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September 20, 2007

Schrodinger's Bat

Taking Advantage

by Dan Fox

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"We don't have a 40 home run guy anymore... We have to reduce mistakes, take advantage of every opportunity we get... We need to improve on moving runners over from second to third and our base running. There can be an eight- to 10-game swing in a season just from base running."
--Syd Thrift, in 2001, when he served as the Orioles Vice President of Baseball Operations

Tuesday night, the Dodgers and Rockies squared off at Coors Field in the second game of a day-night doubleheader. Despite the rather long odds of reaching the playoffs--as calculated by the miracle that is our Playoff Odds Report--both teams still had that glimmer of hope. After Jeff Francis struck out 10 in game one to lead the Rockies to a 3-1 victory, the Dodgers were looking to get off to a quick start to salvage a split.

In the first inning, Juan Pierre led off for the Dodgers and dribbled a ball past Rockies starter Mark Redman for an infield hit. The lefty Redman attempted to hold Pierre, owner of 59 stolen bases, close to the bag, but ended up committing a balk, advancing Pierre to second. Minutes later, Tony Abreu singled up the middle to score Pierre and put the Dodgers on the board. They would go on to score three in the inning, but eventually had their day ruined on a walk-off two-run homer by Todd Helton to seal the 9-8 victory for Colorado.

I recite this little vignette because it calls to mind a column I wrote back in December, where we discussed the best baserunners of 2006. In addition to walking through the four baserunning metrics developed in the summer of 2006, that column also explored the baserunning metrics written about by Bill James in The Bill James Handbook 2007. In particular, I noted that James (or actually Baseball Info Solutions) includes a category called "bases taken," a category which:

...includes a couple of items that I had not considered but, James convinced me, are worthy of consideration. A moment's thought is enough to realize that advancing on wild pitches and passed balls and perhaps even balks are categories that should be included in a total measure of baserunning... They were omitted from the metrics I developed but will be included in the future. However, I'm a little hesitant to include advancing on defensive indifference. While it probably is correlated with speed and, therefore, baserunning, the value of advancing in those scenarios is questionable, and the opportunities to do so coupled with the difficulty of judging when a runner is in such a situation; my conclusion is that including those occasions makes little sense.

The case of Pierre versus Redman is an example where it could certainly be argued that a baserunner "coaxed" a balk from a pitcher and so--just as with advancing on hits and ground outs--it's an event that should be credited to the baserunner. So today, as promised in that earlier column, we'll add a new metric to our baserunning toolbox that not only includes balks, but also includes other mistakes like wild pitches and passed balls.

The Methodology

As with the other metrics we've developed (EqHAR, EqGAR, EqAAR, EqSBR), this new metric (dubbed Equivalent Other Advancement Runs [EqOAR]) is based on the run expectancy matrix. As such, it credits runners with the change in the expected number of runs from that point forward in the inning when they advance on wild pitches, passed balls, and balks, based on which bases are occupied and how many outs there are at the time of the play.

To illustrate, we'll use Curtis Granderson of the Tigers, who in 2006 advanced from first to second three different times on balks. On June 16 against the Cubs, he was on first in the top of the fifth with nobody out. After three attempted pickoffs and a pitchout, Cubs pitcher Angel Guzman balked Granderson to second. To credit Granderson for the rattling of Guzman and the advancement to second, we take the difference between the run expectancy before the balk (runner on first with nobody out) and the run expectancy once Granderson reached second (runner on second and nobody out). Since the run expectancy matrices we're using are based on actual events and are not derived by a model, the values we plug in are three-year averages; in this case, the average run expectancy with a runner on first and nobody out was 0.913, and with a runner on second with no outs it was 1.15. The difference between these two values is .237, so we credit Granderson with about a quarter of a run.

This exercise is then performed for every event during the season that involves a wild pitch, passed ball, or balk where the base in front of the runner was not occupied. The total number of runs contributed above what would be expected is then aggregated into a raw EqOAR. It should be noted that a negative run value will be credited if the runner is thrown out. However, this is a rather rare event, since when a passed ball or wild pitch is credited, another runner has necessarily advanced; in using plays scored as wild pitches or passed balls we can only detect situations in which the lead runner is thrown out. To account for situations where the only runner on base is thrown out attempting to advance on a ball that gets away, we also look at plays designated as "out advancing" and appropriately debit the runner who was thrown out based on the change in run expectancy.

