Fantasy Baseball

Expected RBI Totals: The Top 267 xRBI Totals for 2013

Chris Davis

While there is almost zero skill when it comes to the amount of RBI a player produces, through the creation of an expected RBI metric I have found a way to look at whether or not a player has gotten lucky or unfortunate when it comes to their actual RBI total.

I hope I don’t need to do this for most of our readers, because it’s 2014 and you’re reading about baseball on a far off corner of Internet, so you obviously are more informed than the average fan who consumes ESPN as their main source of baseball information, but lets talk about why RBI, as a stat, and why it is not valuable when you look at a players’ talent. The amount of RBI a player produces are almost—we’ll get into the almost a little later—entirely dependent on the lineup a player plays in. If a player doesn’t have teammates that can get on base in front of them in the lineup, there aren’t very many opportunities for RBIs; that’s the long and short. Really, RBI tell more about the lineup a player plays in than the player himself.

Intuitively, this makes sense.  The more runners there are on base, the more chances the batter will have for RBI, and the more RBI the batter will accumulate. When I said, “The amount of RBI a player produces are almost…entirely dependent on the lineup a player plays in”, lets be a little more precise. My research took the last three years of data (2010 to 2013) and looked at all players that had 180 runners on base (ROB) during their at bats over the course of a season. Over the three seasons, which should be enough data—it was a pain in the ass to obtain the data that I did find—ROB correlated with RBI by a correlation coefficient of .794 (r2 = .63169), which is a very strong positive relationship.

But hey, that doesn’t mean that you can be a lousy hitter get a lot of RBI. That would be like if you threw hobo in the Playboy Mansion and expected him to get a lot of tail; all the opportunity in the world can’t mask the smell of Pall Malls, grain alcohol and a lifetime of deflected introspection; trust me, I worked at a liquor store for three years in college, and I know.  In the same sample of players from 2010 to 2013 as used above, the correlation between wOBA—what we’ll use here to define a player’s ability at the plate—and RBI is .6555. So there is a relationship between a player’s ability and their RBI total, but nowhere near as strong as the relationship between their RBI total and their opportunity—ROB.

However, when we combine a player’s opportunity—ROB—with their talent—wOBA—we should get a good idea of what to expect for a hitter’s RBI total. Here is the formula for the expected RBI totals based on the correlations between ROB and wOBA, and RBI: xRBI =- 85.0997 + 262.7424 * wOBA + 0.1918 * ROB.

When you combine wOBA and ROB into this formula you end up with a correlation coefficient of .878 and an r2 of .771. Wooooo (Rick Flair voice)!!!!!  With the addition of wOBA to ROB we increase our r2, from .63 with just ROB, by fourteen percent.


