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September 13, 2007

Schrodinger's Bat

The Return of the Fish Eye

by Dan Fox

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"They both [statistics & bikinis] show a lot, but not everything."
--Infielder Toby Harrah

Last week in this space we updated our projection of Nationals slugging outfielder Wily Mo Pena. In doing so, we noted anecdotally the difficulty that Pena has had in laying off of pitches out of the strike zone, particularly from right-handers. As we discussed in a previous column, the wealth of data provided by PITCHf/x now allows us to quantify just to what extent our analysis of Pena--or any player for that matter--is on track. So today we'll hail the return of the "Fish Eye" as we update our look at plate discipline.

Revealing a Little More

For those who missed our last installment on this topic, we'll bring you up to speed. Using the location data provided by PITCHf/x (plotted as the pitch reaches the front of home plate), combined with the customized strike zone provided for each plate appearance, we can get a pretty good idea of whether a pitch offered at by a hitter would have been within the regulation strike zone. Likewise, if the hitter did not swing at a pitch that should have been called a strike, we can note that as well. By adding up the "balls" that were swung at, the "strikes" that weren't, and everything in between (as well as making a few adjustments for the count along the way) we can create new metrics that collectively give us a picture of what has traditionally been termed plate discipline.

Although in our previous analyses of umpires we've used a buffer zone to give them the benefit of the doubt, here we do not; we simply use the standard 17-inch-wide plate, along with the actual height customized for the player.

With that in mind, there are two differences this time around. When the earlier column was published, we only had about 60,000 pitches to analyze from a handful of ballparks; now we have four times that many, from all but three of the ballparks (Baltimore, Washington, and Pittsburgh are not operational). The result is that we have many more players with decent sample sizes to look at. Secondly, we previously showed three metrics in addition to the more common percentage of pitches swung at, whereas now we've added a fourth to our collection. Those four are:

  • Square: This is the new metric, defined as the percentage of pitches in the strike zone swung at and made contact with. A high value here (relative to the average of over 87 percent) indicates that when the batter offers at a strike he usually makes contact. On the contrary, a lower value indicates hitters who, for reasons such as a long swing, are more apt to swing through strikes.
  • Fish: Defined as the percentage of pitches out of the strike zone that the hitter swung at. A higher percentage here indicates that the hitter may have trouble recognizing pitches since he is offering at pitches that would likely be called balls. Average values here are between 32 and 33 percent.
  • Bad Ball: Defined as the percentage of pitches out of the strike zone that were swung at where contact was made. This includes foul balls, although there is an argument to be made that a foul ball is not the intended outcome, and so should be discounted in some way. A higher value in this category indicates that, when swinging at bad pitches, the hitter is at least able to get the bat on the ball. Average values lie around 73 percent.
  • Eye: Defined as the percentage of pitches in the strike zone on non-three and zero counts that were taken for strikes. A smaller value in this metric indicates a player who recognizes strikes and aggressively offers at them. I excluded 3-0 counts, since a hitter is much more likely to let a strike go by in this situation, and we don't want to penalize them for that behavior. Average values here are in the range of 25 to 27 percent.

So, with those four fields added to our arsenal, when we look at these metrics for Wily Mo Pena, we find the following:


          Square  Fish   BadBall  Eye
vs RHPs   .765   .432    .458    .148
vs LHPs   .758   .316    .600    .250

This indicates that against both lefties and righties Pena swings through more than his fair share of pitches, as indicated by low Square values that together place him among the bottom five right-handed hitters in the game. Against right-handers he also offers at a lot of pitches out of the strike zone (a high Fish rate) and is not particularly successful in getting the bat on the ball when he does. This is indicated by a low Bad Ball value, which, when combined with his rate against lefties, puts him at the very bottom of all qualifying right-handed hitters. However, he is clearly aggressive on pitches in the strike zone (an Eye of .148). Against southpaws, he lays off the questionable pitches (a Fish rate below average) and is more comfortable in letting the occasional tough strike go by (an average Eye).

