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September 14, 2006

Schrodinger's Bat

The Whole, the Sum, and the Parts

by Dan Fox

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"This is not just a day off. Good baserunning is just as important as good hitting to win baseball games."-Lou Piniella, Mariners manager, on sitting infielder Jeff Cirillo following baserunning errors in 2002

When last we were together, we added up the various baserunning metrics we've been formulating all summer to come up with a total number of theoretical runs contributed on the bases for individual players. This included runs from advancing on ground and air outs, advancing on hits, and runs contributed from stolen base attempts (and pickoffs).

What we found was that in a single season a baserunner may contribute from 8-10 runs over and above what would be expected, or may forfeit an equal number, meaning that the spread between the best and worst runners was on the order of two wins. Over the course of the six seasons that were examined (2000-2005), a runner may contribute up to 25 runs and give up about 20. Using those raw numbers, we christened Carlos Beltran the best baserunner of the past six years at +25.44 runs, and Jorge Posada as the worst at -20.39.

However, we left unexamined two things-team-level performance, and what these numbers tell us about baserunning in general. As Socrates taught us, "the unexamined life is not worth living", so we'll delve into those topics this time around.

Pieces of the Pie

All fans love to grouse at the tube when their team has runners gunned down on the bases, picked off, doubled up, and thrown out stealing. But which fans have suffered the most (and the least)? The following table lists the top and bottom 20 teams in total number of runs contributed on the bases over the past six seasons.

Year    Team       Opps   EqGAR    Opps   EqAAR    Opps   PO   CS   EqSBR   Opps    OA   EqHAR   Total
2004    SLN         319    2.59     282    4.46     159    4   51   -5.76    447     6    9.19   10.47
2000    KCA         326    2.68     307    4.33     156    4   39   -0.68    461     8    3.48    9.81
2001    SEA         297   -1.06     320    2.80     212    7   49   -0.83    421     6    8.67    9.57
2005    NYN         289    2.40     246   -2.57     194    8   48    2.60    372     5    6.86    9.28
2005    ATL         313   -1.32     269    0.61     125    3   35   -0.09    392     4    7.99    7.19
2000    CHA         330    0.10     286    2.23     163    7   49   -3.35    390     6    7.70    6.67
2004    ANA         325    5.08     268    0.57     187    6   52   -0.98    489    13    1.96    6.63
2001    COL         354    3.13     251    0.74     188   10   64   -9.03    379     8   11.47    6.31
2000    COL         315    5.35     299    1.93     191    7   68  -12.45    445     7   11.28    6.12
2004    MON         316    2.54     236   -5.13     147    3   41   -0.50    373     4    9.16    6.07
2001    TEX         252   -1.33     305    4.24     130    8   40   -1.20    372     9    4.34    6.05
2005    TEX         244   -1.71     276    3.58      84    3   18    1.38    402     6    2.68    5.94
2003    OAK         289   -2.49     299    2.26      61    2   16   -0.25    401    11    5.23    4.75
2005    TBA         283   -1.66     277   -2.49     201    7   56   -5.33    447     6   12.42    2.93
2005    SLN         308    3.94     253    4.46     118    4   40   -8.83    448     6    2.62    2.19
2003    SLN         325    2.96     301    2.39     107    3   35   -6.60    478    11    2.74    1.50
2001    OAK         238   -0.95     275    2.58      98    4   33   -5.41    341     4    4.93    1.15
2004    ATL         299   -1.35     228    4.52     119    1   33   -1.72    428     8   -0.51    0.94
2003    NYN         322    2.14     240    3.29     105    6   37   -7.22    379     7    2.68    0.89
2000    CIN         304    2.43     295    4.49     139    7   45   -5.91    382     7   -0.45    0.56
------------------------------------------------------------------------------------------------------
2001    NYN         259   -1.16     297   -8.34     120    7   55  -20.72    328    12   -2.42  -32.64
2001    SFN         267    0.57     281   -4.68     103    5   47  -13.65    332    11  -12.23  -29.99
2002    MIL         339   -1.21     241   -4.92     155   13   63  -17.51    317    12   -4.51  -28.15
2001    BOS         266   -1.07     249   -3.03      83    4   39  -12.77    356    13  -10.39  -27.27
2005    WAS         326   -0.18     237    0.58      97   10   55  -22.49    392     7   -4.42  -26.50
2004    BOS         255   -4.67     299    1.12     100    4   34   -6.60    484    12  -14.80  -24.95
2001    MON         325    0.08     252   -2.74     154    8   59  -16.85    310     6   -3.74  -23.24
2001    PIT         299    3.61     255   -4.43     170    9   82  -26.71    285     8    5.72  -21.81
2005    LAN         312   -3.00     255    0.19      95    4   39   -9.71    396    12   -9.25  -21.78
2000    BOS         282   -0.96     324   -3.86      78    5   35   -9.97    381    10   -6.73  -21.52
2001    MIL         269    2.41     222    0.97     108    8   44  -12.72    311    13  -12.07  -21.41
2005    SDN         298    0.03     297   -1.23     153   12   56  -12.36    427    13   -6.51  -20.07
2002    CHA         254   -1.48     307   -3.35     116   13   44  -12.54    329    12   -2.60  -19.98
2002    SDN         312   -0.96     254   -3.91     114    5   49  -15.11    337    10    0.00  -19.96
2001    CIN         302   -1.09     231    1.04     161    8   62  -16.18    331    12   -2.22  -18.45
2005    PHI         302   -1.65     304   -2.37     144    7   34    2.17    447    18  -16.35  -18.20
2003    CHN         301   -2.22     273    1.50     110    8   39   -6.97    409    15  -10.33  -18.02
2002    ARI         304   -1.13     281    1.25     142    6   52  -12.35    340    11   -5.57  -17.79
2002    ATL         320   -2.81     272   -1.57     118    4   43  -11.67    337     8   -1.41  -17.45
2004    SEA         333    0.00     260    0.46     152    8   50   -8.23    488    10   -9.06  -16.84

