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Projection Hindsight Is 20/20 and It’s Totally Awesome

One of the things you have to get used to when you work with projections is being wrong. Like, All. Of. The. Time. While I’d like to believe that the projections are accurate and it’s just real life that mucked things up, that isn’t quite how they work. There are always events you didn’t see coming, assumptions you made erroneously, and just plain old irreducible error, all of which are going to thwart you.

On a basic level, you’re supposed to be wrong. Imagine a world in which you knew, for an exact fact, that every team was a coin flip to win every game. With this perfect knowledge, you’d still expect nearly a quarter of the league to win either 73 games or fewer, or 89 games or more, through nothing but luck. For the math-inclined, this is a hypergeometric distribution, not a binomial one; the coin flips are not independent because the win totals will still add up to 2,430 and one team’s win invariably is another team’s loss. Here’s a quick table for some of the win totals, showing the probability of a team winning exactly X games and how many of the teams you’d expect to have won up to X games:

Win Probabilities, Major League Coin-Flipping
Wins Probability 1-in-X Chance of Occurring Cumulative
70 1.4% 73 5%
71 1.8% 56 6%
72 2.3% 44 9%
73 2.8% 35 12%
74 3.4% 29 15%
75 4.0% 25 19%
76 4.6% 22 24%
77 5.2% 19 29%
78 5.7% 18 35%
79 6.1% 17 41%
80 6.3% 16 47%
81 6.4% 16 53%
82 6.3% 16 60%
83 6.1% 17 66%
84 5.7% 18 71%
85 5.2% 19 76%
86 4.6% 22 81%
87 4.0% 25 85%
88 3.4% 29 89%
89 2.8% 35 91%
90 2.3% 44 94%
91 1.8% 56 95%

As an example, you’d expect 3.4% of those coin flip teams to win exactly 74 games, with 15% of all teams winning up to 74 games.

But we don’t have anywhere near perfect knowledge about how good a team will be. We’re not even in the same zip code as “near perfect”; we just hope to be on the right continent. As a result, our error bars are going to be significantly larger than even the rather erroneous results you still get with omniscient projections. Read the rest of this entry »


Dan Szymborski FanGraphs Chat – 3/19/2020

1:03
Mac: Does ZiPS come with standard deviations? If so who has the largest assuming you’re able to leave playing time out of equation (Otherwise it would just be the large difference between healthy Trout and out for the season Trout)?

1:03
Avatar Dan Szymborski: Happy Thursday!

1:03
Avatar Dan Szymborski: I don’t specifically spit out a standard deviation, but I do it from the other side: specific events and the probability of those (like a .300 BA, 40 HR, etc)

1:04
Avatar Dan Szymborski: And I have projectile percentages in beta right now as I work out the kinks, mainly due to defensive volatility and projections

1:04
LAXTONTO: Can you do my online recordings for my grad students for me?

1:04
Aceman: Dynasty

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COVID-19 Roundup: Penny Stipends but No Dollar Answers

This is the latest installment of a daily series in which the FanGraphs staff rounds up the latest developments regarding the COVID-19 virus’ effect on baseball.

While there’s no big MLB update on any start to the 2020 season — nor will there likely be for awhile — the hunkering down of baseball teams, along with the rest of the country, continues. MLB announcing there wouldn’t be any games for at least a couple months has moved the focus, as it ought to be, towards the mitigation of the current situation rather than practical questions about how many games will be played, where, or when.

MLB Clubs Establish a Fund for Ballpark Employees

Ballpark employees are some of the people most affected by the suspension of the 2020 season. There’s no telecommuting or even a skeleton crew still working as you see in many customer-facing businesses, so these employees are suffering de facto layoffs, even if hopefully temporary. With the hospitality industry one of the sectors suffering the quickest in this environment, simply finding another job isn’t an option for many of these workers. These employees tend to make up a very small percentage of a team’s costs, and keeping the team’s trained workforce around is at a minimum an exercise in enlightened self-interest. Read the rest of this entry »


How Much Do the Playoff Odds Change in a Shorter Season?

Will there be a 2020 baseball season? How many games will teams play? What will that mean for the 2020 baseball season? Normally, these would be extremely upsetting questions to contemplate; in the world in which we’re currently living, they’re somewhere around the 75,000th most important quandaries facing us. But as someone qualified to serve as a baseball writer rather than an epidemiologist, they’re also the kinds of questions I can actually seek to answer, and the differences between how baseball will eventually look versus what we’re used to are bigger than you might think. Assuming we have a season, that is; if no games are played, the projections will be 100% accurate.