2013 Expected RBI Leaders

Miguel Cabrera1370.455448120.3716.625508
Prince Fielder1060.358536111.77-5.7668792
Paul Goldschmidt1250.404450107.3617.6417704
Mike Trout970.423410104.68-7.6783352
David Ortiz1030.4441104.58-1.58106
Joey Votto730.4441104.58-31.58106
Chris Davis1380.421396101.4736.5323496
Hunter Pence990.356485101.46-2.4595944
Jay Bruce1090.344500101.187.8163144
Adrian Beltre920.379451100.98-8.9814696
Mike Napoli920.36745698.79-6.7875608
Dustin Pedroia840.34747897.75-13.7523128
Victor Martinez830.3447895.91-12.913116
Josh Donaldson930.38441395.01-2.0067816
Andrew Mccutchen840.39340094.88-10.8780632
Adam Jones1080.3545393.7514.25446
Freddie Freeman1090.38739692.5316.4655912
Evan Longoria880.3643192.15-4.153364
Robinson Cano1070.38439892.1314.8702184
Carlos Santana740.36441489.94-15.9437336
Brandon Phillips1030.30749289.9313.0721832
Edwin Encarnacion1040.38837989.5414.4634488
Matt Holliday940.38338589.374.6263608
Ian Desmond800.34142886.59-6.5858584
Michael Cuddyer840.39635286.46-2.4598904
Jayson Werth820.40334086.00-3.9974872
Adrian Gonzalez1000.34641885.9814.0184296
Buster Posey720.35739985.23-13.2275368
Torii Hunter840.34641485.21-1.2143704
Martin Prado820.32843584.51-2.5128072
Pedro Alvarez1000.3343184.2715.728908
Daniel Nava660.36638083.95-17.9480184
Josh Hamilton790.31944383.68-4.6825256
Troy Tulowitzki820.433183.48-1.48306
James Loney750.33941483.38-8.3751736
Jason Kipnis840.35738782.931.0740632
Eric Hosmer790.3539282.05-3.04574
Billy Butler820.34539681.500.500772
Mark Trumbo1000.32242781.4018.5980472
Ben Zobrist710.33441081.29-10.2942616
Carlos Gomez730.36336981.05-8.0499912
Brandon Belt670.36536681.00-14.000076
Kendrys Morales800.34239480.33-0.3274008
Anthony Rizzo800.32541579.890.11142
Jon Jay670.31942379.85-12.8465256
Allen Craig970.36336279.7117.2926088
Jed Lowrie750.34538579.39-4.389428
Pablo Sandoval790.33140379.16-0.1634344
Carlos Beltran840.35935577.316.6861784
Yadier Molina800.36234776.573.4323512
Andre Ethier520.3437576.16-24.157716
Shin-soo Choo540.39329775.12-21.1226632
Ryan Zimmerman790.35335074.784.2216328
Elvis Andrus670.29642874.76-7.7624504
Jonathan Lucroy820.34535974.407.597372
Nick Swisher630.33637074.15-11.1477464
Alex Gordon810.32638374.016.9862776
Manny Machado710.32538473.94-2.94278
Justin Upton700.35734073.91-3.9113368
Matt Carpenter780.38130773.894.1122456
Justin Morneau770.32138973.853.1491896
Brandon Moss870.36932273.6113.3881544
Michael Brantley730.3238873.40-0.396268
Adam Laroche620.32137971.93-9.9328104
Chris Carter820.33735771.9210.0829112
J.j. Hardy760.32237771.814.1880472
Chris Johnson680.35433371.78-3.7805096
Kyle Seager690.33735671.73-2.7252888
Domonic Brown830.35133671.5711.4323176
David Wright580.39128171.53-13.5283784
David Freese600.32237471.24-11.2365528
Carlos Gonzalez700.40825671.20-1.1999992
Adam Lind670.36831071.05-4.0475032
Ian Kinsler720.33435670.941.0629384
Adam Dunn860.33136070.9215.0839656
Stephen Drew670.33735170.77-3.7662888
Nick Markakis590.30439670.73-11.7267896
Todd Frazier730.31937169.873.1270744
Yunel Escobar560.31138169.69-13.6889864
Ryan Doumit550.31138069.50-14.4971864
Omar Infante510.34632968.91-17.9113704
Jose Bautista730.37229168.454.5457272
Bryce Harper580.37129068.00-9.9997304
Jarrod Saltalamacchia650.34932067.97-2.9733976
Gerardo Parra480.31836167.69-19.6921832
Hanley Ramirez570.44219167.67-10.6662408
Daniel Murphy780.3235867.6410.357732
Yoenis Cespedes800.31835766.9213.0750168
Andrelton Simmons590.30337766.82-7.8198472
Giancarlo Stanton620.36828466.06-4.0607032
Chase Headley500.3333666.05-16.050092
Jacoby Ellsbury530.34331866.01-13.0133432
Joe Mauer470.38326365.97-18.9740392
Wilin Rosario790.34831065.7913.2073448
Marlon Byrd880.36428565.2022.7984664
Jedd Gyorko630.32533865.12-2.11998
Jean Segura490.32933265.02-16.0201496
Russell Martin550.31535164.99-9.985956
Howie Kendrick540.33632264.94-10.9413464
Asdrubal Cabrera640.30735764.03-0.0348168
Chase Utley690.35628963.875.1332056
Jhonny Peralta550.35628663.29-8.2913944
Trevor Plouffe520.30935063.22-11.2177016
Alexei Ramirez480.30435663.05-15.0547896
Matt Wieters790.30235662.5316.4706952
Austin Jackson490.33231462.36-13.3559768
Shane Victorino610.35328562.31-1.3113672
Justin Smoak500.33131562.29-12.2850344
Yasiel Puig420.39822362.24-20.2431752
Salvador Perez790.32931561.7617.2404504
Zack Cozart630.28936761.221.7765464
Neil Walker530.33330661.08-8.0843192
Nelson Cruz760.35927061.0114.9891784
Nate Schierholtz680.33130760.757.2493656
Will Venable530.34229060.38-7.3802008
Matt Dominguez770.30134560.1616.8432376
Colby Rasmus660.36525659.906.097924
Raul Ibanez650.34428459.755.2451144
Desmond Jennings540.3330259.53-5.528892
Brandon Crawford430.29634859.42-16.4184504
Jose Altuve520.29734659.30-7.2975928
Coco Crisp660.33928658.827.1752264
Aramis Ramirez490.36624958.82-9.8222184
Brian Dozier660.31931358.757.2514744
Jason Castro560.36125558.66-2.6593064
Josh Willingham480.32230658.19-10.1941528
Wil Myers530.35725457.42-4.4165368
A.j. Pierzynski700.31331457.3612.6361288
Albert Pujols640.32929157.166.8436504
Starlin Castro440.2835857.13-13.132572
Evan Gattis650.32928956.778.2272504
A.j. Ellis520.30432356.73-4.7253896