With that, the remainder of this article will be a data dump of sorts. I'll provide a number of data points and visuals for you pattern-seeking creatures to dissect.

Our Leaders

We can now take a look at the leader boards in these four metrics for hitters from each side of the plate who have seen 250 or more pitches. Keep in mind that despite having more data, there are still a few regular players, mostly switch-hitters, who haven't reached the qualifying number of plate appearances.

Right-Handed Hitters Sorted by Square
Name             Pitches  Square   Fish  BadBall  Eye
Jamey Carroll        263   1.000   .287   .822   .337
Jeff Keppinger       426    .982   .216   .860   .361
David Eckstein       640    .978   .389   .921   .279
Reggie Willits       369    .975   .187   .833   .420
Kevin Mench          308    .970   .293   .925   .363
Ramon Martinez       400    .968   .251   .800   .403
Dustin Pedroia       707    .964   .287   .832   .298
Rafael Furcal        388    .963   .297   .848   .274
Placido Polanco      812    .963   .294   .910   .289
Derek Jeter          440    .962   .346   .796   .130
--------------------------------------------------------
Andruw Jones        1464    .771   .337   .708   .215
Marcus Thames        356    .763   .436   .659   .235
Jayson Werth         400    .763   .309   .836   .426
Sammy Sosa          1043    .759   .354   .576   .215
Nelson Cruz          797    .750   .346   .622   .252
Wily Mo Pena         329    .747   .384   .519   .190
Olmedo Saenz         293    .744   .285   .745   .278
Jonny Gomes          374    .732   .385   .558   .206
John Buck            442    .703   .411   .676   .227
Mark Reynolds        611    .684   .358   .577   .238

Left-Handed Hitters Sorted by Square
Name             Pitches  Square   Fish  BadBall   Eye
Melky Cabrera        295   1.000   .339   .836    .304
Jose Reyes           428    .979   .367   .757    .271
Juan Pierre         1407    .978   .337   .905    .336
Johnny Estrada       290    .971   .493   .838    .125
Luis Castillo        487    .971   .226   .938    .398
Alfredo Amezaga      278    .970   .271   .913    .248
Omar Vizquel         502    .966   .314   .806    .267
David DeJesus        815    .965   .279   .850    .347
Brian Giles         1252    .957   .193   .836    .280
Aaron Miles          292    .957   .462   .895    .260
--------------------------------------------------------
Jim Thome           1279    .782   .243   .626    .267
Carlos Pena          561    .768   .283   .562    .180
Carlos Delgado       520    .754   .382   .688    .200
Terrmel Sledge       527    .746   .278   .607    .238
Jason Smith          289    .736   .483   .453    .241
J. Saltalamacchia    452    .728   .348   .639    .154
Brad Hawpe           643    .727   .280   .616    .172
Jack Cust           1376    .692   .177   .524    .268
Rob Bowen            310    .647   .249   .489    .350
Russ Branyan         430    .597   .347   .495    .163

I know I said I'd leave it to the reader to find the patterns here, but there is something I'd like to point out. The low Square value for Brad Hawpe (.727) helps explain how a player with such a nice combination of Fish (.280) and Eye (.172) metrics (as you'll see in the plots below) still strikes out as much as he does. He avoids swinging at bad pitches and aggressively offers at good ones, and has struck out 122 times in 452 at-bats because of his tendency to swing through pitches. The same can be said, to a lesser degree, of Jim Thome and Terrmel Sledge. Jack Cust, on the other hand, is even better at avoiding bad pitches, but doesn't offer at as many strikes; combine this with his propensity to swing through pitches, and he's K'd an amazing 141 times in 343 at-bats.