So how much do the playoff races change in a shorter season? To answer this, I spent the weekend reconfiguring ZiPS so that it wouldn’t assume a 162-game season — an eventuality I had hoped not to have to deal with unless or until there was a strike — allowing me to run playoff probabilities for seasons of any length. Let’s start with the baseline projections, how ZiPS saw the races before the world turned upside down:

ZiPS Projections Pre-COVID-19 Delay
Team W L GB PCT Div% WC% Playoff% WS Win%
New York Yankees 96 66 .593 61.3% 29.2% 90.5% 12.7%
Tampa Bay Rays 92 70 4 .568 32.6% 44.6% 77.2% 7.8%
Boston Red Sox 85 77 11 .525 6.0% 25.9% 31.9% 2.0%
Toronto Blue Jays 73 89 23 .451 0.0% 0.8% 0.9% 0.0%
Baltimore Orioles 57 105 39 .352 0.0% 0.0% 0.0% 0.0%
Team W L GB PCT Div% WC% Playoff% WS Win%
Minnesota Twins 91 71 .562 60.9% 14.5% 75.4% 8.5%
Cleveland Indians 88 74 3 .543 30.3% 20.9% 51.2% 4.4%
Chicago White Sox 82 80 9 .506 8.7% 10.0% 18.7% 1.3%
Kansas City Royals 71 91 20 .438 0.2% 0.2% 0.3% 0.0%
Detroit Tigers 63 99 28 .389 0.0% 0.0% 0.0% 0.0%
Team W L GB PCT Div% WC% Playoff% WS Win%
Houston Astros 93 69 .574 69.2% 15.0% 84.1% 10.7%
Oakland A’s 88 74 5 .543 25.2% 27.3% 52.5% 4.4%
Los Angeles Angels 82 80 11 .506 5.3% 10.3% 15.6% 1.0%
Texas Rangers 74 88 19 .457 0.4% 1.2% 1.6% 0.1%
Seattle Mariners 62 100 31 .383 0.0% 0.0% 0.0% 0.0%
Team W L GB PCT Div% WC% Playoff% WS Win%
Washington Nationals 91 71 .562 42.1% 29.5% 71.7% 6.5%
Atlanta Braves 90 72 1 .556 34.8% 31.5% 66.3% 5.5%
New York Mets 87 75 4 .537 18.2% 28.1% 46.3% 3.2%
Philadelphia Phillies 82 80 9 .506 4.8% 13.4% 18.2% 1.0%
Miami Marlins 69 93 22 .426 0.0% 0.1% 0.1% 0.0%
Team W L GB PCT Div% WC% Playoff% WS Win%
Chicago Cubs 85 77 .525 38.1% 8.5% 46.6% 3.4%
Milwaukee Brewers 83 79 2 .512 23.5% 7.5% 31.0% 2.1%
St. Louis Cardinals 82 80 3 .506 20.9% 7.2% 28.1% 1.8%
Cincinnati Reds 82 80 3 .506 16.9% 6.2% 23.1% 1.5%
Pittsburgh Pirates 71 91 14 .438 0.6% 0.2% 0.8% 0.0%
Team W L GB PCT Div% WC% Playoff% WS Win%
Los Angeles Dodgers 101 61 .623 92.7% 5.9% 98.7% 18.5%
San Diego Padres 87 75 14 .537 6.0% 43.4% 49.4% 2.7%
Arizona Diamondbacks 82 80 19 .506 1.3% 17.7% 18.9% 0.8%
Colorado Rockies 72 90 29 .444 0.0% 0.7% 0.7% 0.0%
San Francisco Giants 69 93 32 .426 0.0% 0.1% 0.1% 0.0%

Read the rest of this entry »


Dan Szymborski FanGraphs Chat – 3/12/2020

12:01
Avatar Dan Szymborski: Welcome to SzymChat where the only thing contagious is friendship! And maybe chickenpox.

12:01
Outta my way, Gyorkass: Let’s start with the obvious one: Will there be baseball on March 26th?

12:01
Avatar Dan Szymborski: No

12:01
jz: dan,

12:01
Avatar Dan Szymborski: I haven’t even DONE anything yet.

12:01
Outta my way, Gyorkass: Will players be paid their full salaries this season if games do get cancelled, or if they only play, say, 120 games, will players only get paid 120/162 of their salary?