As some readers may suspect, simply totaling the run values using this technique only gets us halfway there. We also need to account for the opportunity that each runner had and further adjust their totals based on that opportunity. In The Handbook, James hints that this should be considered when discussing Ichiro Suzuki, who he credits with 33 bases taken but doesn't make any adjustment for opportunities. In order to do this here, we calculate the number of times a batter came to the plate with the runner on base in the scenarios under consideration, and break them down by base state and number of outs. By totaling this information for all runners in a given year, we can find the average number of plate appearances per attempted runner advancement, as well as the average number of runs credited for each attempt. For example, the matrix that includes all data from 2000 through 2006 is shown below:


Base Outs  Opps  AttAdv     Adv    Adv%  AttAdv/Opp R/Adv
----------------------------------------------------------
 1    0   11571     242     230   .950      47.8    .190
 1    1   14159     313     307   .981      45.2    .165
 1    2   15072     365     355   .973      41.3    .094
----------------------------------------------------------
 2    0    6478     142     138   .972      45.6    .248
 2    1   10854     250     245   .980      43.4    .229
 2    2   13982     321     319   .994      43.6    .035
----------------------------------------------------------
 3    0    2981      39      29   .744      76.4    .061
 3    1    8000     131     111   .847      61.1    .253
 3    2   10366     172     144   .837      60.3    .580

Opps is the number of plate appearances with a runner on the given base and without a lead runner, AttAdv are the attempted number of advancements, Adv are the successful advancements, Adv% is the success rate, AttAdv/Opp is the attempted advancements per opportunity, and R/Adv is the average number of runs credited per attempted advancement.

As you look at the table, it's probably not that surprising that advancement attempts are slightly more frequent with two outs, especially when the runner is on third, and that the success rate is lowest for runners on third. This latter fact might be explained by runners incurring more risk when a run is just 90 feet away: the ball is in closer proximity to the plate, making it easier for the catcher and pitcher to make a play.

Armed with this table (or actually tables for each individual season), we can now adjust the aggregate run value calculated earlier by essentially removing the league average number of advancement attempts and their associated run values. The end result is that players who were simply on base a lot don't receive extra credit. To illustrate this idea, we can come back to Curtis Granderson, whose raw EqOAR came to 2.16 for 2006. He advanced 14 times in 404 opportunities, which is overall a good rate, equivalent to once every 29 opportunities, against the league average of once every 47 opportunities. Even so, accounting for the league average number of advancements just in those scenarios in which he advanced, his raw total shrinks from 2.16 to 1.30 runs. But in addition, there were four other scenarios in which Granderson did not advance at all, encompassing 140 of his opportunities. Those scenarios prove to be the most costly--by not advancing with one out when he occupied second and never advancing when he was on third, he's dinged -0.83 runs, bringing his overall total down to +0.47 runs. Lest you think that all runners are punished so severely, rest assured that Granderson's is a more severe case; by not advancing when on third base, he's debited with the higher opportunity cost, as indicated in the table above.

Ichiro Suzuki, who led in James' system, advanced 12 times and saw his raw EqOAR of +2.53 shaved to +0.44 runs once the context of those advancements was considered. This ranked him 93rd out of 785 players. Overall, since 2000 he is also below average. Incidentally, this once again underscores the puzzling fact (also mentioned by James) that Suzuki scores more poorly than one would think in most of the baserunning metrics, with the exception of advancing on ground outs, where I have him as a positive contributor in all seasons from 2000 through 2006.

