Z-SCORE ANALYSIS FOR THE 2019 MLB AWARDS

(Photo: Jeff Roberson, AP)

Starting today, Major League Baseball will announce the winners of the 2019 regular season awards, including the Rookie of the Year, Cy Young and MVP awards. Traditionally, the Baseball Writers Association of America (BBWAA) evaluates players for these awards based on each player’s raw statistics. However, as many of you know I have long believed that using z-scores (a standardized measure used in various disciplines of science) to evaluate performance is superior to using raw statistics.

For an expanded explanation of what a z-score is I invite you to click this link to an excerpt from my book (Z-score: How a Statistic Used in Psychology Will Revolutionize Baseball) explaining the concept. In short, any statistic – from home runs to the height of 18 year-old men in the United States – can be converted into z-scores. While z-scores can technically run to infinity in both positive and negative directions, in most cases they tend to range from -4 to +4 and are computed using a formula that includes the mean and standard deviation of the group in question. Essentially, z-scores give detailed information on how a specific performance within a particular group compares to the average performance of that group.

In the book, my colleague Jason Wirchin and I discuss the advantages of using z-scores to compare players across eras, given that the statistics of players in the current era have been skewed by steroid use and other factors. However, when comparing current players against each other, an assessment of z-scores offers a major advantage over that of raw scores: Since each statistic is converted to the same standardized metric, performances in different categories can be directly compared to each other, even across pitching and hitting categories. Hence, with statistics in every category converted to z-scores it can be easily determined whether Gerrit Cole’s AL leading ERA of 2.50 was statistically better than Justin Verlander’s AL leading 21 wins or Mike Trout’s AL leading 1.080 OPS.

At the end of this page I report z-scores for the statistics of the major hitting and pitching categories for the contenders of each of the four MLB awards. However, I would first like review the race for the AL Cy Young Award in more depth as the race for this award is certain to be the closest of all the races and it also highlights how a z-score analysis can be helpful in distinguishing between league-leading performances in different categories.

American League Cy Young Award:

Though MLB listed three finalists for the AL Cy Young Award, including Gerrit Cole (Astros), Justin Verlander (Astros) and Charlie Morton (Rays), only Cole and Verlander are considered serious contenders for the award. Since the end of the season Gerrit Cole has been widely considered the favorite to win the award (as he led the AL in ERA and strikeouts), even though Justin Verlander led two of the four major pitching categories (wins and WHIP) himself. The Cy Young race between Cole and Verlander offers a unique opportunity to highlight how z-scores can help distinguish between player performances that are measured on different scales. Without converting statistics to a common metric there would be no direct way to compare Gerrit Cole’s AL leading marks in ERA (2.50) and strikeouts (326) with Justin Verlander’s AL leading performances in wins (21) and WHIP (0.80). Fortunately, z-score analysis provides us with a method to make direct comparisons on a statistical level.

GERRIT COLE JUSTIN VERLANDER

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(ERA – League Average: 4.04)

ERA – Raw Score: 2.50 ERA – Raw Score: 2.58

ERA – Z-score: 1.84 ERA – Z-score: 1.75

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(Wins – League Average: 13.68)

Wins – Raw Score: 20 Wins – Raw Score: 21

Wins – Z-score: 1.75 Wins – Z-score: 2.03

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(Strikeouts – League Average: 186.05)

Strikeouts – Raw Score: 326 Strikeouts – Raw Score: 300

Strikeouts – Z-score: 2.21 Strikeouts – Z-score: 1.81

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(WHIP – League Average: 1.25)

WHIP – Raw Score: 0.89 WHIP – Raw Score: 0.80

WHIP – Z-score: 1.97 WHIP – Z-score: 2.47

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(HIGHEST SINGLE Z-SCORE)

Highest Z-score: 2.21 (Strikeouts) Highest Z-score: 2.47 (WHIP)

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(AVERAGE Z-SCORE ACROSS CATEGORIES)

Average Z-score: 1.94 Average Z-score: 2.02

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As shown in the table above, Justin Verlander’s 0.80 WHIP yielded the highest z-score of any of the statistics examined. This means that Verlander led the category of WHIP to a greater extent than either he or Gerrit Cole led any of the other pitching categories. Gerrit Cole’s best category was strikeouts, where his total of 326 earned him a z-score of 2.21, however, his dominance in this category was not as great Verlander’s dominance in WHIP. Furthermore, when you compare the average z-score across the four categories, Verlander’s average of 2.02 was greater than Cole’s average z-score of 1.94.

