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August 3, 2006

Schrodinger's Bat

Advancing in Context

by Dan Fox

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"My dad taught me that there's three parts: There's hitting, there's defense, and there's baserunning. And as long as you keep those three separated, you're going to be a good player."

--Ken Griffey Jr.

Over the last several weeks we've been looking at advancing on outs (one could even say we're examining "productive outs" but let's not dredge up bad memories). We've gone further than counting the number of bases a runner gains when advancing on ground ball and fly ball outs; instead, we created a framework that allows us to credit each runner for his contribution above and beyond what a typical runner would have done given the same opportunities. And that's really the important point since the situations the runner finds himself in often determine how far and how often he advances.

For example, we've seen in two previous installments that advancing from second to third on a grounder to second base with nobody out is basically a no-brainer (occurring as it does over 97% of the time) while advancing from second to third on a flyball to left field with nobody out is a rare occurrence at only 12%.

To that basic framework we also added the Run Expectancy matrix, which allows us to quantify each runner's contribution given the base/out state he finds himself in, and that in which he left his team after the out was made (with a few adjustments in order to credit the runner with the things more or less under his control). This allows us to convert a runner's contribution to the currency of the game: runs.

When you add it all up, you find that advancing on groundouts (termed Equivalent Ground Advancement Runs or EqGAR) can be worth as many as five to six runs to a player per season (or do you?, more on that a bit later).

Advancing on fly ball outs (Equivalent Air Advancement Runs, EqAAR) can be worth around two runs. Because there have been several questions from interested readers raised as a response to the work that's been presented here, this week we'll provide a quick sync point for folks while exploring the nature of park effects as it relates to the recalculation of EqGAR.

Contextual Matters

Last week I contributed a short piece to the Colorado Springs Sky Sox web site titled "Security Service Field: Context Matters" which provided a gentle introduction to park effects for Sky Sox fans, whose team plays at 6,531 feet. Well, after the column last week introducing EqAAR, reader Cris E. from St. Paul wondered how parks affected these ratings.

"I was curious to hear what you made of MIN having three guys in the bottom ten for 2005 Tagging (with Castillo still in FL). That has to be a park factor thing tied to the short RF wall, right? I surmise that they get hosed on the gimmees to RF because any caught ball is only 327 ft away and they can't go as often."

In regards to this issue I had noted in the previous column that the framework used for the calculations did not in fact use actual distance, but rather simply the type of hit (Fly Ball, Line Drive, or Popup) that served as a kind of proxy for the distance of the batted ball. This is obviously an imperfect measure and as a result I made no allusions that park did not play a role.

This week I went back and took a look at fly advancement by park by the position that fielded the ball because, as Cris notes, many parks are anything by symmetrical. Those familiar with park factors will know that one simple way to calculate them is to compare what happened at the home park with what happened in road games for the team whose home park you're analyzing. By dividing the home value for the metric in question by that calculated on the road you can produce a number that indicates how much the home park influences the metric. At that point if you divide the distance of the ratio from 1.0 by two (since players play only half of their games at home) you end up with a number you can multiply by the metric for the entire season to park adjust it. A value of 1.0 indicates a perfectly neutral park.

This is what was done for EqAAR. I simply calculated the expected and actual air advancement runs in home and road games for 2000 through 2005 for each of the 37 parks in the majors (the 2003 and 2004 data for Montreal conflates Stade Olympique with Hiram Bithorn Stadium, hence they are treated as one park for this analysis while Stade Olympique for 2000-2001 is treated separately) and after calculating the ratio and dividing the effect in half, produced an Air Advancement Park Factor (AAPF).

Rather than produce AAPF values for each season or weight them as is often done with park factors for hitting and pitching, I instead calculated a single AAPF for each park. This was done primarily because the sample sizes for the number of air outs in each season were small enough that there was significant variability from year to year. And even in producing a single AAPF that included all available seasons, some of the values appear a bit out of whack. For the most part, what this means is that for some parks like R.F.K. Stadium and Petco Park where only one or two years of data is available, the values should be digested with a heavy helping of salt.

That said, how did the subject of Cris' query, the Hubert H. Humphrey Metrodome, stack up? Below is a diagram of the park with the AAPF for each field denoted.

chart one

As you can see, Cris seems to be on to something. Air advancement on outs was "helped" by 3% when the ball was caught by the left fielder, 6% when caught by the center fielder, and hindered 3% when the right fielder made the play. These values correspond roughly with what you might expect given the dimensions of the dome.

How about other parks? Take a look at these two.

chart two chart three
The park on the left is obviously Fenway, where the Green Monster decreases the expected EqAAR by around 13%, while center and left field are basically neutral. Coors Field is on the right and increases the expected EqAAR by 10% and 6% in left and center while decreasing it slightly in right. How about one more?

chart four

Yankee Stadium, as you might expect, also seems reasonable as left field increases the EqAAR by 6%, center field by 2% while right field depresses the rate by 2%.

