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# The Most Unexpected Players of 2013

Projections are often a little off, especially in baseball. What players have most exceeded and fell furthest short of their projected levels?

Prediction is very difficult, especially about the future.

What do a three-time American League MVP and a Nobel-winning Physicist have in common? Both have had this quote attributed to them. Yogi Berra and Neils Bohr both supposedly have this quote to their name, although I'd probably defer to Neils Bohr on the subject of predictions.

Regardless who originated the quote, they're decidedly correct. Nothing is more difficult than predicting future events, especially when you don't have good data to go off of. Baseball is especially difficult to predict, because baseball is one of the noisiest sources of data.

Despite this, people still try to project what players will accomplish in the coming season. Around February-March, we see projections for players and teams starting to come out of the woodwork. Some involve complex formulas, while others merely involve general feelings about a player.

Part of the fun over the course of a season is seeing which players exceed their levels. Probably nothing is more talked about on television, radio, fantasy chats, and general conversation, than breakout/bust players. A fair question to ask is, "Who has had the best breakout season?" Or, more specifically, who has most exceeded expectations?

Now, an easy way to look at this is to merely scale the player's full-season WAR for their current number of plate appearances, and look at the differences. Now, this would be a little short-sighted, because players of different hitting types have different amounts of variability expected with their seasons. And anyways, what fun is it going with the simple answer?

So instead, why don't we look at the probability that a player exceeds their current level, given that their projection is correct. While this is can be difficult to look at directly, we are able to look at this through a few simulations.

Of course, to start, we need a projection system to start off from. For this, I decided to choose Dan Szymborski's ZiPS projections. Now, we need to discuss how we can get at the probability estimate we want to look at.

Many times before this, I've mentioned using Bootstrapping to assess the variability in an estimator. Well, I will again be using bootstrap-esque procedure, and I want to explain a little how the bootstrap method works in this case. Consider it "Bootstrapping For Baseball Applications." If you aren't interested, jump to the next header.

#### Bootstrapping: A Primer

Bootstrapping is a useful method when looking at the distribution or properties of an estimator when observing these properties directly may be difficult. Though looking at variability often needs multiple observations, i.e. multiple point estimates, we often only have one sample. Baseball is an excellent example of this, where we may want to know the distribution of, say, wOBA for a player, but can only observe one single season of wOBA.

However, our one sample has many data points which should be representative of the population as a whole. In baseball terms, a player's season is made up of individual plate appearances which should be representative of his overall talent level. Why couldn't we create seasons out of this sample?

This is what bootstrap does. It essentially takes our sample, and creates a new dataset by resampling with replacement from our real sample. So in baseball, we could create as many seasons as we want by sampling with replacement from the plate appearances seen in our season. Suddenly, we have a large number of point estimates, allowing us to estimate variances, probabilities, or anything we may want to investigate.

So, we'll use this bootstrap-esque technique to look at the probability that a player could exceed is expectations. To start with, we assume that the ZiPS projection is an accurate projection of the player's expected level. Then we sample from the plate appearances seen in the projection with replacement x times, where x is the number of plate appearances for the player at this point. Then, we calculate the player's WAR by adding the player's bootstrap RAA to his actual UZR, Replacement, and Positional levels. Then, we can look at the number of times a player exceeds his current level, out of 10,000 created seasons.

### The Most Unexpected Players of 2013

So, of the 253 players who had at least 150 PAs by this past Monday, who exceeded their projection by the largest amount? And what was the probability that we'd see a better season from this player? In the table below, we have the player, their actual WAR, and the probability they exceeded their current level based on preseason projections.