Of course, consideration for postseason awards encompasses more than just statistics: an assessment of clutch performances and overall value to a team’s success are some of the qualitative factors that are considered. However, if you are interested in just a quantitative analysis of the pitching statistics between Justin Verlander and Gerrit Cole, the z-score analysis shown above reveals that it should be Verlander, not Cole, who had the better season.

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NATIONAL LEAGUE ROOKIE OF THE YEAR:

Pete Alonso (Mets)

(Batting Average – League Average: .273)

Batting Average – Raw Score: .260

Batting Average – Z-score: - 0.51

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(Home Runs – League Average: 25.53)

Home Runs – Raw Score: 53

Home Runs – Z-score: 2.56

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(RBIs – League Average: 81)

RBIs – Raw Score: 120

RBIs – Z-score: 1.92

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(OPS – League Average: .829)

OPS – Raw Score: .941

OPS – Z-score: 1.22

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Highest Single Z-score: 2.56 (Home Runs)

Average Z-score: 1.23

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Fernando Tatis, Jr. (Padres)

(Batting Average – League Average: .273)

Batting Average – Raw Score: .317

Batting Average – Z-score: 1.71

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(Home Runs – League Average: 25.53)

Home Runs – Raw Score: 22

Home Runs – Z-score: - 0.32

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(RBIs – League Average: 81)

RBIs – Raw Score: 53

RBIs – Z-score: - 1.39

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(OPS – League Average: .829)

OPS – Raw Score: .969

OPS – Z-score: 1.48

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Highest Single Z-score: 1.71 (Batting Average)

Average Z-score: 0.37

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Mike Soroka (Braves)

(ERA – League Average: 3.70)

ERA – Raw Score: 2.68

ERA – Z-score: 1.96

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(Wins – League Average: 11.88)

Wins – Raw Score: 13

Wins – Z-score: 0.41

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(Strikeouts – League Average: 183.97)

Strikeouts – Raw Score: 255

Strikeouts – Z-score: 1.82

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(WHIP – League Average: 1.21)

WHIP – Raw Score: 0.97

WHIP – Z-score: 1.67

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Highest Single Z-score: 1.96 (ERA)

Average Z-score: 1.47

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NATIONAL LEAGUE CY YOUNG:

Jacob deGrom (Mets)

(ERA – League Average: 3.70)

ERA – Raw Score: 2.43

ERA – Z-score: 1.96

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(Wins – League Average: 11.88)

Wins – Raw Score: 11

Wins – Z-score: - 0.32

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(Strikeouts – League Average: 183.97)

Strikeouts – Raw Score: 255

Strikeouts – Z-score: 1.82

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(WHIP – League Average: 1.20)

WHIP – Raw Score: 0.97

WHIP – Z-score: 1.67

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Highest Single Z-score: 2.43 (ERA)

Average Z-score: 1.28

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Hyun-Jin Ryu (Dodgers)

(ERA – League Average: 3.70)

ERA – Raw Score: 2.32

ERA – Z-score: 2.13

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(Wins – League Average: 11.88)

Wins – Raw Score: 14

Wins – Z-score: 0.78

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(Strikeouts – League Average: 183.97)

Strikeouts – Raw Score: 163

Strikeouts – Z-score: - 0.54

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(WHIP – League Average: 1.20)

WHIP – Raw Score: 1.01

WHIP – Z-score: 1.38

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Highest Single Z-score: 2.13 (ERA)

Average Z-score: 0.94

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Max Scherzer (Nationals)

(ERA – League Average: 3.70)

ERA – Raw Score: 2.92

ERA – Z-score: 1.20

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(Wins – League Average: 11.88)