So now we need to apply the AAPF. Like park factors used to adjust offensive metrics like EqA, the higher the AAPF, the more we'll need to adjust the EqAAR down. The lower the AAPF, the more we'll need to adjust it upwards.

In other words, a high AAPF indicates a field and park where it's relatively easy to advance and so we'll raise the expectations for runners, thereby lowering the number of runs above what is expected. Conversely, lower AAPFs will allow us to lower the expectations and therefore raise EqAAR values for players playing in those parks. So below are the new leaders and trailers for park-adjusted 2005 EqAAR along with raw unadjusted EqAAR:

Top 10 for 2005
                    Opps   EqAAR     EqAAR
                             Raw      AAPF
------------------------------------------
Chone Figgins         39    1.79      1.87
Johnny Damon          54    1.66      1.77
Alex Rios             19    1.88      1.74
Ichiro Suzuki         38    1.49      1.56
Tony Graffanino       23    1.65      1.54
Marcus Giles          41    1.75      1.49
Reed Johnson          24    1.49      1.40
Michael Young         32    1.35      1.38
Mike Young            32    1.35      1.38
Ronnie Belliard       32    1.28      1.36

Bottom 10 for 2005
                    Opps   EqAAR     EqAAR
                             Raw      AAPF
------------------------------------------
Vladimir Guerrero     28   -2.35     -2.45
Miguel Olivo          14   -2.09     -2.05
Tadahito Iguchi       33   -2.00     -2.04
Joe Mauer             30   -2.02     -2.02
Victor Diaz            9   -1.85     -1.88
Shannon Stewart       25   -1.74     -1.76
Marlon Byrd           14   -1.70     -1.76
Luis Castillo         37   -1.68     -1.64
Michael Cuddyer       15   -1.55     -1.59
Lance Niekro           9   -1.42     -1.46
You can compare this list with the list of the previous column and you'll notice that the players in the list stay substantially the same with some slight reshuffling. Chone Figgins moves from second to take the top spot, since Angels Stadium of Anaheim has an AAPF slightly below 1.0 for both left and center field, although for right field it is a hefty 1.07. Alexis Rios on the other hand, by virtue of playing at Rogers Centre in Toronto is dinged a bit, as all three outfield positions have AAPFs greater than 1.0.

Alas, and unfortunately for Cris, the park factors don't seem to make a big enough adjustment for the Twins triplets--Joe Mauer, Shannon Stewart, and Michael Cuddyer--who still occupy 4th, 6th, and 9th respectively. In fact, both Cuddyer and Stewart actually go down slightly while Mauer ends up looking just a bit better.

And now here are the adjusted leaders for the entire 2000 through 2005 period:

Top 10 for 2000-2005
                    Opps   EqAAR     EqAAR
                             Raw      AAPF
------------------------------------------
Derek Jeter          252    6.93      6.79
Ray Durham           230    4.49      4.48
Kevin Millar         105    3.58      3.95
Gary Sheffield       188    4.15      3.86
Tom Goodwin           83    3.74      3.66
Carlos Guillen       137    3.26      3.49
Gabe Kapler           94    3.22      3.47
Jose Valentin        104    3.25      3.45
John Olerud          159    3.21      3.45
Albert Pujols        151    3.56      3.45

Bottom 10 for 2000-2005
                    Opps   EqAAR     EqAAR
                             Raw      AAPF
------------------------------------------
Moises Alou          153   -5.25     -5.34
Benito Santiago       78   -4.56     -4.88
D'Angelo Jimenez     110   -4.56     -4.32
Jim Thome            135   -4.49     -4.19
Timo Perez            87   -3.69     -3.81
Jose Offerman         96   -4.07     -3.79
Vladimir Guerrero    162   -4.38     -3.71
Richard Hidalgo      112   -3.45     -3.66
Tim Salmon           138   -3.55     -3.60
Tony Clark            69   -3.43     -3.36
Once again, you see that Kevin Millar gains about four-tenths and Gabe Kapler two-tenths of a run from Fenway Park.

What you can take away from this is that park factors do shuffle the deck a little, but don't have a large effect on the big picture--the various fields in the ballparks tend to even out and most individual players get few opportunities in extreme fields.

Lineup Position and Productive Outs

After the first column introducing EqGAR, I received several questions related to which players may do well in metrics like these based on characteristics other than their baserunning ability. For example, one reader wrote in to say:

"It seems to be that there is a very obvious explanation for this table (published in my recent chat), and it has little to do with base-running skill. Most of these guys have spent a substantial amount of time batting leadoff (none of them on sabermetrically-inclined teams) or batting 8th for National League clubs. As such, I find it highly likely that many of the outs that these runners were advancing on were either sacrifice bunts or balls intentionally pulled to the right side of the infield to advance a runner to third. Sort of a corollary to ESPN's old productive outs."

