Filed under:

# Introducing awOBA -- Adjusting wOBA for Quality of Opposition

We adjust each player's 2012 season for quality of opposition and introduce awOBA, including a complete 2012 leader board.

Sometimes I look at a hitter's wOBA, or any metric for that matter, and wonder the quality of pitching he faced. Other times I think, "What if Player X played in the AL West instead of the AL Central?". Is this guy succeeding because he regularly faces teams in his division with quality of pitching that is better than most of the league? Is Player X faltering because of the same reason?

There is a story behind every wOBA total. Maybe Player X faced Justin Verlander 20 PA's too many, leading to a skewed wOBA in comparison to the league and Player X's true skill.

Most player's are victims of circumstance. They play in the AL West and they have to face Yu Darvish and Felix Hernandez a handful more times every year than the given AL player. Other lucky players face a 2013 version of Clayton Richard or Dan Haren, more than the usual player. The matter of the fact is, some guys have it better than others, and others have it worse than the rest.

To solve for this problem, or simply make a composite tiered wOBA based on the quality of opposition, we first have to quantify the quality of opposition.

We are going to group pitchers into four groups, the top 25%, top 50%, top 75% and top 100%, based on their wOBA against.

The requirements for each quantile are as follows for the 2012 season:

Top 25% Top 50% Top 75% Top 100%
< = 0.284 > 0.284 and < = 0.313 > 0.313 and < = 0.354 > 0.354 and < =1.374

Now, before we get into adjusting, let's look at some quality distributions amongst pitchers:

### Quality Distributions -- Pitchers

Now that we have the requirements for each quantile, lets look at which percentages of the league falls under each category:

Top 25% Top 50% Top 75% Top 100%
24.75% 27.57% 25.75% 21.93%

So according to the distribution, there are more pitchers of quality in terms of wOBA against than those of terrible quality. Now this is probably because we are just looking at large percentage gaps and wOBA against, but this distribution looks good for what we want to do -- adjusting a hitter's wOBA based on the pitchers they faced, and will come in handy later.

Now that we have seen the league-wide distribution of wOBA, let's break down the analysis into each division. This will give us a good look into which divisions had a abnormal distribution of pitchers for each quantile:

##### TOP 25% -- Percentage of top 25% pitchers in each division compared to the total number of pitchers.
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
4.43% 2.62% 4.43% 4.23% 3.42% 5.63%

The AL East has the highest density of top 25% pitchers, with the NL West and NL East tying for second. The NL Central, comes in last by far.

##### TOP 50%
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
3.62% 6.64% 6.44% 3.22% 3.82% 3.82%

Meanwhile, the NL Central, despite having the smallest amount of top 25% pitchers, has the majority of the league's share in top 50% -- the NL East coming in close second.

##### TOP 75%
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
4.63% 4.02% 2.62% 3.02% 7.04% 4.43%

Now, the AL Central has the highest density of top 75% pitchers, which is quite auspicious for the hitters that play in that division. Meanwhile, the NL West comes in second with the AL East not far behind.

##### TOP 100%
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
3.82% 3.62% 2.82% 2.21% 4.02% 5.43%

Lastly, 5% of the league's worst pitchers reside in the AL East. Combine that with the previous quantile and the AL East has 9.86% of the league's bottom half of pitchers. The AL East, however, comes in first with the most pitchers in the 75 and 100 quantiles at 11.06%.

Now I split up the percentages based on the top half and bottom half quantiles:

##### TOP HALF:
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
8.05% 9.26% 10.87% 7.45% 7.24% 9.45%

The NL East is the most top heavy division in terms of quality pitching, with the AL East coming in close behind.

##### BOTTOM HALF:
NL WEST NL CENTRAL NL EAST AL WEST AL CENTRAL AL EAST
8.45% 7.64% 5.44% 5.23% 11.06% 9.86%

The AL Central is the most bottom heavy in terms of pitching quality, with the AL East coming into second again.

Given what we see here, it only makes sense to adjust a player's wOBA based on the quality of pitching he faces. So let's dive in:

### ADJUSTING FOR QUALITY OF OPPOSITION -- INTRODUCING awOBA

Essentially we want to be able to adjust a player's wOBA in two ways:

1. Adjusting performance in each quantile by comparing league average to total PA.
2. Weighting opportunities by comparing PA in each quantile by league average PA.

In order to fulfill number one we will use the following formula:

1) (wOBA_quantile - lg_wOBA_quantile) * (PA_quantile/ PA)

This will give us a number of a player's performance against a certain tier of pitching relative to his opportunities as a whole against that group.

The next formula will allow us to weight the product of the first formula, so as to adjust for quality of opposition:

2) PA_quantile / lg_PA_quantile

This should give us a number that we will use as a weight in our final calculations of awOBA.

For the final calculations, we will add each number produced from the first formula and multiply it with the weight. Next we will add the products to a league average wOBA constant.