Right-Handed Hitters Sorted by Fish
Name             Pitches  Square   Fish  BadBall   Eye
Ivan Rodriguez       588   .841   .544    .766    .208
Alfonso Soriano      766   .792   .509    .730    .191
Delmon Young         533   .805   .508    .651    .133
Tony Pena            512   .861   .500    .792    .198
Miguel Olivo         304   .838   .487    .527    .223
Vladimir Guerrero   1180   .874   .467    .746    .136
Craig Biggio         509   .860   .461    .667    .238
Brandon Phillips     698   .899   .446    .705    .215
Reed Johnson         528   .905   .442    .732    .383
Jose Molina          361   .833   .438    .730    .219
--------------------------------------------------------
Ryan Spilborghs      341   .865   .235    .660    .220
Morgan Ensberg       357   .832   .233    .583    .187
Jeff Conine          298   .888   .229    .872    .280
Troy Glaus          1236   .805   .228    .658    .297
Jeff Keppinger       426   .982   .216    .860    .361
Rickie Weeks         586   .874   .213    .649    .364
Marco Scutaro        910   .961   .211    .838    .287
Pat Burrell          649   .932   .210    .840    .346
Nick Swisher         472   .882   .199    .754    .396
Reggie Willits       369   .975   .187    .833    .420

Left-Handed Hitters Sorted by Fish
Name             Pitches  Square  Fish  BadBall   Eye
Scott Thorman        535   .845   .493   .654    .227
Johnny Estrada       290   .971   .493   .838    .125
Corey Patterson      357   .854   .491   .750    .191
Jason Smith          289   .736   .483   .453    .241
Aaron Miles          292   .957   .462   .895    .260
A.J. Pierzynski     1053   .857   .448   .748    .150
Garret Anderson      939   .903   .447   .747    .319
Ross Gload           441   .903   .438   .821    .148
Erick Aybar          311   .929   .435   .850    .238
Alex Cintron         340   .878   .433   .767    .279
--------------------------------------------------------
Scott Hatteberg      519   .911   .229   .866    .245
Felipe Lopez         398   .916   .229   .768    .311
Luis Castillo        487   .971   .226   .938    .398
Barry Bonds          619   .908   .226   .816    .220
Wilson Betemit       535   .830   .224   .714    .278
Dan Johnson         1173   .886   .218   .765    .311
Reggie Willits       995   .931   .206   .770    .376
Bobby Abreu          586   .918   .194   .545    .336
Brian Giles         1252   .957   .193   .836    .280
Jack Cust           1376   .692   .177   .524    .268

Right Handed Hitters Sorted by Bad Ball
Name             Pitches  Square  Fish BadBall   Eye
Kevin Mench          308   .970   .293   .925   .363
David Eckstein       640   .978   .389   .921   .279
Randy Winn           282   .935   .303   .920   .281
Placido Polanco      812   .963   .294   .910   .289
Paul Lo Duca         333   .952   .350   .901   .254
Jason Kendall       1132   .939   .296   .889   .362
Mike Redmond         320   .930   .302   .882   .307
Ryan Theriot         866   .954   .311   .876   .309
Chipper Jones        414   .820   .297   .875   .266
Jeff Conine          298   .888   .229   .872   .280
--------------------------------------------------------
Brandon Inge         898   .837   .271   .565   .270
Josh Willingham      505   .823   .295   .562   .255
Royce Clayton        412   .852   .356   .560   .236
Jason Larue          275   .807   .364   .559   .191
Jonny Gomes          374   .732   .385   .558   .206
B.J. Upton           646   .784   .275   .551   .283
Dan Uggla            584   .814   .317   .547   .232
Jeff Mathis          452   .819   .365   .543   .226
Miguel Olivo         304   .838   .487   .527   .223
Wily Mo Pena         329   .747   .384   .519   .190