Read the rest of this entry »


Let’s Pretend to Injure All of the Yankees

The 2019 Yankees may have been the best direct-to-video sequel ever. Usually these types of movies are the worst, mainly cheap forgettable cash-ins missing all the actors who were some of the biggest reasons the original was good. At various times, the Yankees lost Luis Severino, Giancarlo Stanton, Aaron Judge, Didi Gregorius, Dellin Betances, Miguel Andújar, Aaron Hicks, and others. But surprisingly, everything just kinda worked out. DJ LeMahieu earned a place at the back of the MVP ballot, the pitching held together, and the team got tremendous years from Gio Urshela and Mike Tauchman. The Yankees didn’t win the World Series, but they got closer than almost every other team in baseball, light years away from being, say, A Christmas Story 2 starring Daniel Stern, a movie that actually exists for some mysterious reason.

The Yankees survived the injuries, but it certainly wasn’t the desired outcome going into the year. Unfortunately for the Bronx Bombers, history has started repeating itself very quickly, leaving the team with the prospect of entering the 2020 season with a whole new slate of crucial injuries.

At the time of the ZiPS projection post for the Yankees, they were forecast for an obscene 102-103 wins (which would have been the best-ever ZiPS win projection). While this wasn’t with injury-free assumptions — ZiPS was already skeptical about the health of Hicks, Stanton, Severino, and James Paxton — this projection assumed that most of the stars would have healthier seasons. Paxton’s surgery to remove a cyst from his spine and the initial reports of Severino’s forearm soreness reduced these playing time estimates, dropping the Yankees to a “mere” 100 wins in the first public ZiPS run for the year. Read the rest of this entry »


The Rangers Should Turn Their Outfield Situation From Precarious to Puigcarious

In 2020’s scariest baseball moment so far, on Sunday, Willie Calhoun’s face took a direct hit from a Julio Urías fastball, leaving Calhoun on the ground in a great deal of pain. Any baseball to the head is a scary situation, and Calhoun hopefully is escaping from this incident with “just” a broken jaw. Further tests are scheduled for Monday, which will tell us more about the extent of the damage to Calhoun’s face. While the team’s first concern should be the health of their player, the Rangers still need to make baseball decisions.

The result, in the short-term at least, appears to be using Nick Solak in left field. Both the ZiPS projections and I are big fans of Solak, but this move likely simply shifts where Solak gets his playing time, and doesn’t necessarily represent a significant increase in usage.

Even before the Calhoun injury, the Rangers’ offense looked the worst of the plausible playoff contenders, at least if you buy into projections. As of this morning, assuming that Calhoun comes back and manages 448 plate appearances combined in left field and designated hitter, our Depth Charts rank Texas position players 28th in baseball. That’s ahead of only the Orioles and Tigers; the Rangers’ 11.3 projected wins are barely half that of the worst-projected playoff teams from last season, the Brewers and Cardinals.

I don’t believe the Rangers think of themselves as being among the most serious of Wild Card contenders in 2020. But I also don’t think they would have signed Kyle Gibson, Todd Frazier, and Robinson Chirinos if 2020 was seen as a lost cause, nor would they have been so insistent on getting a good price for Mike Minor at the trade deadline last year in order to make a deal. The most recent ZiPS run has the Rangers at 77 wins, while the Depth Charts forecast 78 wins; that’s a team that could at least make a little noise if things broke the right way.

That’s where Yasiel Puig comes in. The Rangers are light on offense, light on corner outfielders, and light on power from the right side. Puig is a fairly limited player these days, no longer the kind of star he was when he broke into the league. What Puig does remain, however, is a roughly league-average slugger who will give you right-handed power and not embarrass you in the outfield. After two years of lefties throwing fastballs against Puig with impunity, he finally made them pay in 2019. My colleague Jay Jaffe wrote more about this, but Puig slugged just .203 with a single homer against lefty fastballs in 2017-2018 combined. In 2019, Puig flipped the script, slugging .540 against lefty fastballs.