Player Actual WAR P(Higher WAR)
Chris Davis 3.8 0.0001
Everth Cabrera 3.3 0.002
Josh Donaldson 2.7 0.0042
Carlos Gomez 4.3 0.0053
Marco Scutaro 1.9 0.0096
Jean Segura 3 0.0147
James Loney 1.6 0.0177
Matt Carpenter 3.4 0.0196
Jhonny Peralta 2.7 0.0221
Coco Crisp 2.3 0.0237
Daniel Nava 1.1 0.0282
Howie Kendrick 2.1 0.0318
Gerardo Parra 2.5 0.0325
Brandon Crawford 1.9 0.0334
Carlos Gonzalez 4.2 0.0351
Jason Castro 1.8 0.0358
Nate Schierholtz 1.5 0.0404
Kyle Blanks 1.2 0.0443
Troy Tulowitzki 4.3 0.0495
Mitch Moreland 1.6 0.0544
Hunter Pence 2.9 0.0553
Miguel Cabrera 4.1 0.0642
Michael Cuddyer 1.5 0.0647
Paul Goldschmidt 2.9 0.0679
Chris Johnson 0.7 0.0731
Didi Gregorius 1.7 0.0756
Marlon Byrd 1.4 0.0819
Brandon Barnes 1.1 0.0907
Evan Gattis 1.9 0.0938
Bryce Harper 1.8 0.1077
Kyle Seager 2.1 0.1221
Jarrod Saltalamacchia 1.5 0.1222
Jedd Gyorko 1.6 0.1226
Matt Joyce 1.3 0.1231
Shin-Soo Choo 2.5 0.1235
Alex Rios 2.4 0.1273
David Wright 3.1 0.1322
Nate McLouth 1.5 0.1497
Joe Mauer 2.8 0.151
Carlos Santana 1.8 0.1576
Carl Crawford 1.9 0.1578
Munenori Kawasaki 0.6 0.1613
Brett Gardner 2.5 0.1618
Jason Kipnis 2 0.1623
Dexter Fowler 3.1 0.1639
Evan Longoria 3.6 0.167
Carlos Beltran 1.1 0.1841
Starling Marte 2.3 0.1959
Kelly Johnson 1.2 0.1991
Luis Valbuena 1.8 0.1995
Domonic Brown 1.4 0.2017
Trevor Plouffe 0.2 0.2037
Mike Trout 3.6 0.2057
Ian Desmond 2 0.2182
Russell Martin 2 0.2223
Endy Chavez -0.1 0.2374
Seth Smith 1 0.2388
Raul Ibanez -0.4 0.239
Michael Morse -0.1 0.2409
Nick Punto 0.6 0.2431
Jason Bay 0.6 0.2502
Jed Lowrie 1.1 0.2517
Brandon Moss 1 0.2603
Mark Trumbo 1.7 0.2638
Colby Rasmus 2 0.268
Lorenzo Cain 1.6 0.2739
Marcell Ozuna 1.4 0.2767
Gregor Blanco 1.1 0.2788
J.J. Hardy 2.1 0.2833
Ian Kinsler 1.1 0.2858
Buster Posey 2.5 0.2867
John Mayberry 0.5 0.287
Justin Upton 1.7 0.2886
Omar Infante 1.4 0.2969
Norichika Aoki 1 0.3076
Dustin Pedroia 2.9 0.3101
Kendrys Morales 0.8 0.3413
Lucas Duda -0.3 0.3415
Daniel Murphy 1.8 0.3459
Freddie Freeman 0.8 0.3461
A.J. Pierzynski 0.8 0.3651
Michael Bourn 1 0.3704
Nelson Cruz 0.9 0.3805
Drew Stubbs 0.7 0.3947
Mike Aviles 0.6 0.396
Desmond Jennings 1.4 0.3974
A.J. Ellis 1.3 0.4029
Chris Iannetta 0.8 0.4042
Justin Smoak -0.1 0.4077
Skip Schumaker -0.8 0.4102
David Freese 0.8 0.4128
David Ortiz 1.8 0.4132
Chase Utley 1.6 0.4168
Michael Young 0.5 0.4199
Lyle Overbay 0.2 0.425
Brandon Phillips 1.8 0.4253
Pedro Florimon 1.3 0.4265
Pete Kozma 0.9 0.4284
David DeJesus 1.4 0.4318
Todd Frazier 2.2 0.4333
Allen Craig 0.6 0.4344
Neil Walker 1.2 0.442
Eric Sogard 0.3 0.4422
Carlos Quentin 1.1 0.4475
Mark Ellis 0.3 0.4476
J.D. Martinez -0.5 0.4579
Edwin Encarnacion 1.7 0.4613
Prince Fielder 1.3 0.4638
Mark Reynolds 0.3 0.4679
Garrett Jones 0 0.4801
Nick Hundley 0.5 0.4817
A.J. Pollock 1.7 0.4828
Jonathan Lucroy 1.1 0.4836
Chris Denorfia 1.4 0.4869
Leonys Martin 0.5 0.4875
Alex Gordon 1.8 0.5007
Yonder Alonso 0.4 0.5033
Conor Gillaspie 0.8 0.5104
John Buck 0.9 0.5119
Will Venable 0.7 0.5158
Jay Bruce 1.3 0.5248
Derek Norris 0.5 0.5256
Nick Markakis 0.8 0.5476
Asdrubal Cabrera 0.4 0.5485
Travis Hafner 0.5 0.5501
John Jaso 0.9 0.5559
Wilin Rosario 1.2 0.5594
Yunel Escobar 1 0.5607
Ryan Zimmerman 0.5 0.5616
Michael Brantley 0.5 0.5651
Joey Votto 3.1 0.5652
Erik Kratz 0.7 0.5667
Alejandro De Aza 0.8 0.5675
Andres Torres 0.8 0.5735
Mike Napoli 1.7 0.5769
Marwin Gonzalez 0.2 0.5873
Jayson Werth 0.3 0.6015
Angel Pagan 0.4 0.6068
Dan Uggla 0.4 0.6098
Robinson Cano 2.1 0.613
Brian Dozier 0.6 0.6144
Ryan Doumit -0.1 0.6161
Austin Jackson 0.8 0.6192
Ryan Braun 1.9 0.6242