First, it's apparent that looked at this way, teams don't really gain much from all their work on the bases. The top team, the 2004 Cardinals, came out with just ten and half runs to the good, or the equivalent of about a win. In fact, of the 180 teams in the study, only 23 accumulated positive totals. A quick glance at the list reveals that this is the case because the aggregate values for EqSBR are almost always negative and can be quite large in comparison to the other metrics. The reason? As a general-purpose strategy, stealing bases turns out to be a high-risk and low-reward endeavor as evidenced by the matrix showing the positive and negative run values associated with stolen base attempts in the previous column. This means that in order to accumulate runs, an individual or team is required to be successful a very high percentage of the time. Only 7 of the 180 teams came out on the plus side in EqSBR (as shown below), with the average team losing a bit more than eight runs.

Year    Team       Opps   EqGAR    Opps   EqAAR    Opps   PO   CS   EqSBR   Opps    OA   EqHAR   Total
2004    NYN         320   -2.19     240   -1.79     132    3   26    4.47    360    11   -5.79   -5.30
2005    NYN         289    2.40     246   -2.57     194    8   48    2.60    372     5    6.86    9.28
2005    PHI         302   -1.65     304   -2.37     144    7   34    2.17    447    18  -16.35  -18.20
2004    PHI         315    0.77     269   -1.23     129    3   30    1.95    425    12   -9.30   -7.81
2005    TEX         244   -1.71     276    3.58      84    3   18    1.38    402     6    2.68    5.94
2000    CLE         280   -1.67     290   -6.41     143    2   36    0.44    395    11   -2.43  -10.07
2004    TBA         279   -0.30     293    0.31     175    5   47    0.40    398     6    0.06    0.47

The recent versions of the Mets and Phillies, along with these other three clubs, are the only ones to keep their heads above water in this regard, by minimizing their caught stealing and pickoffs, and by selecting higher percentage running opportunities. Teams that run a great deal, like the Marlins of 2000-2003, usually do poorly and often come out with EqSBR values in the -5.00 to -10.00 range or worse. The poorest team was the 2001 Pirates, who in 170 opportunities were caught stealing a remarkable 82 times, and picked off another 9 times, which amounted to an EqSBR of -26.71.

That doesn't mean that stealing bases is always a bad idea. On the contrary it's a strategy that is sometimes the best option. It's knowing when to take those opportunities and with whom to take them that is the trick. In fairness (and as pointed out in a previous column), these raw stolen base numbers also include busted hit-and-runs, since there is no way to differentiate based on the play-by-play data, and that automatically drags down every team's numbers.

Getting back to the first table above, on the negative side, the 2001 Mets were at -32.64 runs on the strength of an EqSBR of -20.72. This points out that the range for EqSBR is on the order of +10 to -30 runs, repeating the point that the upside is clearly not as high as the downside is low. At first glance, the implication here is that even if a team works to inculcate good baserunning in general-as suggested by Lou Piniella at the start, or the attempt to do so earlier this season when the Rockies benched Matt Holliday and Jason Smith after carelessness on the bases-the advantage can easily be wiped away by attempting to steal bases in low percentage and poor leverage situations.