While a lot of teams would be able to find fill-ins for Calhoun from their backups or minor-league depth, outside of the starters and Nick Solak, the Rangers don’t really have any interesting options. If you don’t believe me, here are the ZiPS projections for the at least minimally possible internal options in left, with everyone re-projected as a left fielder:

ZiPS Projections – Rangers LF Options
Player BA OBP SLG AB R H 2B 3B HR RBI BB SO SB OPS+ DR WAR
Henry Ramos .261 .304 .407 548 65 143 29 3 15 66 34 118 6 81 0 -0.3
Scott Heineman .246 .310 .396 601 78 148 28 4 18 63 47 169 14 80 1 -0.4
Sam Travis .261 .321 .390 510 62 133 22 1 14 48 43 128 7 82 -4 -0.4
Adolis García .230 .275 .430 570 76 131 28 4 26 86 28 186 13 77 2 -0.5
Leody Taveras .235 .286 .334 626 67 147 21 7 9 48 46 160 25 59 15 -0.8
Rob Refsnyder .244 .312 .365 496 60 121 24 3 10 48 47 139 3 74 0 -0.9
Eli White .228 .293 .348 589 68 134 27 4 12 51 46 187 14 65 1 -1.4
Blake Swihart .198 .272 .322 454 60 90 13 2 13 48 45 150 4 53 2 -2.2
Yadiel Rivera .207 .249 .309 434 46 90 13 2 9 42 22 140 11 43 3 -3.1

Not a single one of these options projects as better than replacement-level in left. Suffice it to say, Puig murderizes these projections.

ZiPS Percentile Projection – Yasiel Puig
Percentile BA OBP SLG AB R H 2B 3B HR RBI BB SO SB OPS+ WAR
90% .289 .361 .558 529 83 153 34 3 34 107 57 100 27 132 4.0
80% .282 .351 .526 532 82 150 31 3 31 101 54 107 22 122 3.2
70% .279 .345 .503 535 80 149 30 3 28 98 51 111 20 115 2.8
60% .276 .341 .489 536 78 148 29 2 27 95 50 114 19 110 2.4
50% .276 .339 .480 537 77 148 28 2 26 92 49 118 17 108 2.3
40% .273 .334 .469 539 76 147 27 2 25 91 47 122 16 104 2.0
30% .272 .331 .455 541 75 147 26 2 23 88 45 127 14 100 1.7
20% .268 .326 .443 542 74 145 25 2 22 85 44 133 12 96 1.4
10% .263 .319 .417 544 72 143 25 1 19 81 42 142 10 88 0.8

Even Puig’s 10th-percentile projection adds a win over a full season compared to the rest of the team’s options (he forecasts as an average player in 62% of his projections, an All-Star in 12%, and replacement level in just 3%). He’s also good enough that, like Hunter Pence was last year, he can carve out a significant role even as a non-starter, though he likely won’t match Pence’s surprising 2019 production.

Texas would be smart to treat a Puig signing with a bit of urgency rather than taking a wait-and-see approach. Puig was ineligible to receive a qualifying offer from the Indians, so unlike last year’s free agent stragglers, most notably Dallas Keuchel and Craig Kimbrel, there is no particular incentive to force him to spend April in street clothes. Nor are the Rangers the only team with a reason to give Puig a call. The Yankees are now without Aaron Judge and while Giancarlo Stanton ought to return from his calf injury soon, his recent injury record is likely enough to give the Yankees’ front office pause.

The Rangers already had a narrow path to the playoffs, and losing Calhoun and his possible upside makes that path even narrower. Texas is absolutely awash in cash, nowhere near any of the luxury tax thresholds, and Puig can help the team long after a Calhoun recovery. Sign Puig. Do it yesterday.


Mike Trout’s Inevitable Decline

Time is the ultimate badass. No matter how great you are, no matter how amazing you are at planning, time always wins in the end. And so it is in baseball as in other things. Mike Trout is, in many ways, the reigning king of baseball, that rare player who enters every season as the nearly-undisputed best in the game. Trout is no longer the young phenom and will turn 30 in just under 18 months, the threshold past which your baseball youth is symbolically gone. Young talent debuts every year while Trout inches closer and closer to retirement, and the day will come when he’s no longer baseball’s clear best.