For Joey Votto, the calculation will look like this:

##### Joey Votto's awOBA calculation
dwOBAt25 dwOBAt50 dwOBAt75 dwOBAt100 dwOBAt25 PAwt50 PAwt75 PAwt100 awOBA
0.0148 0.0480 0.0371 0.0148 0.999 1.18 0.815 0.631 0.442

The formula is as follows, using the headings from above:

awOBA = (dwOBAt25 * dwOBAt25) + (dwOBAt50 * PAwt50) + (dwOBAt75 * PAwt75)+ (dwOBA100 * PAwt100) + (lg_wOBA)

In the end it will look like this:

0.442 = (0.0148 * 0.999) + (0.0480 * 1.18) + (0.0371 * 0.815) + (0.0148 * 0.631) + 0.331

Unfortunately, Retrosheet does not release play by play data for 2013 until the end of the season. For this reason, we will have to look back at this retrospectively on the 2012 season:

##### Top 25 in awOBA:
NAME wOBA awOBA DIFF
Joey Votto 0.438 0.442 0.004
Ryan Braun 0.413 0.426 0.013
Mike Trout 0.409 0.423 0.014
Andrew McCutchen 0.403 0.417 0.014
Buster Posey 0.406 0.416 0.010
Miguel Cabrera 0.417 0.413 -0.004
David Wright 0.376 0.406 0.030
Edwin Encarnacion 0.396 0.402 0.006
Matt Holliday 0.378 0.402 0.024
Carlos Ruiz 0.398 0.396 -0.002
David Ortiz 0.425 0.395 -0.030
Carlos Gonzalez 0.374 0.395 0.021
Melky Cabrera 0.387 0.391 0.004
Robinson Cano 0.394 0.387 -0.007
Joe Mauer 0.376 0.386 0.010
Alex Gordon 0.357 0.385 0.028
Allen Craig 0.374 0.377 0.003
Josh Hamilton 0.387 0.377 -0.010
Josh Willingham 0.380 0.375 -0.005
Billy Butler 0.377 0.375 -0.002
Prince Fielder 0.398 0.374 -0.024
Jason Kubel 0.352 0.374 0.022

##### Bottom 25 in awOBA:
NAME wOBA awOBA DIFF
Brendan Ryan 0.252 0.259 0.007
Dustin Ackley 0.274 0.263 -0.011
J.J. Hardy 0.290 0.273 -0.017
Jemile Weeks 0.276 0.277 0.001
Ichiro Suzuki 0.300 0.278 -0.022
Casey Kotchman 0.271 0.278 0.007
Jeff Francoeur 0.285 0.280 -0.005
Gordon Beckham 0.295 0.280 -0.015
Brennan Boesch 0.288 0.281 -0.007
Darwin Barney 0.287 0.281 -0.006
Jamey Carroll 0.299 0.281 -0.018
Jhonny Peralta 0.301 0.284 -0.017
Drew Stubbs 0.271 0.287 0.016
Cliff Pennington 0.263 0.287 0.024
Alexei Ramirez 0.282 0.287 0.005
Robert Andino 0.265 0.287 0.022
Carlos Pena 0.309 0.287 -0.022
Daniel Descalso 0.278 0.288 0.010
James Loney 0.272 0.288 0.016
Mike Moustakas 0.305 0.288 -0.017
Eric Hosmer 0.291 0.289 -0.002
Brandon Crawford 0.284 0.289 0.005
Alcides Escobar 0.316 0.289 -0.027
Kurt Suzuki 0.264 0.293 0.029
Yunel Escobar 0.284 0.293 0.009
##### BIGGEST WINNERS (HIGH DIFF):
NAME wOBA awOBA DIFF
Maicer Izturis 0.287 0.328 0.041
Sean Rodriguez 0.269 0.302 0.033
Miguel Olivo 0.267 0.299 0.032
John Buck 0.284 0.316 0.032
David Wright 0.376 0.406 0.030
Kurt Suzuki 0.264 0.293 0.029
Raul Ibanez 0.325 0.354 0.029
Alex Gordon 0.357 0.385 0.028
Eric Thames 0.290 0.317 0.027
Pablo Sandoval 0.338 0.365 0.027
Brian Bogusevic 0.271 0.296 0.025
Justin Upton 0.341 0.365 0.024
Cliff Pennington 0.263 0.287 0.024
Matt Holliday 0.378 0.402 0.024
Jacoby Ellsbury 0.300 0.324 0.024
Placido Polanco 0.279 0.302 0.023
Jarrod Dyson 0.291 0.314 0.023
John Mayberry 0.303 0.326 0.023
Rod Barajas 0.272 0.295 0.023
Nate McLouth 0.305 0.327 0.022
Robert Andino 0.265 0.287 0.022
Jason Kubel 0.352 0.374 0.022
Mark Teixeira 0.345 0.367 0.022
Freddie Freeman 0.342 0.364 0.022
##### BIGGEST LOSERS (LOWEST DIFF):
NAME wOBA awOBA DIFF
Brandon Moss 0.402 0.371 -0.031
David Ortiz 0.425 0.395 -0.030
Alcides Escobar 0.316 0.289 -0.027
Prince Fielder 0.398 0.374 -0.024
Matt Wieters 0.331 0.307 -0.024
David Murphy 0.369 0.346 -0.023
Andy Dirks 0.368 0.346 -0.022
Ichiro Suzuki 0.300 0.278 -0.022
Carlos Pena 0.309 0.287 -0.022
Hunter Pence 0.323 0.302 -0.021
Evan Longoria 0.378 0.359 -0.019
Matt Kemp 0.383 0.364 -0.019
Jonathan Lucroy 0.378 0.359 -0.019
Eric Chavez 0.360 0.342 -0.018
Jamey Carroll 0.299 0.281 -0.018
Jhonny Peralta 0.301 0.284 -0.017
J.J. Hardy 0.290 0.273 -0.017
Corey Hart 0.358 0.341 -0.017
Jonny Gomes 0.376 0.359 -0.017
Mike Moustakas 0.305 0.288 -0.017
Coco Crisp 0.324 0.308 -0.016
A.J. Pierzynski 0.351 0.335 -0.016
Gordon Beckham 0.295 0.280 -0.015
Chris Nelson 0.348 0.334 -0.014
David Freese 0.365 0.351 -0.014