Dan Uggla550.30332356.46-1.4626472
Erick Aybar540.29932655.99-1.9870776
Juan Uribe500.33427755.78-5.7848616
Brian Mccann570.34725955.751.2518872
Mike Moustakas420.28734155.71-13.7111688
Andy Dirks370.30631355.33-18.3328744
Leonys Martin490.30830754.71-5.7075592
Ryan Raburn550.38919554.510.4919064
Alejandro De Aza620.3228954.417.591932
Matt Joyce470.3327454.16-7.158492
Marco Scutaro310.32528054.00-22.99558
Paul Konerko540.29831653.810.1936648
Lyle Overbay590.30330953.785.2225528
Brett Gardner520.33526453.55-1.554204
Matt Adams510.36522253.38-2.380876
Chris Denorfia470.32327953.28-6.2782952
Aaron Hill410.35823153.27-12.2678792
Todd Helton610.32227953.027.9844472
Mitch Moreland600.3228052.687.318132
Jimmy Rollins390.29531252.25-13.250908
Jonny Gomes520.33825352.23-0.2326312
Denard Span470.31328251.23-4.2262712
Alcides Escobar520.24737251.150.8527272
Dayan Viciedo560.31827451.014.9944168
Carlos Quentin440.37220051.00-7.0004728
Nolan Arenado520.30828750.871.1284408
J.b. Shuck390.30828650.68-11.6797592
Alex Rios810.3325350.1330.869308
Yan Gomes380.35921049.50-11.5028216
Ichiro Suzuki350.28131649.34-14.3397144
Alfonso Soriano1010.3423549.3151.694284
Alex Avila470.3127448.90-1.903644
Justin Ruggiano500.30727848.881.1173832
Gregor Blanco410.30727848.88-7.8826168
Dexter Fowler420.34722348.84-6.8433128
Garrett Jones510.30927548.832.1672984
Nate Mclouth360.32325448.48-12.4832952
Mark Reynolds670.3127148.3318.671756
Gaby Sanchez360.33823248.20-12.2048312
Mark Ellis480.328448.19-0.19422
David Murphy450.28929847.99-2.9892536
Lucas Duda330.3422847.96-14.963116
Michael Young460.3225547.89-1.886868
Brett Lawrie460.31426347.84-1.8448136
Lorenzo Cain460.29129447.75-1.7475384
Miguel Montero420.29528747.46-5.455908
Vernon Wells500.27930747.092.9119704
Josh Reddick560.30327447.068.9355528
Seth Smith400.31825346.98-6.9777832
Michael Saunders460.31525346.19-0.189556
Chris Iannetta390.3323045.72-6.719292
A.j. Pollock380.32124245.66-7.6562104
Norichika Aoki370.32623545.63-8.6273224
Welington Castillo320.33122845.60-13.5984344
Yonder Alonso450.31125445.33-0.3303864
Starling Marte350.34420845.18-10.1780856
Darwin Barney410.25233445.17-4.1725848
Oswaldo Arcia430.32223845.15-2.1517528
Adeiny Hechavarria420.25133344.72-2.7180424
Jason Heyward380.34420344.22-6.2190856
Drew Stubbs450.29626643.691.3091496
Cody Ross380.32622443.52-5.5175224
Carl Crawford310.32222843.23-12.2337528
Darin Ruf300.35418443.20-13.2023096
Eric Chavez440.34419743.070.9317144
Mike Aviles460.28427943.032.9686584
Michael Bourn500.325743.026.98438
Kelly Johnson520.31423642.679.3337864
Pedro Florimon440.27329242.631.3654248
Conor Gillaspie400.30324842.08-2.0776472
Eric Sogard350.30324842.08-7.0776472
Ryan Howard430.33420441.781.2165384
Skip Schumaker300.30124941.74-11.7439624
John Mayberry390.29825241.53-2.5311352
Didi Gregorius280.31123441.49-13.4943864
Wilson Ramos590.33719841.4217.5791112
John Buck620.28726541.1320.8656312
J.p. Arencibia550.25930341.0713.9340184
Will Middlebrooks490.324640.918.09418
Anthony Rendon350.31821940.46-5.4565832
Dustin Ackley310.29624940.43-9.4302504
Dj Lemahieu280.29524940.17-12.167508
Gordon Beckham240.30623239.80-15.7970744
Derek Norris300.33519239.74-9.744604
Nick Hundley440.29524639.594.407892
Everth Cabrera310.32919839.32-8.3189496
Jordy Mercer270.33319139.03-12.0273192
Chris Young400.28925138.971.0253464
Nick Franklin450.30423038.896.1120104
David Lough330.31621338.78-5.7802984
Jeff Keppinger400.26628138.691.3144216
Rajai Davis240.30521836.85-12.849132
Matt Kemp330.31620236.67-3.6704984
Ike Davis330.29722836.67-3.6651928
Logan Morrison360.31220536.19-0.1949288
Luke Scott400.32618536.043.9626776
Juan Lagares340.27525335.68-1.67986
Alberto Callaspo580.31220035.2422.7640712
Carlos Ruiz370.30321235.171.8271528
Pete Kozma350.24129534.800.1977816
Jose Lobaton320.31619234.75-2.7524984
Luis Valbuena370.31519134.302.702044
Travis Hafner370.30220733.953.0488952
Rickie Weeks240.29921133.93-9.9300776
Devin Mesoraco420.28223133.308.7005432
Yuniesky Betancourt460.25726232.6813.3233032
Lance Berkman340.31318532.621.3783288
B.j. Upton260.25226732.32-6.3219848
Chris Parmelee240.29820332.13-8.1329352
Jesus Guzman350.29920132.012.9879224
Brett Wallace360.31418031.934.0745864
Brandon Barnes410.28321931.269.7394008
Marcell Ozuna320.30418830.831.1676104
Daniel Descalso430.28421230.1812.8192584
Kyle Blanks350.30218730.124.8848952
Eduardo Nunez280.29819129.83-1.8313352
Ed Lucas280.28920229.58-1.5764536
Maicer Izturis320.26922929.502.4997944
J.d. Martinez360.28420829.416.5864584
Placido Polanco230.27921329.06-6.0588296
Carlos Pena250.29818528.68-3.6805352
Donovan Solano340.27721328.535.4666552
Lonnie Chisenhall360.29318427.188.8249768
Jurickson Profar260.29118627.03-1.0331384
Alexi Amarista320.27420526.215.7892824
Omar Quintanilla210.26221925.74-4.7430088
Michael Morse270.28618525.531.4723736
Chris Stewart250.26121825.29-0.2884664
Jayson Nix240.27919124.84-0.8392296
Cliff Pennington180.27319323.65-5.6463752
Aaron Hicks270.26619722.574.4256216
Logan Schafer330.26919122.2110.7881944
Jose Molina180.26618520.27-2.2727784
Greg Dobbs220.26518219.432.565364
Tyler Flowers240.26518019.054.948964
Miguel Cabrera