Just being the best player projected coming into the season is practically enough to ensure your baseball immortality. I went back to the start of the modern era (1901) and collected the top WAR projection for every season, instructing ZiPS to calculate a Marcel-like method for the seasons prior to 2003, when the ZiPS projections did not exist. This is a quick way to demonstrate Trout’s dominance compared to other elite players in baseball history:

Top WAR Projection, 1901-2020
Season Name
1901 John McGraw
1902 Cy Young
1903 Cy Young
1904 Honus Wagner
1905 Honus Wagner
1906 Honus Wagner
1907 Honus Wagner
1908 Honus Wagner
1909 Honus Wagner
1910 Honus Wagner
1911 Ty Cobb
1912 Ty Cobb
1913 Ty Cobb
1914 Ty Cobb
1915 Tris Speaker
1916 Eddie Collins
1917 Walter Johnson
1918 Ty Cobb
1919 Ty Cobb
1920 Ty Cobb
1921 Babe Ruth
1922 Babe Ruth
1923 Rogers Hornsby
1924 Babe Ruth
1925 Babe Ruth
1926 Rogers Hornsby
1927 Babe Ruth
1928 Babe Ruth
1929 Babe Ruth
1930 Rogers Hornsby
1931 Babe Ruth
1932 Babe Ruth
1933 Babe Ruth
1934 Jimmie Foxx
1935 Jimmie Foxx
1936 Lou Gehrig
1937 Lou Gehrig
1938 Lou Gehrig
1939 Mel Ott
1940 Joe DiMaggio
1941 Joe DiMaggio
1942 Joe DiMaggio
1943 Ted Williams
1944 Charlie Keller
1945 Stan Musial
1946 Snuffy Stirnweiss
1947 Hal Newhouser
1948 Hal Newhouser
1949 Ted Williams
1950 Ted Williams
1951 Stan Musial
1952 Jackie Robinson
1953 Jackie Robinson
1954 Stan Musial
1955 Duke Snider
1956 Duke Snider
1957 Mickey Mantle
1958 Mickey Mantle
1959 Mickey Mantle
1960 Ernie Banks
1961 Willie Mays
1962 Mickey Mantle
1963 Willie Mays
1964 Willie Mays
1965 Willie Mays
1966 Willie Mays
1967 Willie Mays
1968 Ron Santo
1969 Carl Yastrzemski
1970 Carl Yastrzemski
1971 Bob Gibson
1972 Fergie Jenkins
1973 Johnny Bench
1974 Bert Blyleven
1975 Joe Morgan
1976 Joe Morgan
1977 Joe Morgan
1978 Mike Schmidt
1979 Mike Schmidt
1980 Mike Schmidt
1981 George Brett
1982 Mike Schmidt
1983 Mike Schmidt
1984 Mike Schmidt
1985 Cal Ripken
1986 Rickey Henderson
1987 Wade Boggs
1988 Wade Boggs
1989 Wade Boggs
1990 Wade Boggs
1991 Rickey Henderson
1992 Barry Bonds
1993 Barry Bonds
1994 Barry Bonds
1995 Barry Bonds
1996 Barry Bonds
1997 Barry Bonds
1998 Barry Bonds
1999 Barry Bonds
2000 Pedro Martinez
2001 Pedro Martinez
2002 Randy Johnson
2003 Barry Bonds
2004 Barry Bonds
2005 Barry Bonds
2006 Alex Rodriguez
2007 Albert Pujols
2008 Albert Pujols
2009 Albert Pujols
2010 Albert Pujols
2011 Albert Pujols
2012 Clayton Kershaw
2013 Mike Trout
2014 Mike Trout
2015 Mike Trout
2016 Mike Trout
2017 Mike Trout
2018 Mike Trout
2019 Mike Trout
2020 Mike Trout

There are a couple of oddities in there, mostly caused by the difficulty of projecting a player who missed seasons due to war service, but otherwise it’s a Who’s Who of the Hall’s inner circle. I’d wager that in 50 years, all but two of these players will be in the Hall of Fame, with Charlie Keller likely on the outside, and Snuffy Stirnweiss certainly so. (If I’m still around in 50 years to test this prediction, I also wager I’ll be a very shouty, curmudgeonly 91-year-old.)

In terms of the number of years at the top of the heap, Trout’s eight seasons already puts him in third place in modern baseball, behind only Babe Ruth and Barry Bonds. In terms of uninterrupted reigns, Trout’s eight consecutive seasons ties Bonds’ 1992-1999 stretch, meaning that if he has the top projection entering 2021, he’ll have earned his spot as the giocatore di tutti giocatori in baseball.

