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September 7, 2006

Schrodinger's Bat

The Running Man

by Dan Fox

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"When I got hurt this year I feel that really affected me, took a lot away from me. I wasn't able to steal bases. Every time I hit the ball in the hole I wasn't able to run. I just couldn't run. It's kind of frustrating because you feel like you would have done a better job. To me this year has been a learning experience about a lot of things, about knowing where I'm playing, knowing the city of New York, knowing myself. I feel good with it."
--Carlos Beltran, on his 2005 season

So we've finally reached a turning point in our series on quantifying baserunning. Since mid-July we've developed a methodology and framework for crediting baserunners for advancing on ground outs (Equivalent Ground Advancement Runs, or EqGAR), advancing on outs in the air (Equivalent Air Advancement Runs, or EqAAR), and attempted stolen bases as well as pick offs (Equivalent Stolen Base Runs, or EqSBR). This week we'll look at total picture and evaluate which players got the most and least from their legs over the past six years.

Adding to the Toolbox

To get those readers up to speed who may not have seen this framework before, the final piece of the puzzle is crediting runners with advancing on hits. To that end we can use the same basic methodology as we did when creating the other metrics by relying on the Run Expectancy matrix. Simply put, we'll credit or debit runners for changes in Run Expectancy in the following scenarios:

  • Runner on first, second not occupied, and the batter singles
  • Runner on second, third not occupied, and the batter singles
  • Runner on first, second not occupied, and the batter doubles
In each scenario we create a table that shows how often runners typically advance to each subsequent base or get thrown out; this will be broken down by the number of outs, handedness of the batter, and the position of the fielder who fielded the ball.

As we saw with advancing on ground and air outs, the probabilities of advancing and the number of bases a runner can advance change dramatically as the number of outs and the position of the fielder change. For example, when a batter singles with nobody out and a runner on second, the runner reaches third around 55% of the time and scores 45% of the time. With two outs, however, those probabilities change to 6% and 89%, respectively, with an increasing percentage of the runners getting thrown out (less than 1% up to 5%).

Totaling the credit assigned to each opportunity (and not crediting the runner for advancing the minimum number of bases) for players and teams allows us to assign a number of theoretical runs above and beyond what a typical player or team would have contributed given the same opportunities. Finally, as we did when looking at advancing on outs in the air, we apply a park factor in order to take into account the fact that at some parks it is easier or more difficult to advance given the dimensions or configuration (wall height for example).

Some readers will recall that this is essentially the framework I published last fall in an essay in The Hardball Times Baseball Annual 2006 with the metric called Incremental Runs (IR), and its associated rate statistic Incremental Run Percentage (IRP). Since that time, I've made a couple small refinements to the framework and have recalculated the park factor to equally weight all of the previous six years worth of data in order to smooth it out a bit. Along with those changes, we'll also take this opportunity to rechristen IR, Equivalent Hit Advancement Runs (EqHAR) so that it fits nicely into our toolbox.

It should be mentioned that EqHAR is essentially the same in both methodology and in what it attempts to quantify as James Click's metric discussed in the 2005 Baseball Prospectus. Both systems were being developed at the same time.

So then let's take a look at the leaders and trailers in EqHAR for 2005 as well as the individual leader and trailer for each of the six seasons in our study. The table below lists the number of opportunities, the number of times the runner was thrown out advancing, the number of runs we credited them with, and a rate statistic that removes the bias associated with a greater number of opportunities.

