• Apr
    27

    Kerry Leibowitz - Run Differential: 2013 Introduction


    by Kerry Leibowitz

    Remember last season (of course you do)?  The Orioles—based mainly on the team’s record in one-run and extra inning games—were largely dismissed as “lucky.”  The club overperformed its Pythagorean expectations by 11 wins.

    I've been fascinated by run differentials and baseball's version of the Pythagorean Theorem ever since I began reading the annual Bill James Baseball Abstracts back in the early 1980's.  The notion that there is a relationship between a team's cumulative performance as measured by its ability to outscore its opponents and its record is breathtakingly intuitive, and I've fiddled with that relationship ever since, even transferring the logic of scoring differential to football, hockey and basketball.  In case you’re interested, James determined that there was a non-linear relationship between runs scored and allowed and a team’s record.  The formal equation he proposed was:

    PW% = (R*R)/((R*R)+(OR*OR))

    Where:

    PW% = Pythagorean Winning Percentage

    R = Runs Scored

    OR = Opponents’ Runs Scored

     

    In fact, using an exponent of 1.8 provides an even more predictive result than simply squaring the factors, but we’ll stick with the square for the sake of simplicity.

    For the last 15 years or so I’ve been running roughly monthly checks on run differential during the major league season and recently completed compiling results for the modern history of Major League Baseball.

    If you read my series of articles on the Orioles and the draft, you know that I’m big on context.  The 2012 Orioles finished 11 wins above Pythagorean expectations.  How rare is that?

    Historical Context

    The average historical win differential for major league clubs through last season—that’s 2322 team seasons—is -0.37.  That is, the average team has won about a 1/3 fewer games than projected by the Theorem.  (This is where the 1.8 alternative exponent would come in.)  The standard deviation for this population is 4.17 wins.  The non-linear transformation of the population represented by the “squares” model that is the Pythagorean Theorem creates something akin to a normal distribution.  So, roughly 95% of the sample is within eight wins of the projected win total, one way or the other.

    If you’re still paying attention, you’ll see that the 2012 Orioles finished well outside the two standard deviation range in terms of expected wins.

    Of the 2322 teams in the sample, the following teams finished as far off their expected win total (either way) as much or more as the 2012 Orioles:

    UNDERPERFORMANCE

    Year

    Team

    Win Differential

    1947

    Cleveland Indians

    -11

    1999

    Kansas City Royals

    -11

    1905

    Chicago White Sox

    -11

    1970

    Chicago Cubs

    -11

    1949

    New York Giants

    -11

    1924

    St. Louis Cardinals

    -11

    1911

    Chicago White Sox

    -11

    1972

    Baltimore Orioles

    -11

    1975

    Houston Astros

    -11

    2006

    Cleveland Indians

    -12

    1967

    Baltimore Orioles

    -12

    1984

    Pittsburgh Pirates

    -13

    1986

    Pittsburgh Pirates

    -13

    1907

    Cincinnati Reds

    -13

    1904

    Cleveland Indians

    -13

    1993

    New York Mets

    -14

    1911

    Pittsburgh Pirates

    -14

    1906

    Cleveland Indians

    -14

    1905

    Chicago Cubs

    -16

     

    OVERPERFORMANCE

    Year

    Team

    Win Differential

    1905

    Detroit Tigers

    15

    2005

    Arizona Diamondbacks

    13

    1972

    New York Mets

    12

    1955

    Kansas City Athletics

    12

    1984

    New York Mets

    12

    1974

    San Diego Padres

    12

    1943

    Boston Braves

    12

    2004

    New York Yankees

    12

    2008

    Los Angeles Angels

    11

    2007

    Arizona Diamondbacks

    11

    2012

    Baltimore Orioles

    11

    1954

    Brooklyn Dodgers

    11

    1970

    Cincinnati Reds

    11

    A grand total of 32 teams missed their Pythagorean projections by at least 11 wins, including the 2012 Orioles.  That’s 1.4% of the total sample.  In other words, this is rarified air.

    What the Theorem implicitly projects, given how rare these events are, is that these extreme win differential seasons very, very unlikely to be replicated.  In other words, these outlying cases can be expected to regress to the mean the next year.

    So has this in fact been the case?  Let’s see.

    UNDERPERFORMANCE

    Year

    Team

    Win Differential

    Next Year Win Diff

    1947

    Cleveland Indians

    -11

    -10

    1999

    Kansas City Royals

    -11

    1

    1905

    Chicago White Sox

    -11

    0

    1970

    Chicago Cubs

    -11

    3

    1949

    New York Giants

    -11

    -1

    1924

    St. Louis Cardinals

    -11

    -5

    1911

    Chicago White Sox

    -11

    0

    1972

    Baltimore Orioles

    -11

    -7

    1975

    Houston Astros

    -11

    3

    2006

    Cleveland Indians

    -12

    4

    1967

    Baltimore Orioles

    -12

    -2

    1984

    Pittsburgh Pirates

    -13

    -6

    1986

    Pittsburgh Pirates

    -13

    1

    1907

    Cincinnati Reds

    -13

    3

    1904

    Cleveland Indians

    -13

    2

    1993

    New York Mets

    -14

    1

    1911

    Pittsburgh Pirates

    -14

    -4

    1906

    Cleveland Indians

    -14

    5

    1905

    Chicago Cubs

    -16

    -3

    OVERPERFORMANCE

    Year

    Team

    Win Differential

    Next Year Win Diff

    1905

    Detroit Tigers

    15

    6

    2005

    Arizona Diamondbacks

    13

    -3

    1972

    New York Mets

    12

    1

    1955

    Kansas City Athletics

    12

    -3

    1984

    New York Mets

    12

    1

    1974

    San Diego Padres

    12

    7

    1943

    Boston Braves

    12

    -2

    2004

    New York Yankees

    12

    5

    2008

    Los Angeles Angels

    11

    4

    2007

    Arizona Diamondbacks

    11

    -1

    2012

    Baltimore Orioles

    11

    ?

    1954

    Brooklyn Dodgers

    11

    0

    1970

    Cincinnati Reds

    11

    -3

     

    The absolute value of the Year 1 Win Differential is 12.1.  The absolute value of the Year 2 Win Differential (excluding the 2012 Orioles, of course) is 3.1.  So we’re obviously seeing a major regression to the mean for these extreme outliers.  The only team to be an extreme outlier two years in a row is the Cleveland Indians in 1947-48.

    So, it should come as no surprise that, for the Orioles to approach last year’s win total of 93, they’re almost certainly going to have to significantly improve their run differential from 2012 to 2013.  It’s highly, highly unlikely that we’ll see them come close to duplicating last year’s overperformance.

    Going Forward

    My plan is to provide a Pythagorean MLB update with each completed month of the season, beginning with April.  The results obviously become less subject to anomalies as the year unfolds and we’ll almost certainly see that during the 2013 campaign. 


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