Top WAR Reigns, 1901-2020
Name Reigned Years
Barry Bonds 11 1992-1999, 2003-2005
Babe Ruth 10 1921-1922, 1924-1925, 1927-1929, 1931-1933
Mike Trout 8 2013-2020
Honus Wagner 7 1904-1910
Ty Cobb 7 1911-1914, 1918-1920
Mike Schmidt 6 1978-1980, 1982-1984
Willie Mays 6 1961, 1963-1967
Albert Pujols 5 2007-2011
Mickey Mantle 4 1957-1959, 1962
Wade Boggs 4 1987-1990
Joe DiMaggio 3 1940-1942
Joe Morgan 3 1975-1977
Lou Gehrig 3 1936-1938
Rogers Hornsby 3 1923, 1926, 1930
Stan Musial 3 1945, 1951, 1954
Ted Williams 3 1943, 1949-1950
Carl Yastrzemski 2 1969-1970
Cy Young 2 1902-1903
Duke Snider 2 1955-1956
Hal Newhouser 2 1947-1948
Jackie Robinson 2 1952-1953
Jimmie Foxx 2 1934-1935
Pedro Martinez 2 2000-2001
Rickey Henderson 2 1986, 1991

Read the rest of this entry »


It’s Time to Commit or Quit on Lindor

While the Brewers showed a disappointing inclination to cut costs this winter in a division that’s ripe for dominating, they didn’t disappoint when it came to their franchise player, Christian Yelich. Some of the team’s secondary talent, names like Eric Thames, Gio González, and Travis Shaw, were left to find richer pastures, but the Brewers made sure to lock up the services of the player who was truly indispensable. Yelich didn’t get Bryce Harper or Gerrit Cole money, but that was never in the cards with free agency years away, him hitting the market in his 30s, and coming off a significant injury. My colleague Jay Jaffe has smithed up many additional words on Yelich which you should go read now.

When seeing the Brewers close a long-term pact with their superstar, it’s not hard to contrast it with the behavior of the Cleveland Indians. A team with a larger market but worse attendance, the Indians were very close to the Brewers in revenue in the most recent Forbes estimates, with $282 million in revenue compared to $288 million for the Brew Crew. There’s some give and take in these numbers with baseball’s books not being open for all to peruse, but the figures probably aren’t that far off the mark. After all, compared to companies in other industries with similar revenues, baseball teams are relatively simple corporations. The big-ticket revenues and costs are in fact quite well-known, so there’s only so far these numbers can miss.

My fellow FanGraphier Craig Edwards convincingly argued last week that the question of the Indians being able to afford to extend Francisco Lindor a new contract is more a question of willingness than ability. Read the rest of this entry »


The Padres Have a First Base Problem

Two years ago, the rebuilding San Diego Padres made a big free agent splash, signing first baseman Eric Hosmer, late of the Kansas City Royals, to a five-year, $105 million contract. If Hosmer decided not to exercise his opt-out clause after the fifth year, the contract would become an eight-year, $144 million pact, then the largest deal signed in the history of the San Diego Padres.

The argument against the Hosmer signing was pretty simple: Eric Hosmer wasn’t very good. Among first basemen from 2011-2017, the years since Hosmer’s rookie season, he ranked just 17th in WAR. When a rate stat like wRC+ is used, Hosmer drops to 26th among first basemen with 1000 plate appearances:

Top 20 First Basemen by WAR, 2011-2017
Rank Player AVG OBP SLG wRC+ WAR
1 Joey Votto .313 .440 .533 161 37.1
2 Miguel Cabrera .321 .403 .554 158 36.9
3 Paul Goldschmidt .299 .399 .532 144 31.1
4 Freddie Freeman .291 .377 .497 137 25.5
5 Edwin Encarnación .270 .365 .527 140 23.7
6 Anthony Rizzo .268 .368 .487 131 22.3
7 Adrian Gonzalez .292 .352 .471 124 18.4
8 Chris Davis .245 .334 .498 123 17.6
9 Brandon Belt .268 .358 .461 127 17.5
10 Joe Mauer .291 .376 .408 114 17.2
11 Jose Abreu .301 .359 .524 139 14.8
12 Carlos Santana .249 .363 .445 122 13.0
13 Ryan Zimmerman .272 .334 .469 115 12.7
14 Prince Fielder .286 .379 .475 129 12.2
15 Albert Pujols .267 .325 .470 117 10.9
16 Mike Napoli .243 .346 .470 118 10.5
17 Eric Hosmer .284 .342 .439 111 10.4
18 Mark Teixeira .234 .327 .455 112 9.4
19 Brandon Moss .236 .317 .470 114 8.5
20 Lucas Duda .243 .342 .458 122 8.3

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