), 7 (.315)

26. Paul Molitor (MIL Brewers, TOR Blue Jays, MIN Twins). Leaderboard Score: 78
"The Ignitor". 6' 0", 185 lbs. Bats Right. Throws Right. 7-Time All-Star (Started 2). HOF Player.
Peak Years: 1978-1997
Rankings: 44 (.273), 6 (.322), 12 (.304), -, 10 (.302), 40 (.270), -, 9 (.297), -, 2 (.353), 5 (.312), 6 (.315), -, 5 (.325), 4 (.320), 2 (.332), 6 (.341), 50 (.270), 3 (.341), 14 (.305)

29. George Brett (KC Royals). Leaderboard Score: 73
"Mullet". 6' 0", 185 lbs. Bats Left. Throws Right. 13-Time All-Star (Started 9). HOF Player. MVP (1980), Gold Glove (1985).
Peak Years: 1975-1991
Rankings: 6 (.308), 1 (.333), 9 (.312), 12 (.294), 2 (.329), 1 (.390), 6 (.314), 14 (.301), 8 (.310), -, 2 (.335), 18 (.290), 24 (.290), 12 (.306), 24 (.282), 1 (.329), 54 (.255)

32. Al Kaline (DET Tigers). Leaderboard Score: 68
6' 1", 175 lbs. Bats Right. Throws Right. 15-Time All-Star (Started 7). HOF Player. Gold Glove (1957 - 1959, 1961 - 1967).
Peak Years: 1954-1972
Rankings: 21 (.276), 1 (.340), 7 (.314), 9 (.295), 4 (.313), 2 (.327), 17 (.278), 2 (.324), -, 2 (.312), 7 (.293), -, 3 (.288), 3 (.308), -, 30 (.272), 21 (.278), 8 (.294), -

33. Willie Mays (NY Giants, SF Giants). Leaderboard Score: 68
"Say Hey Kid". 5' 10", 170 lbs. Bats Right. Throws Right. 20-Time All-Star (Started 14). HOF Player. MVP (1954, 1965), Gold Glove (1957 - 1968).
Peak Years: 1953-1966
Rankings: -, 1 (.345), 2 (.319), 12 (.296), 2 (.333), 2 (.347), 5 (.313), 3 (.319), 8 (.308), 11 (.304), 6 (.314), 16 (.296), 3 (.317), 16 (.288)

39. Bill Madlock (CHI Cubs, SF Giants, PIT Pirates). Leaderboard Score: 63
"Mad Dog". 5' 11", 180 lbs. Bats Right. Throws Right. 3-Time All-Star.
Peak Years: 1974-1984
Rankings: 5 (.313), 1 (.354), 1 (.339), 13 (.302), 4 (.309), 14 (.298), 29 (.277), -, 2 (.319), 1 (.323), -

49. Manny Ramirez (CLE Indians, BOS Red Sox, LA Dodgers). Leaderboard Score: 58
"Man-Ram,Manny Being Manny,Mannywood". 6' 0", 200 lbs. Bats Right. Throws Right. 12-Time All-Star (Started 6).
Peak Years: 1996-2008
Rankings: 22 (.309), 5 (.328), 28 (.294), 5 (.333), 3 (.351), 14 (.306), 1 (.349), 2 (.325), 13 (.308), 23 (.292), 8 (.321), 23 (.296), 3 (.332)

50. Frank Robinson (CIN Redlegs, BAL Orioles). Leaderboard Score: 58
"The Judge". 6' 1", 183 lbs. Bats Right. Throws Right. 12-Time All-Star (Started 6). HOF Player. Gold Glove (1958), MVP (1961, 1966), Triple Crown (1966).
Peak Years: 1956-1971
Rankings: 16 (.290), 3 (.322), 22 (.269), 6 (.311), 8 (.297), 6 (.323), 2 (.342), 29 (.259), 10 (.306), 14 (.296), 1 (.316), 2 (.311), 13 (.268), 4 (.308), 5 (.306), 16 (.281)