Yoenis Cespedes 1.6 0.6382
Nick Swisher 0.9 0.651
Josh Willingham 0.5 0.6519
Freddy Galvis 0 0.6544
Justin Morneau 0.6 0.6547
Torii Hunter 0.8 0.6563
Jimmy Rollins 1.3 0.6582
Andrew McCutchen 2.7 0.6593
Jayson Nix 0.4 0.661
Ben Zobrist 1.4 0.6638
Ryan Howard 0.3 0.6643
Pedro Alvarez 1 0.6644
Pablo Sandoval 0.8 0.6684
Welington Castillo 0.9 0.6777
Matt Dominguez -0.3 0.6778
Billy Butler 0.7 0.68
Stephen Drew 1.3 0.6828
Travis Snider 0 0.6889
Chris Carter -0.4 0.6981
Matt Holliday 1.1 0.6991
Justin Ruggiano 1.4 0.7098
Jacoby Ellsbury 2.2 0.7156
Jonny Gomes 0.7 0.7209
Shane Victorino 1.6 0.7246
Chris Parmelee -0.5 0.7278
Jose Altuve 0.9 0.7298
Ichiro Suzuki 0.3 0.735
Josh Reddick 0.5 0.7367
Todd Helton 0 0.7388
Lance Berkman 0.6 0.7419
Brandon Belt 1 0.7475
J.P. Arencibia 0.3 0.7488
Alberto Callaspo -0.6 0.749
Zack Cozart 1.1 0.7532
Juan Pierre 0.3 0.7549
Vernon Wells -0.1 0.7595
Denard Span 0.8 0.7664
Carlos Pena 0.3 0.7665
Ben Revere 0.3 0.7705
Jose Bautista 2.5 0.7778
Erick Aybar -0.1 0.7846
Michael Saunders 0 0.7895
Anthony Rizzo 1.2 0.7925
Tyler Flowers 0.4 0.7929
Matt Wieters 1.2 0.7967
Alfonso Soriano 0.6 0.8073
Rob Brantly 0 0.8102
Greg Dobbs -0.3 0.8129
Juan Francisco -0.1 0.8133
Cliff Pennington 0.5 0.8161
Andre Ethier 0.5 0.8262
Eric Young -0.5 0.8281
Placido Polanco -0.6 0.8306
Eric Hosmer 0.3 0.8327
Brendan Ryan -0.4 0.8442
Alexei Ramirez 1.1 0.8456
Darwin Barney 0 0.8584
Will Middlebrooks -0.5 0.8622
Chris Young -0.3 0.8674
Andy Dirks 0.8 0.8716
Andrelton Simmons 0.9 0.8726
Alcides Escobar 0.7 0.8727
Yuniesky Betancourt -0.5 0.8728
Jon Jay -0.3 0.8731
Jason Heyward 0.9 0.8782
Kurt Suzuki 0 0.8817
Cody Ross 0.1 0.8921
Josh Rutledge -0.2 0.8922
Melky Cabrera 0.1 0.8964
Aaron Hicks -0.4 0.9081
Emilio Bonifacio -0.6 0.9104
Albert Pujols 0.2 0.9113
Dayan Viciedo -0.4 0.9114
Jeff Francoeur -0.6 0.919
Brett Lawrie 0.3 0.9322
Rickie Weeks -0.2 0.9329
David Murphy -0.2 0.9412
Clint Barmes -0.3 0.9527
Josh Hamilton 0.2 0.9619
Maicer Izturis -1.4 0.9709
Elvis Andrus 0.9 0.9729
Victor Martinez -1.1 0.9737
Dustin Ackley -0.3 0.9738
Ryan Flaherty -0.2 0.974
Miguel Montero 0.3 0.9815
Paul Konerko -0.9 0.9826
Steve Lombardozzi -0.7 0.9835
Alex Avila -0.2 0.9844
Starlin Castro -0.3 0.9868
Mike Moustakas -0.5 0.9874
B.J. Upton 0.4 0.9879
Matt Kemp -1.3 0.994
Danny Espinosa -0.6 0.9971
Ike Davis -1.1 0.9993
Jeff Keppinger -1.3 0.9994

So to add to all his accomplishments this year, Chris Davis is the most unexpected player of 2013 so far, and it's not even close. The season he is having is roughly 20 times less likely than any other player, at least when compared to their respective projections. Other players who exceeded expectations by far were breakout players Everth Cabrera, Josh Donaldson, and Carlos Gomez.

On the other end of the spectrum fall the season busts. Some are down there because of injuries, other just because they haven't produced so far. Jeff Keppinger barely edges out Ike Davis for the most underwhelming, with Danny Espinosa and Matt Kemp close behind.

One final comment to make about these projections is about how difficult projections really are. We can assess this by looking at how the probabilities from the above table are distributed.

The better the projection, the closer the probability of a better season is to 0.5. As we can see, the distribution of probabilities is pretty close to uniform throughout [0,1]. Just a reminder about how difficult these projections can be to get correct.

All statistics courtesy of Fangraphs. Statistical work done in R.