Wins – Raw Score: 11

Wins – Z-score: - 0.32

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(Strikeouts – League Average: 183.97)

Strikeouts – Raw Score: 243

Strikeouts – Z-score: 1.51

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(WHIP – League Average: 1.20)

WHIP – Raw Score: 1.03

WHIP – Z-score: 1.24

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Highest Single Z-score: 1.51 (Strikeouts)

Average Z-score: 0.91

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AMERICAN LEAGUE MVP:

Alex Bregman (Astros)

(Batting Average – League Average: .273)

Batting Average – Raw Score: .296

Batting Average – Z-score: 0.80

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(Home Runs – League Average: 25.72)

Home Runs – Raw Score: 41

Home Runs – Z-score: 1.53

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(RBIs – League Average: 80.23)

RBIs – Raw Score: 112

RBIs – Z-score: 1.60

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(OPS – League Average: 0.83)

OPS – Raw Score: 1.02

OPS – Z-score: 2.03

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Highest Single Z-score: 2.03 (OPS)

Average Z-score: 1.49

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Marcus Semien (Athletics)

(Batting Average – League Average: .273)

Batting Average – Raw Score: .285

Batting Average – Z-score: .41

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(Home Runs – League Average: 25.72)

Home Runs – Raw Score: 33

Home Runs – Z-score: 0.73

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(RBIs – League Average: 80.23)

RBIs – Raw Score: 92

RBIs – Z-score: 0.59

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(OPS – League Average: 0.83)

OPS – Raw Score: .892

OPS – Z-score: 0.71

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Highest Single Z-score: 0.73

Average Z-score: 0.61

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Mike Trout (Angels)

(Batting Average – League Average: .273)

Batting Average – Raw Score: .291

Batting Average – Z-score: 0.62

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(Home Runs – League Average: 25.72)

Home Runs – Raw Score: 45

Home Runs – Z-score: 1.93

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(RBIs – League Average: 80.23)

RBIs – Raw Score: 104

RBIs – Z-score: 1.20

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(OPS – League Average: 0.83)

OPS – Raw Score: 1.08

OPS – Z-score: 2.76

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Highest Single Z-score: 2.76 (OPS)

Average Z-score: 1.63

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NATIONAL LEAGUE MVP:

Cody Bellinger (Dodgers)

(Batting Average – League Average: .272)

Batting Average – Raw Score: .305

Batting Average – Z-score: 1.29

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(Home Runs – League Average: 47)

Home Runs – Raw Score: 47

Home Runs – Z-score: 2.00

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(RBIs – League Average: 81.32)

RBIs – Raw Score: 115

RBIs – Z-score: 1.68

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(OPS – League Average: .830)

OPS – Raw Score: 1.04

OPS – Z-score: 2.25

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Highest Single Z-score: 2.25 (OPS)

Average Z-score: 1.81

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Anthony Rendon (Nationals)

(Batting Average – League Average: .272)

Batting Average – Raw Score: .319

Batting Average – Z-score: 1.84

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(Home Runs – League Average: 47)

Home Runs – Raw Score: 34

Home Runs – Z-score: 0.79

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(RBIs – League Average: 81.32)

RBIs – Raw Score: 126

RBIs – Z-score: 2.28

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(OPS – League Average: .830)

OPS – Raw Score: 1.01

OPS – Z-score: 1.97

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Highest Single Z-score: 2.28 (RBIs)

Average Z-score: 1.72

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Christian Yelich (Brewers)

(Batting Average – League Average: .272)

Batting Average – Raw Score: .329

Batting Average – Z-score: 2.24

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(Home Runs – League Average: 47)

Home Runs – Raw Score: 44

Home Runs – Z-score: 1.72

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(RBIs – League Average: 81.32)

RBIs – Raw Score: 97

RBIs – Z-score: .78

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(OPS – League Average: .830)

OPS – Raw Score: 1.10

OPS – Z-score: 2.96

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Highest Single Z-score: 2.96 (OPS)

Average Z-score: 1.93