Attentive readers may have noticed that EqSBR is calculated slightly differently than the other metrics here. Remember that EqGAR, EqAAR, and EqHAR all are measured in terms of runs contributed above what would be expected, given the specific opportunities that each team encountered. In contrast, EqSBR is simply an accounting of total runs, and is not base-lined by looking at what the average team would have done with the same opportunities. For most of the analysis, this is exactly what we want, since stolen base attempts are purely at the discretion of the offense. But if we wish to get a feel for the total magnitude of these metrics, we can instead simply show the total number of runs contributed in each area, and reformulate our top and bottom 20 list in the following table where, for example, GAR simply stands for Ground Advancement Runs.

Year    Team       Opps     GAR    Opps     AAR    Opps   PO   CS   EqSBR   Opps    OA     HAR   Total
2000    KCA         326   26.75     307   46.66     156    4   39   -0.68    461     8   76.54  149.28
2001    SEA         297   23.04     320   46.11     212    7   49   -0.83    421     6   78.83  147.16
2000    COL         315   29.32     299   45.68     191    7   68  -12.45    445     7   74.96  137.51
2004    SLN         319   26.17     282   40.09     159    4   51   -5.76    447     6   75.75  136.25
2004    SDN         315   26.10     333   39.12      78    3   28   -6.16    490     9   74.70  133.77
2004    ANA         325   30.19     268   28.44     187    6   52   -0.98    489    13   74.57  132.22
2003    BOS         260   15.49     318   42.96     126    4   39   -4.76    475     7   76.75  130.43
2003    KCA         304   22.54     284   35.62     165    9   51   -3.54    490    10   72.26  126.88
2005    TBA         283   18.26     277   32.05     201    7   56   -5.33    447     6   81.32  126.31
2003    OAK         289   20.32     299   33.76      61    2   16   -0.25    401    11   72.16  125.99
2001    COL         354   31.04     251   30.64     188   10   64   -9.03    379     8   73.30  125.95
2003    TOR         283   19.52     324   35.86      63    2   27   -7.63    463     9   76.84  124.58
2000    CHA         330   20.81     286   37.57     163    7   49   -3.35    390     6   69.27  124.30
2005    OAK         259   14.38     320   28.15      54    1   23   -5.79    478     3   86.70  123.44
2005    ANA         321   33.55     265   24.34     218    5   62  -10.44    474    10   75.66  123.11
2004    COL         351   26.83     249   24.28      81    4   37  -10.34    445    10   82.27  123.03
2003    SLN         325   25.08     301   37.03     107    3   35   -6.60    478    11   67.34  122.86
2003    MIN         338   25.46     280   32.64     145   10   54   -8.88    461     8   72.78  121.99
2002    ANA         306   26.93     357   42.25     169    5   56   -8.71    437     8   60.10  120.57
2004    PHI         315   23.93     269   32.27     129    3   30    1.95    425    12   61.89  120.04
------------------------------------------------------------------------------------------------------
2002    MIL         339   24.05     241   21.53     155   13   63  -17.51    317    12   36.63   64.71
2001    NYN         259   16.21     297   19.67     120    7   55  -20.72    328    12   51.66   66.82
2001    MIL         269   20.84     222   25.44     108    8   44  -12.72    311    13   35.43   68.99
2001    MON         325   21.49     252   28.00     154    8   59  -16.85    310     6   37.80   70.44
2001    BOS         266   18.03     249   27.47      83    4   39  -12.77    356    13   37.72   70.45
2001    PIT         299   24.37     255   19.77     170    9   82  -26.71    285     8   53.90   71.32
2001    LAN         274   16.64     257   25.14     134    6   48   -8.60    292    13   38.40   71.59
2002    PIT         272   19.35     267   25.24     132    5   54  -12.50    294     5   39.83   71.92
2002    CLE         292   16.73     228   25.89      91    2   39  -11.20    319     8   41.02   72.44
2002    OAK         247   13.46     273   24.00      67    4   24   -5.24    351     7   41.57   73.79
2005    LAN         312   19.30     255   22.32      95    4   39   -9.71    396    12   44.75   76.66
2001    SFN         267   18.98     281   32.20     103    5   47  -13.65    332    11   40.70   78.23
2002    SDN         312   21.26     254   21.81     114    5   49  -15.11    337    10   50.27   78.23
2001    CIN         302   23.06     231   24.51     161    8   62  -16.18    331    12   46.86   78.24
2002    CHA         254   17.61     307   32.58     116   13   44  -12.54    329    12   42.25   79.90
2002    BAL         285   19.81     266   30.96     161    5   53   -7.11    297    11   37.39   81.04
2002    HOU         268   14.73     235   22.62     102    6   33   -7.63    365    13   51.80   81.52
2000    TBA         292   19.25     282   26.82     135    2   48   -7.65    352    11   43.95   82.36
2002    ATL         320   19.94     272   29.72     118    4   43  -11.67    337     8   44.57   82.56
2000    TOR         274   15.82     267   23.83     128    6   40   -4.01    385    10   47.29   82.94