Yes and No, or rather No and Yes. Keep in mind that the expected number of runs contributed through ground ball and air advancement takes into consideration where the ball was hit and only credits a runner with how far they advance relative to other players in the exact same situations. In other words, a player does not receive any extra credit if the batter behind him is left handed and hits lots of ground balls to the right side. Now, with that said, players who are bunted over more frequently will do slightly better than others since the bunts do count as ground balls.

For example, Mike Matheny was the leader in being on base during a sacrifice bunt (95 times in the six years) which helped him place 26th in the overall rankings at +2.67. Brad Ausmus was second with 81 opportunities during sacrifices and he placed 166th at 0.57.

Because there is an influence here, in a future version we may factor bunt grounders into their own category.

Another Skirmish in the Ground War

Finally, and most importantly, I received some excellent feedback both from within Baseball Prospectus and from readers regarding the table of expected run values used in the column introducing EqGAR. Typical was this response from reader John Proulx:

"The value lost when a runner is thrown out advancing to third on a ground ball isn't (-0.704), but is instead the difference between having a runner on 2nd and one out and having a runner on 1st and one out (since the batter will reach first when he otherwise wouldn't have done so), which is only (-0.152). Potentially, the chance of the batter being safe at first on such a grounder should be factored into the equation as well, but that is, of course, a separate issue."

True enough. As noted, what should have been done is to subtract the run expectancy for a runner on first with one out (0.552) from that for a runner on second with one out (0.704) to produce a value of -0.152. This is the case since if the runner were thrown out advancing to third the runner on first would ostensibly be safe.

The other issue this brings up, however, is an interesting one and one I had considered. The framework is tracking the end base state and the outs for each play, and so we could factor this in as John notes. However, the thought was that the runner doesn't really have any control over whether the defense decides to make a poor decision and gamble or not. The fact that the ball was fielded in the infield and was not credited a hit or an error typically should mean an out somewhere. So I decided not to reward the runner for a fielder's choice that didn't succeed.

But most importantly related to EqGAR is that the feedback from readers forced a reevaluation of the entire derived matrix and an error was discovered in attributing run value for advancing from first to second. Correcting this had the effect of lowering the run value significantly for a scenario in which there were relatively many opportunities. To make a long story short, I now offer a recalculation of EqGAR for 2005 and the leaders for 2000 to 2005.

Top 10 for 2005
Name Opps EqGAR ----------------------------------- Chone Figgins 53 4.52 Juan Pierre 54 3.52 Brady Clark 65 2.63 Jason Ellison 33 2.25 Jose Reyes 52 1.76 Brian Roberts 49 1.67 Willy Taveras 40 1.41 Jose Cruz Jr. 29 1.35 Ryan Freel 22 1.33 Juan Uribe 29 1.30 Bottom 10 for 2005
Name Opps EqGAR ----------------------------------- Travis Hafner 29 -1.43 Emil Brown 31 -1.40 Brandon Inge 57 -1.18 David Ortiz 22 -1.16 Robinson Cano 24 -1.13 Bobby Abreu 26 -1.05 Shea Hillenbrand 25 -1.04 Ivan Rodriguez 21 -1.01 Travis Lee 21 -1.00 Melvin Mora 24 -0.99
Top 10 for 2000-2005
Name Opps EqGAR ----------------------------------- Juan Pierre 279 9.37 Adam Kennedy 206 9.05 Ichiro Suzuki 246 5.31 Ray Durham 196 5.10 Chone Figgins 107 4.94 Alex Sanchez 122 4.79 Tony Womack 201 4.26 Pokey Reese 110 4.22 David Eckstein 233 3.90 Craig Counsell 184 3.82 Bottom 10 for 2000-2005
Name Opps EqGAR ----------------------------------- Paul Lo Duca 154 -4.16 Rafael Palmeiro 129 -3.92 Luis Gonzalez 133 -3.41 J.T. Snow 138 -3.28 Ryan Klesko 117 -3.20 Dmitri Young 132 -3.14 Bobby Abreu 148 -3.10 Jim Thome 149 -3.04 Javier Lopez 137 -3.01 Paul Konerko 142 -2.98
As you can see, the recalculation lowers the EqGAR by a significant amount. For example, Juan Pierre falls from 7.52 to 3.52 while Figgins is affected to a smaller degree moving from 4.90 down to 4.52. You can also see the difference made by changing the calculation discussed above as the trailers move from the -2.5 to -3.5 range to just -1.0 to -1.5.

From a cumulative perspective, Pierre and Adam Kennedy stand head and shoulders above the rest. Kennedy was credited with a negative run value in just five of his 206 opportunities while Pierre was assigned negative credit just four times in 279 opportunities.

Adding it Up

As you look at the above lists, one of the things that starts to become clear is that a player can help or hurt his team in a small way through advancing on outs. For example, Figgins at +1.87 EqAAR and +4.52 for EqGAR puts him at +6.39 runs for 2005. In the coming weeks, we'll add advancing on hits, stolen bases, and perhaps a few other goodies in order to round out the picture.

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