Left-Handed Hitters Sorted by Bad Ball
Name             Pitches  Square  Fish BadBall   Eye
Luis Castillo        487   .971   .226   .938   .398
Alfredo Amezaga      278   .970   .271   .913   .248
Juan Pierre         1407   .978   .337   .905   .336
Todd Helton          642   .924   .261   .904   .242
Aaron Miles          292   .957   .462   .895   .260
Josh Bard            746   .914   .293   .877   .217
Nick Punto           398   .945   .292   .870   .253
Scott Hatteberg      519   .911   .229   .866   .245
Brian Roberts        416   .951   .300   .865   .303
Sean Casey           619   .946   .409   .857   .357
--------------------------------------------------------
Luke Scott           528   .868   .325   .606   .153
Lance Berkman        627   .844   .308   .598   .143
Nick Swisher        1229   .835   .255   .595   .267
Ryan Howard          712   .793   .368   .575   .244
Carlos Pena          561   .768   .283   .562   .180
Bobby Abreu          586   .918   .194   .545   .336
Jack Cust           1376   .692   .177   .524   .268
Russ Branyan         430   .597   .347   .495   .163
Rob Bowen            310   .647   .249   .489   .350
Jason Smith          289   .736   .483   .453   .241

Right-Handed Hitters Sorted by Eye
Name            Pitches  Square  Fish BadBall   Eye
Angel Gonzalez      434   .894   .252   .754   .435
Jayson Werth        400   .763   .309   .836   .426
Reggie Willits      369   .975   .187   .833   .420
Ramon Martinez      400   .968   .251   .800   .403
Nick Swisher        472   .882   .199   .754   .396
Ryan Zimmerman      543   .896   .375   .680   .394
Reed Johnson        528   .905   .442   .732   .383
J.J. Hardy          708   .890   .279   .841   .367
Rickie Weeks        586   .874   .213   .649   .364
Albert Pujols       829   .956   .294   .839   .364
--------------------------------------------------------
Ty Wigginton        630   .839   .368   .609   .164
Jeff Kent          1188   .910   .274   .665   .163
Ryan Ludwick        458   .839   .363   .657   .154
Jay Payton          352   .920   .399   .740   .153
Jeff Francoeur     1320   .792   .434   .717   .142
Nomar Garciaparra   914   .909   .391   .785   .141
Vladimir Guerrero  1180   .874   .467   .746   .136
Delmon Young        533   .805   .508   .651   .133
Derek Jeter         440   .962   .346   .796   .130
Matt Holliday       643   .845   .399   .667   .124

Left-Handed Hitters Sorted by Eye
Name            Pitches  Square  Fish BadBall   Eye
Joe Mauer           591   .930   .259   .800   .418
Luis Castillo       487   .971   .226   .938   .398
Reggie Willits      995   .931   .206   .770   .376
Darin Erstad        749   .945   .289   .763   .373
Scott Podsednik     488   .914   .260   .849   .366
Sean Casey          619   .946   .409   .857   .357
Danny Richar        452   .925   .312   .732   .355
Rob Bowen           310   .647   .249   .489   .350
Jimmy Rollins       552   .928   .340   .806   .349
David DeJesus       815   .965   .279   .850   .347
--------------------------------------------------------
A.J. Pierzynski     1053   .857  .448   .748   .150
Ross Gload           441   .903  .438   .821   .148
Lance Berkman        627   .844  .308   .598   .143
Rick Ankiel          372   .809  .422   .685   .140
Milton Bradley       562   .817  .229   .654   .138
Carl Crawford        599   .832  .411   .675   .131
Johnny Estrada       290   .971  .493   .838   .125
Miguel Montero       259   .853  .363   .721   .122
Geoff Jenkins        572   .799  .428   .615   .103
Josh Hamilton        435   .858  .349   .711   .102

Graphically Speaking

Finally, as we talked about in the earlier column, the Fish and Eye metrics can be combined in a visual form that more clearly shows where players fall on the continuum of approaches to plate appearances. The resulting plot can then roughly be subdivided into four quadrants using the average values that characterize these approaches. The difference in what follows from what was developed previously is that on the advice of Russell Carleton, among others, I've inverted the values on both axes so that the more desirable outcomes are higher and to the right in the graph.

First, here are all qualifying (250 or more pitches seen) right-handed hitters:

fish eye, righties

Because that's pretty noisy, we'll break it down into individual plots of each quadrant, beginning in the upper left-hand corner, and moving clockwise:

fish eye, clearer

And now for the left-handed hitters:

fish eye, lefties

Once again, the following breaks it down by quadrant:

fish eye, clearer

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