Photo by: Keith Allison

Lets think about why Chris Davis xRBI is so much lower than his 2013 actual RBI total.

Davis had 396 runners on base while he batted in 2013, which is 140 ROB less than Prince Fielder who led the league with 536 ROB; Davis’ opportunity was limited.

Davis’ RBI total was considerably higher than what his opportunity would suggest his RBI total should be, and one of the reasons that he outperformed his xRBI total by so much was because of the amount of home runs he hit. Davis, or any batter, doesn’t need a runner on base to get an RBI when he hits a home run. But beyond home runs there is another reason why Davis and other batters outperform their xRBI totals: luck.

Hitting with runners on base is not a skill. A batter has the same probability, regardless of the base/out state, of a hit. Lets forget pitcher handedness and Davis’ platoon splits at the moment. With a runner on second base and two outs Chris Davis will get a hit .272 (27%) of the time—I averaged his Steamer and Oliver projections for 2014 together. Davis, and Alfonso Soriano for that matter, who was the only player to outperform his xRBI by more than Davis in 2013, was lucky and happened to have runners on base the majority of the 28.6%—Davis’ 2013 batting average—of the time he got a hit in 2013.

To put Davis’ 2013 136 RBI season into perspective, in the last five seasons there have been eight players to record 130 or more RBI in a season. Of those eight players, only two—Ryan Howard (2008-9) and Miguel Cabrera (2012-13)—were able to duplicate the performance the following year.

While the combination of ROB and wOBA has allowed us come up with a reliable xRBI, the next step, to increase the reliability of xRBI and account for players who produce a large amount of their RBI from home runs (i.e. Davis), is to include a power component in xRBI: HR/FB ratio.

Follow Me on TwitterDevin Jordan is obsessed with statistical analysis, non-fiction literature, and electronic music. If you enjoyed reading him, follow him on Twitter @devinjjordan.



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