One could interpret the table above as indicating that the 2001 Royals cashed in approximately 150 runs with their baserunning, while the 2002 Brewers got only about 65. Unfortunately, that's not quite right. A better interpretation is that the aggregate of the actions by Royals baserunners in 2001 put their team in a position to score 150 more runs than they would have otherwise had they never advanced on the bases, tagged up, attempted a stolen base, or been picked-off. In other words, had they played absolute station-to-station baseball. The actual number of runs individual teams did gain from their baserunning is not what is being measured since the run values used in the calculations are taken from the overall Run Expectancy matrix for the period and therefore simply help us model the impact of baserunning actions.

This does, however, give us the opportunity to sum each run value across all teams to get a feel for how important each metric is in its contribution to the running game. When this is done, you can chart the results to show the contribution that each makes to the total picture:

chart 1

EqSBR is not in the total pie, since it turns out to be negative to the tune of 7%. The interesting aspect of this graphic is that while air advancement makes up a greater percentage of the pie than does ground advancement, air advancement is both more variable (and hence less impacted by skill) and has a smaller range which makes it more difficult for teams to capitalize on their opportunities. Advancing on hits is where the real opportunity lies, since it is a repeatable skill to a larger degree, and it provides the chance for teams to increase their run-scoring. That said, it should be remembered that the contribution of the running game pales in comparison to hits and walks, Piniella's quote above notwithstanding, and according to the analysis above, using the totals across all teams accounts for only 13% of the offensive output over the past six years.

Getting Older and Smarter?

Throughout this series, we've seen that players that do better in these metrics are generally faster than those who don't. During my chat session earlier this week one reader suggested correlating these metrics with BP's Speed Scores in order to find the speed threshold at which risk-aversion becomes the optimal strategy. Although I didn't appreciate it at the time, doing so would allow us to see which metrics are most dependent on pure speed, and which on other attributes such as judgment. Alas, time pressures did not permit that analysis to be done this week.

Another way to do this perhaps, albeit a little less directly, is to look at how aging affects the metrics based primarily on the assumption that speed decreases with age. To do this, we can simply group all the players by age and compare the rate statistics for each measure. This was done for ages 21 through 39 (those are the ages between which there were more than 1,200 opportunities), and is presented in the following three graphs with the best-fit linear regression line thrown in for good measure.

chart 2

chart 3

chart 4

As you can see, all three of these metrics show a downward slope, so indicating that the younger a player is, generally speaking, the better they'll do. Looking more closely, you'll also notice that the slope of the line for EgHAR (advancing on hits) is greater than that for the other two, with EqGAR (advancing on grounders) coming in second followed by EqAAR (advancing on flyouts). In fact, the correlation coefficients with age for the three measures pictured above are:

Metric    r
EqHAR  0.86
EqGAR  0.80
EqAAR  0.48

This provides support for the view that speed is more important when advancing on hits than when advancing on ground and air outs. This makes sense intuitively, since players have more opportunities to take multiple bases on hits, which can better exploit their speed. As mentioned previously, the correlation between EqAAR and age is lower because there's simply more variability inherent in that metric. On the other side, it might also indicate that judgment is more important when advancing on ground and air outs, and is therefore a skill less affected by the affects of aging.

We don't see quite the same kind of smooth trend for EqSBR as shown below using EqSBR per opportunity (since we have no rate statistic for EqSBR):

chart 5

The likely reason for this bumpy track is that the combination of running only when the odds of success are good and running in higher leverage situations play a larger role as a player ages. The increase after age 32 likely reflects a selection bias, as some players that remain in the league past that age continue to be productive (at least in terms of the league as a whole), if not prolific, base stealers, while the guys that can't run, don't.

Under the Tag

In an early article in this series, we began with a quote from Bill James from the 1984 Baseball Abstract, where he lamented the fact that baserunning would be perfectly measurable if we simply tracked game events differently from the start. The last 20 years have seen revolutions in the collection of play-by-play data and in our ability to analyze that data. The happy result is that baserunning can be explored in more depth than ever before.

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