The Leaders and Trailers

With that, we're now ready to show the top and bottom five in EqOAR for each year stretching back to 2000:


Player              Year   Adv  AdvOpps   Opps    EqOAR
Troy Glaus          2000    11      12     345     2.98
J.D. Drew           2000     9       9     268     2.24
Johnny Damon        2000    19      20     493     2.12
Jay Bell            2000    13      13     364     1.95
Corey Koskie        2000    10      10     298     1.79
----------------------------------------------------------
Nomar Garciaparra   2000     3       3     374    -1.17
Darin Erstad        2000     3       5     454    -1.37
Phil Nevin          2000     4       5     302    -1.41
Dave Martinez       2000     4       5     374    -1.47
Tony Womack         2000     4       5     350    -1.71
Mike Sweeney        2000     4       5     428    -1.89

Troy Glaus scored so well in 2000 since he was fortunate to advance multiple times from third to home, where the gain is the greatest. You'll notice that most of the trailers were caught at least once, but were more hurt by the fact that they simply didn't advance very often.


Player              Year   Adv  AdvOpps   Opps    EqOAR
Geoff Blum          2001     8       8     249     2.12
Craig Biggio        2001    14      14     456     1.87
Mike Piazza         2001     7       8     290     1.62
Einar Diaz          2001     8       8     258     1.61
A.J. Pierzynski     2001    12      12     201     1.61
----------------------------------------------------------
Albert Pujols       2001     5       7     346    -1.06
Mark Little         2001     0       2      65    -1.14
Travis Fryman       2001     2       3     194    -1.17
Henry Blanco        2001     1       2     144    -1.18
Jolbert Cabrera     2001     2       3     157    -1.34
Mike Cameron        2001     3       5     274    -1.84


Player              Year   Adv  AdvOpps   Opps    EqOAR
Luis Castillo       2002    13      13     431     2.57
Cristian Guzman     2002    12      12     328     2.34
Johnny Damon        2002    16      16     379     2.18
Felipe Lopez        2002     9       9     140     1.95
Roger Cedeno        2002    11      11     306     1.85
----------------------------------------------------------
Milton Bradley      2002     1       2     163    -1.28
Juan Uribe          2002     4       5     288    -1.30
Bobby Abreu         2002     4       5     371    -1.46
Steve Finley        2002     0       1     286    -1.98
Luis Gonzalez       2002     5       7     332    -1.98


Player              Year   Adv  AdvOpps   Opps    EqOAR
Ray Durham          2003    16      16     308     2.72
Mike Lowell         2003    11      11     207     2.17
Garret Anderson     2003    12      12     337     2.11
Ivan Rodriguez      2003    12      12     323     2.03
Carl Everett        2003    12      12     412     1.95
----------------------------------------------------------
Alex Sanchez        2003     5       6     304    -1.52
Shawn Green         2003     2       3     366    -1.63
Chris Singleton     2003     2       3     182    -1.81
Paul Konerko        2003     2       3     187    -1.91
Edgardo Alfonzo     2003     3       6     308    -2.34


Player              Year   Adv  AdvOpps   Opps    EqOAR
Carl Crawford       2004    17      17     395     2.57
Craig Biggio        2004    16      17     422     2.15
Michael Young       2004     9      10     405     1.97
John Buck           2004     6       6      95     1.94
Angel Berroa        2004     8       8     297     1.80
----------------------------------------------------------
Cesar Izturis       2004     2       2     409    -1.37
Lance Berkman       2004     6       7     384    -1.37
Todd Zeile          2004     2       3     203    -1.54
Mike Cameron        2004     1       2     194    -1.81
David Bell          2004     2       3     271    -1.97


Player              Year   Adv  AdvOpps   Opps    EqOAR
Juan Pierre         2005    15      15     438     2.93
Angel Berroa        2005    10      10     306     2.65
Tony Graffanino     2005    13      13     309     2.61
Mark Teahen         2005    12      12     247     2.03
Terrence Long       2005     7       7     236     1.99
----------------------------------------------------------
Brent Abernathy     2005     0       1      29    -1.19
Tadahito Iguchi     2005     6       8     300    -1.24
Ben Broussard       2005     0       1     208    -1.38
Michael Cuddyer     2005     4       5     236    -1.53
Michael Young       2005     1       2     404    -1.64