2005 Leaders and Trailers in EqHAR
Name                 Opp      OA   EqHAR    Rate
Carlos Beltran        45       1    3.53    1.66
Robinson Cano         54       1    3.36    1.49
Edgar Renteria        49       0    3.21    1.37
Grady Sizemore        59       0    3.14    1.31
Darin Erstad          59       0    2.99    1.38
David DeJesus         50       0    2.99    1.47
Scott Podsednik       45       0    2.98    1.43
Rafael Furcal         52       0    2.94    1.38
Julio Lugo            58       0    2.85    1.40
David Wright          41       0    2.82    1.39
------------------------------------------------
Pat Burrell           34       4   -5.60    0.17
Luis Gonzalez         44       4   -5.33   -0.05
Lance Berkman         37       3   -4.56    0.00
David Ortiz           41       1   -4.12    0.25
Bengie Molina         34       0   -4.06    0.22
Mark Loretta          46       4   -4.02    0.58
Matt Lawton           49       3   -3.70    0.40
Kevin Millar          47       1   -3.59    0.34
Aramis Ramirez        45       2   -2.82    0.57
Rickie Weeks          30       5   -2.81    0.46
Yearly Leaders and Trailers in EqHAR
Year    Name                 Opp      OA   EqHAR    Rate
2000    Luis Castillo         57       0    4.78    1.52
2001    Juan Pierre           41       0    4.04    1.81
2002    David Eckstein        60       0    3.66    1.52
2003    Raul Ibanez           55       0    4.75    1.54
2004    Vernon Wells          34       0    4.90    1.73
2005    Carlos Beltran        45       1    3.53    1.66
--------------------------------------------------------
2000    Joe Randa             50       2   -3.91    0.42
2001    Adrian Beltre         25       4   -4.59   -0.14
2002    Frank Thomas          40       4   -5.17    0.08
2003    Jim Thome             51       3   -5.15    0.49
2004    Bill Mueller          47       3   -5.17    0.29
2005    Pat Burrell           34       4   -5.60    0.17
From these lists it's apparent that at the extremes EqHAR falls roughly in the +5 to -5 range, or the equivalent of about one win, putting it in the same category as EqSBR in terms of magnitude, as shown below.
Magnitude of Baserunning Metrics / Single Player, Single Year

Metric Min Max EqGAR -1.50 4.00 EqAAR -3.00 2.00 EqSBR -6.00 5.00 EqHAR -5.00 5.00

Interestingly, EqSBR actually has a slightly larger range on the negative side since there are more potential opportunities for stolen base attempts coupled with the fact that some players don't know when to quit (see Guerrero, Vladimir). Both EqSBR and EqHAR, however, have larger ranges than EqGAR and EqAAR. This reflects two primary factors. First, there are a greater number of opportunities available to runners in terms of stolen base attempts and advancing on hits. The leaders in EqHAR and EqSBR typically had more than 50 opportunities in the 2000-2005 time period while those for EqGAR had slightly fewer; for EqAAR it's in the 30s.

Second, the success rates for EqHAR and EqSBR are such that good (or bad) baserunners have a bit more room to distance themselves from the pack. For example, with EqAAR almost all runners score from third on fly balls and so the difference between a good runner and one that is merely average is compressed to less than 5%. On the other hand, with EqHAR a good runner may take 16 to 20% more bases than an average one in a given scenario (for example when advancing from first to third on a single).

But as we mentioned earlier in this series, those seasonal ranges don't mean that the best players and worst baserunners over the six year span will be credited with -30 to +30 runs. As with any metric, part of the derived value simply reflects random variation and so that variation--combined with the fact that the same players don't necessarily end up at the top and bottom each season--means that over the entire period that span between the leaders and trailers is on the order of 25 to 30 runs, or three wins:

Leaders and Trailers in EqHAR for 2000-2005
Name                 Opp      OA   EqHAR    Rate
Juan Pierre          315       4   15.22    1.41
Luis Castillo        331       6   14.64    1.32
Rafael Furcal        272       3   12.09    1.33
Ray Durham           249       0   11.87    1.37
Mike Cameron         188       2   11.59    1.37
Darin Erstad         288       6   11.43    1.23
Jay Payton           201       3   11.35    1.36
Carlos Beltran       253       1   11.23    1.27
David Eckstein       280       4   10.98    1.30
Cristian Guzman      226       3   10.36    1.37
------------------------------------------------
Edgar Martinez       178       3  -12.50    0.58
Rafael Palmeiro      231       9  -11.50    0.63
Dmitri Young         181      10  -11.04    0.60
Richie Sexson        153       6  -10.83    0.53
Juan Encarnacion     201      12  -10.73    0.66
Carlos Delgado       237       8  -10.71    0.73
Rich Aurilia         185       9  -10.48    0.62
David Ortiz          172       5  -10.36    0.63
Bill Mueller         168       9   -9.91    0.58
Luis Gonzalez        266      10   -9.58    0.77
Finally, and as mentioned previously, EqHAR also has a rate stat (calculated as the ratio of actual runs to expected runs); if we want to see which runners performed the best regardless of the quantity of opportunities (and remember we've already controlled for the quality of those opportunities by comparing what they did against the league average for each situation they found themselves in and then park adjusting the results) we can rank them according to rate:
Leaders and Trailers in EqHAR rate for 2000-2005
(100 or more opportunities)
Name                 Opp      OA   EqHAR    Rate
Timo Perez           100       1    4.86    1.42
Juan Pierre          315       4   15.22    1.41
Raul Mondesi         126       1    6.25    1.38
Scott Podsednik      132       1    7.03    1.37
Mike Cameron         188       2   11.59    1.37
Cristian Guzman      226       3   10.36    1.37
Ray Durham           249       0   11.87    1.37
Jay Payton           201       3   11.35    1.36
Miguel Cairo         125       1    5.33    1.36
Felipe Lopez         110       1    5.35    1.34
------------------------------------------------
Richie Sexson        153       6  -10.83    0.53
Kevin Millar         163       3   -9.38    0.56
Edgar Martinez       178       3  -12.50    0.58
Bill Mueller         168       9   -9.91    0.58
Dmitri Young         181      10  -11.04    0.60
Bengie Molina        140       1   -9.44    0.61
John Olerud          130       5   -6.86    0.62
Javy Lopez           104       4   -5.56    0.62
Rich Aurilia         185       9  -10.48    0.62
Rafael Palmeiro      231       9  -11.50    0.63
Of active players with fewer than 100 opportunities Robinson Cano (1.49), David DeJesus (1.46), and Ryan Freel (1.46) also all come out very well.

This list once again highlights the situation where a player like Cano does well in one metric but poorly in others. In Cano's case, his EqHAR was among the leaders in 2005 at 3.36, while his EqGAR, EqAAR, and EqSBR values were at -1.13, -0.93, and -1.5 respectively, putting him on the negative side (-0.21) when you add it all up. This may reflect the fact that different skills are required to do well in the different metrics (for example, judgment may be more important in EqGAR and EqSBR than in EqHAR where sheer speed is what counts most), or simply that random variation and small sample size is at work--after all, Cano had just 4 stolen base attempts in 2005. I would bet on a mix of the two, although it will be interesting to see how Cano stacks up this season.

And because I know I'll be asked, Bobby Abreu and Juan Encarnacion lead all players in getting thrown out on the bases in these scenarios at 12, with Lance Berkman and Matt Lawton close behind at 11.

Contributing with their Legs

Finally, we can now provide a more complete picture of baserunning. Today we'll focus on individuals, and next week we'll take it to the team level. So first, here are the leaders and trailers for 2005:

2005 Leaders and Trailers in Total Baserunning
Name                 Opp   EqGAR     Opp   EqAAR     Opp   EqSBR     Opp   EqHAR   Total
Chone Figgins         53    4.52      39    1.79      80   -0.30      58    2.27    8.29
Jose Reyes            52    1.76      33    1.34      77    1.73      50    1.98    6.81
Juan Pierre           54    3.52      30   -0.07      75    0.82      56    2.25    6.52
Alfonso Soriano       31   -0.08      45   -0.07      32    4.92      42    1.10    5.86
Jason Bay             20    0.82      29    1.02      22    2.39      54    1.39    5.63
Marcus Giles          27   -0.59      41    1.75      18    2.04      42    2.29    5.49
Johnny Damon          42    0.66      54    1.66      19    2.84      66    0.04    5.20
Carlos Beltran        19    1.16      22    0.24      22    0.14      45    3.53    5.07
Rafael Furcal         41    0.32      38   -0.71      57    2.36      52    2.94    4.90
Ichiro Suzuki         47    0.55      38    1.49      42    1.23      63    1.34    4.61
----------------------------------------------------------------------------------------
Pat Burrell           19   -0.48      25   -0.69       1   -0.46      34   -5.60   -7.23
Brad Wilkerson        48   -0.80      26    0.09      19   -6.23      43    0.31   -6.64
Matt Lawton           35   -0.12      38   -0.30      28   -1.91      49   -3.70   -6.03
David Ortiz           22   -1.16      34   -0.73       1    0.09      41   -4.12   -5.92
Mark Loretta          20   -0.33      29    0.02      12   -1.29      46   -4.02   -5.62
Bengie Molina         14    0.51      16   -0.80       2   -1.07      34   -4.06   -5.41
Oscar Robles          20   -0.59      19    0.46       8   -4.26      26   -0.23   -4.63
Luis Gonzalez         16   -0.47      32    1.44       4   -0.03      44   -5.33   -4.39
Jeromy Burnitz        17   -0.28      35    0.41      12   -4.02      61   -0.40   -4.29
Carlos Lee            18   -0.78      21   -1.27      18    0.61      29   -2.64   -4.07
Again, you can see that although some players do well in all categories (Jose Reyes and Jason Bay, for example) there are others who excel in just one, like Alfonso Soriano. You'll also notice that in total the player who comes out on top contributes about 7 runs and those who do poorly cost their teams about 7 runs; historically, as shown in the next table, the leaders and trailers have a span of more like -8 to +8.
Yearly Leaders and Trailers in Total Baserunning
Year    Name               Opp   EqGAR    Opp   EqAAR    Opp   EqSBR   Opp   EqHAR   Total
2000    Tom Goodwin         41    0.94     34    1.38     66    4.66    40    3.45   10.43
2001    David Eckstein      44    1.17     41    0.35     33    2.68    51    3.75    7.95
2002    Derek Jeter         34   -0.61     39    1.55     35    4.20    56    2.70    7.84
2003    Scott Podsednik     38    1.66     29    1.21     54    3.14    44    3.16    9.16
2004    Tony Womack         46    1.59     33    0.68     33    2.12    55    2.55    6.94
2005    Chone Figgins       53    4.52     39    1.79     80   -0.30    58    2.27    8.29
------------------------------------------------------------------------------------------
2000    Vladimir Guerrero   27   -0.07     40   -1.00     22   -4.87    30   -1.77   -7.72
2001    Doug Mientkiewicz   31   -0.75     25    0.62      9   -3.23    43   -3.50   -6.86
2002    Deivi Cruz          27   -0.97     18   -2.08      4   -1.56    31   -0.75   -5.35
2003    D'Angelo Jimenez    30   -1.11     24   -3.51     19   -1.97    52   -1.04   -7.62
2004    Jim Thome           19   -0.41     28   -3.04      2   -1.41    60   -3.38   -8.24
2005    Pat Burrell         19   -0.48     25   -0.69      1   -0.46    34   -5.60   -7.23
To wrap up, we want to provide a first order answer to the question of just who may be the best and worst total baserunners in baseball since 2000. And so without further ado, the following table lists the top and bottom 10 in total runs from the combination of all four metrics:
2000-2005 Leaders and Trailers in Total Baserunning
Name                 Opp   EqGAR     Opp   EqAAR     Opp   EqSBR     Opp   EqHAR   Total