51. Vladimir Guerrero (MON Expos, ANA Angels, LA Angels). Leaderboard Score: 57
"Vlad the Impaler". 6' 3", 235 lbs. Bats Right. Throws Right. 9-Time All-Star (Started 7). MVP (2004).
Peak Years: 1998-2008
Rankings: 7 (.324), 11 (.316), 3 (.345), 19 (.307), 3 (.336), -, 3 (.337), 4 (.317), 5 (.329), 8 (.324), 15 (.303)

53. Al Oliver (PIT Pirates, TEX Rangers, MON Expos). Leaderboard Score: 55
"Scoop". 6' 0", 195 lbs. Bats Left. Throws Left. 7-Time All-Star (Started 1).
Peak Years: 1971-1983
Rankings: 21 (.282), 6 (.312), 17 (.292), 2 (.321), 31 (.280), -, 9 (.308), 2 (.324), 5 (.323), 8 (.319), 8 (.309), 1 (.331), 9 (.300)

55. Frank Thomas (CHI White Sox). Leaderboard Score: 55
"Big Hurt". 6' 5", 240 lbs. Bats Right. Throws Right. 5-Time All-Star (Started 2). MVP (1993 - 1994).
Peak Years: 1991-2001
Rankings: 9 (.318), 3 (.323), 6 (.317), 3 (.353), 17 (.308), 2 (.349), 1 (.347), 65 (.265), 21 (.305), 9 (.328), -

59. Matty Alou (PIT Pirates, STL Cardinals, OAK Athletics). Leaderboard Score: 53
5' 9", 160 lbs. Bats Left. Throws Left. 2-Time All-Star (Started 1).
Peak Years: 1966-1973
Rankings: 1 (.342), 3 (.338), 2 (.332), 4 (.331), 19 (.297), 8 (.315), 5 (.307), 15 (.295)

60. Mike Piazza (LA Dodgers, FL Marlins, NY Mets). Leaderboard Score: 52
6' 3", 200 lbs. Bats Right. Throws Right. 12-Time All-Star (Started 10).
Peak Years: 1993-2001
Rankings: 7 (.318), 12 (.319), 2 (.346), 2 (.336), 3 (.362), 4 (.328), 23 (.303), 10 (.324), 26 (.300)

110. Moises Alou (MON Expos, HOU Astros). Leaderboard Score: 30
6' 3", 185 lbs. Bats Right. Throws Right. 6-Time All-Star.
Peak Years: 1993-2002
Rankings: 33 (.286), 3 (.339), -, 34 (.281), 24 (.292), 16 (.312), -, 2 (.355), 3 (.331), 40 (.275)

178. Jeff Cirillo (MIL Brewers, COL Rockies). Leaderboard Score: 19
6' 2", 190 lbs. Bats Right. Throws Right. 2-Time All-Star.
Peak Years: 1997-2001
Rankings: 33 (.288), 8 (.321), 5 (.326), 8 (.326), 15 (.313)

287. Luis Gonzalez (ARI Diamondbacks). Leaderboard Score: 12
"Gonzo". 6' 2", 180 lbs. Bats Left. Throws Right. 5-Time All-Star (Started 1).
Peak Years: 1998-2002
Rankings: 63 (.267), 2 (.336), 20 (.311), 10 (.325), 23 (.288)

437. Cristian Guzman (WAS Nationals). Leaderboard Score: 7
6' 0", 210 lbs. Switch Hitter. Throws Right. 2-Time All-Star.
Peak Years: 2007-2009
Rankings: -, 5 (.316), 31 (.284)

600. Jason Bartlett (TB Rays). Leaderboard Score: 4
6' 0", 190 lbs. Bats Right. Throws Right. 1-Time All-Star.
Peak Years: 2008-2010
Rankings: -, 7 (.320), 51 (.254)


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