Player              Year   Adv  AdvOpps   Opps    EqOAR
Freddy Sanchez      2006    15      15     383     2.14
Damian Jackson      2006     5       5      61     1.94
Grady Sizemore      2006    16      17     466     1.94
Alex Gonzalez       2006     5       5     199     1.80
Orlando Hudson      2006     9       9     321     1.70
----------------------------------------------------------
Sean Casey          2006     1       2     229    -1.31
Matt Holliday       2006     6       7     334    -1.35
Josh Barfield       2006     2       3     313    -1.40
Eric Chavez         2006     2       3     265    -1.67
Nick Johnson        2006     6      10     388    -1.76

In perusing these lists, you'll notice that Juan Pierre in 2005 had the single highest season total at 2.93 runs, while Edgardo Alfonzo was at the bottom at -2.34 runs in 2003. The range then is typically between +2.5 and -2.0 runs for individuals. In that sense, EqOAR has an individual seasonal magnitude similar to but slightly smaller than that of advancement on fly ball outs (EqAAR):


Typical Seasonal Range
Metric     Min    Max
EqOAR    -2.00   2.50
EqGAR    -1.50   4.00
EqAAR    -3.00   2.00
EqSBR    -6.00   5.00
EqHAR    -5.00   5.00

You'll also probably note that while you can begin to see some patterns with faster runners like Pierre, Carl Crawford, and Luis Castillo occupying the top of the lists, and Henry Blanco, Luis Gonzalez, and Paul Konerko at the bottom, the results from year to year are not very consistent. As with EqAAR, this is both a product of small sample size--with runners rarely getting more than 15 opportunities to advance per season--and the fact that those opportunities are not evenly distributed in terms of impact on equivalent runs. The case of Troy Glaus in 2000 illustrates the point; he advanced five times in six opportunities from third to home when on third with two outs. Since scoring from third with two outs is the most impactful advancement event (as evidenced by the matrix discussed previously), he was able to record a raw EqOAR of 3.55 runs. The fact that he failed to advance in other scenarios that weren't as costly wasn't enough to bring his total back towards zero. The end result is that there are no statistically significant year-to-year correlations for runners with 100 or more opportunities.

Over the past seven years as a whole, the picture becomes a little different, as shown in the following table listing the aggregate leaders and trailers for the entire period:


Player            Adv   AdvOpps  Opps    EqOAR
Juan Pierre        72      76    2789    6.12
Johnny Damon       79      80    2939    6.07
Craig Biggio       61      63    2627    5.62
Rafael Furcal      69      73    2554    5.35
Grady Sizemore     34      35     942    4.51
Corey Patterson    47      53    1294    4.48
Edgar Renteria     58      58    2398    4.44
Angel Berroa       29      30    1213    4.24
Tony Graffanino    47      48    1382    3.73
Luis Castillo      64      69    2821    3.72
------------------------------------------------
Chris Singleton    17      19     973   -2.76
Cesar Izturis      12      12    1303   -2.79
Darin Erstad       34      36    2105   -2.83
Phil Nevin         25      26    1654   -2.99
Sammy Sosa         17      19    1651   -3.01
Brian Schneider    12      15     983   -3.04
Aaron Boone        19      22    1438   -3.13
Milton Bradley     15      16    1241   -3.41
Eric Chavez        28      29    2025   -3.91
Paul Konerko       32      36    1970   -4.81

Here, we can clearly discern that the runners on the top of the list do indeed fit our preconceived notions more than the runners on the bottom.

Another Piece of the Puzzle

In the big picture, the addition of advancement runs through wild pitches, passed balls, and balks clearly doesn't provide anything earth-shattering in terms of new knowledge. The fact that this metric varies more than the others and is smaller in magnitude means that, by itself, it isn't all that helpful in terms of being actionable or reflecting skill to a high degree. However, it does add yet another small piece to the bigger puzzle of measuring baserunning, and helps to illuminate the overall contribution that baserunners make in terms of runs and, ultimately, wins.

Related Content:  Paul Konerko,  The Who,  Juan Pierre,  Balk,  2003,  2002,  Luis Castillo,  Baserunning,  Juan Abreu,  Base 3

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