Carlos Beltran       126    0.66     169    1.80     204   11.75     253   11.23   25.44
Derek Jeter          218   -0.51     252    6.93     149   10.59     317    8.09   25.09
Johnny Damon         258    1.78     265    3.15     217    9.03     322    9.40   23.36
Rafael Furcal        224    3.17     192    2.58     246    2.76     272   12.09   20.60
Tom Goodwin           90    2.59      83    3.74     147    5.15      97    7.43   18.91
Juan Pierre          279    9.37     204    2.91     378   -8.85     315   15.22   18.64
Tony Womack          201    4.26     178    3.18     219    2.68     224    7.65   17.77
Jimmy Rollins        212    3.49     180    3.28     223    1.69     243    8.62   17.08
Scott Podsednik      126    2.43     103    1.95     227    4.52     132    7.03   15.94
Darin Erstad         176    1.04     195   -2.23     136    4.10     288   11.43   14.35
----------------------------------------------------------------------------------------
Jorge Posada         158   -2.67     149   -1.46      26   -8.08     199   -8.18  -20.39
Jim Thome            139   -3.12     129   -4.07      10   -3.74     222   -8.22  -19.16
Carlos Delgado       141   -1.06     177   -3.55       8   -3.65     237  -10.71  -18.95
Richie Sexson        104   -1.60     100   -1.73      14   -3.78     153  -10.83  -17.94
Paul Lo Duca         154   -4.16     133   -2.91      30   -6.09     190   -4.07  -17.23
Luis Gonzalez        133   -3.41     170    0.02      36   -4.00     266   -9.58  -16.97
Edgar Martinez       113   -2.97     142   -0.56      12   -0.55     178  -12.50  -16.58
Dmitri Young         132   -3.14     119    2.62      22   -4.95     181  -11.04  -16.51
Matt Lawton          185    1.65     198   -3.48     164   -9.32     258   -5.13  -16.28
Rafael Palmeiro      129   -3.92     159    0.22      15   -0.90     231  -11.50  -16.10
Juan Encarnacion     145   -1.61     145    1.60     113   -5.16     201  -10.73  -15.90
Carlos Beltran came out on top at +25.44 by virtue of his ability to steal bases at a high percentage and advance on hits. Meanwhile, Jorge Posada had trouble in all departments and ended up at -20.39. You'll notice that had Juan Pierre at least come out neutral in EqSBR he would have taken the top spot. But still, the difference between the top and bottom is on the order of four to five wins, a difference far smaller than that between the best and worst offensive players and best and worst fielders. The upshot is that while good baserunning pays off and is repeatable (more on that next week) to a certain extent, its primary uses from an offensive perspective are probably more strategic than general--even the best baserunners seemingly cannot contribute a significant number of wins in the long haul. Not a surprising conclusion, to be sure, but one that is often forgotten.

Interestingly, although Beltran's injury last season affected his stolen bases and despite his comments to the contrary, it didn't appear to have quite the same effect on other parts of his running game as his totals from each season show:

Year      Opp   EqGAR     Opp   EqAAR     Opp   EqSBR     Opp   EqHAR   Total
2000        7   -0.11      12    0.10      14    1.29      33    0.30    1.57
2001       29    0.20      31   -0.09      34    3.20      43    0.75    4.06
2002       18    0.38      26   -0.88      45   -0.33      39    2.47    1.64
2003       28   -0.80      31    1.80      44    3.69      42    2.40    7.08
2004       25   -0.17      47    0.63      45    3.76      51    1.79    6.01
2005       19    1.16      22    0.24      22    0.14      45    3.53    5.07
Alas, by adding up the metrics as we've done here, those on this list are heavily influenced by the number of their opportunities. To correct for this, next week we'll develop a rate statistic that encompasses all four metrics, and we'll discuss the relative importance of each, and perhaps even delve into aging patterns, how teams stack up, and any other interesting avenue we happen to wander down.

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