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August 17, 2006

Schrodinger's Bat

Using The House Advantage

by Dan Fox

"I do think running the bases aggressively is something that should be the tendency in every team. I do. That aggressiveness is part of baseball whether you believe in waiting for the three-run homer or not. If you can get that guy to third instead of to second that's a lot better statistical position to be in. If you can create more of those situations, you're going to have more runs on the bottom line."--Angels Manager Mike Scioscia

After taking a break last week to lament the Cubs swap of Greg Maddux for Cesar Izturis, I'm back to dissecting the running game this week. However, this time, rather than look at individuals we'll travel up the ladder to create a team perspective. We're taking this detour in our series because the most frequently asked questions by readers pertaining to the entire topic is probably how the calculation of Equivalent Ground Advancement Runs (EqGAR) and Equivalent Air Advancement Runs (EqAAR) applies to teams and whether we can learn anything about coaching or team philosophies as a result.

This week, we'll perform a few aggregations and take a look at the seasonal team leaders in both metrics, as well as examine the seasonal fluctuations that are in play, and then delve a little deeper into the meaning of metrics such as these. Keep in mind that this is just a pit stop--next week we'll move the ball forward a bit in hopes of eventually actually ending this series, as we visit an old friend well-known to those in the performance analysis community by adding stolen bases and pickoffs to our baserunning toolbox.

Be the House

Let's get right to it. First, here are the 2005 results, ranked first by the Ground Advancement Rate (GA Rate, calculated as the ratio of total ground advancement runs to expected ground advancement runs) and then by Air Advancement Rate (AA Rate). We're using the rate statistic since teams differ in the number of opportunities they receive in a given season, with National League teams getting fewer opportunities for both ground and air advancement.

Team Totals for 2005 Sorted by GA Rate
         GA Opps   EqGAR GA Rate AA Opps   EqAAR AA Rate
ANA          321    5.99    1.22     265   -2.83    0.90
SLN          308    3.94    1.18     253    4.46    1.22
CHN          314    2.97    1.12     252   -2.22    0.92
SFN          360    3.10    1.12     259   -5.95    0.81
PIT          287    2.40    1.11     265   -4.23    0.87
CHA          281    2.35    1.10     273    1.58    1.06
NYN          289    2.40    1.09     246   -2.57    0.90
FLO          324    1.68    1.08     280    1.25    1.04
COL          311    1.47    1.06     259    1.08    1.05
MIL          297    0.79    1.03     239   -0.82    0.97
ARI          310    0.77    1.03     249    3.32    1.13
HOU          307    0.38    1.02     237    3.01    1.12
SDN          298    0.03    1.00     297   -1.23    0.96
CIN          255   -0.11    0.99     242    0.34    1.01
WAS          326   -0.18    0.99     237    0.58    1.02
KCA          294   -0.95    0.96     293    2.43    1.08
MIN          329   -1.07    0.95     241   -4.78    0.83
ATL          313   -1.32    0.94     269    0.61    1.02
SEA          286   -1.30    0.94     273   -1.80    0.92
PHI          302   -1.65    0.93     304   -2.37    0.93
TBA          283   -1.66    0.92     277   -2.49    0.93
CLE          290   -1.82    0.91     280    4.30    1.17
BAL          295   -2.21    0.90     280    3.07    1.12
TOR          292   -2.37    0.89     257    4.22    1.13
NYA          264   -1.84    0.88     294   -0.73    0.98
TEX          244   -1.71    0.88     276    3.58    1.18
BOS          255   -2.03    0.88     329    3.64    1.10
LAN          312   -3.00    0.87     255    0.19    1.01
OAK          259   -2.24    0.87     320   -2.58    0.92
DET          285   -4.57    0.79     260    5.07    1.17

Team Totals for 2005 Sorted by AA Rate
         GA Opps   EqGAR GA Rate AA Opps   EqAAR AA Rate
SLN          308    3.94    1.18     253    4.46    1.22
TEX          244   -1.71    0.88     276    3.58    1.18
DET          285   -4.57    0.79     260    5.07    1.17
CLE          290   -1.82    0.91     280    4.30    1.17
TOR          292   -2.37    0.89     257    4.22    1.13
ARI          310    0.77    1.03     249    3.32    1.13
BAL          295   -2.21    0.90     280    3.07    1.12
HOU          307    0.38    1.02     237    3.01    1.12
BOS          255   -2.03    0.88     329    3.64    1.10
KCA          294   -0.95    0.96     293    2.43    1.08
CHA          281    2.35    1.10     273    1.58    1.06
COL          311    1.47    1.06     259    1.08    1.05
FLO          324    1.68    1.08     280    1.25    1.04
WAS          326   -0.18    0.99     237    0.58    1.02
ATL          313   -1.32    0.94     269    0.61    1.02
CIN          255   -0.11    0.99     242    0.34    1.01
LAN          312   -3.00    0.87     255    0.19    1.01
NYA          264   -1.84    0.88     294   -0.73    0.98
MIL          297    0.79    1.03     239   -0.82    0.97
SDN          298    0.03    1.00     297   -1.23    0.96
TBA          283   -1.66    0.92     277   -2.49    0.93
PHI          302   -1.65    0.93     304   -2.37    0.93
SEA          286   -1.30    0.94     273   -1.80    0.92
CHN          314    2.97    1.12     252   -2.22    0.92
OAK          259   -2.24    0.87     320   -2.58    0.92
ANA          321    5.99    1.22     265   -2.83    0.90
NYN          289    2.40    1.09     246   -2.57    0.90
PIT          287    2.40    1.11     265   -4.23    0.87
MIN          329   -1.07    0.95     241   -4.78    0.83
SFN          360    3.10    1.12     259   -5.95    0.81

There are a couple things we can learn from these lists. First, the range for teams who do well in EqGAR and those who do well in EqAAR is in the range of -5 to +5 runs a season, or a spread equivalent to about a win. So, at the team level, we're really talking about small differences over the course of a season.

I'm sure some readers will scoff at the notion that something that seems so important could add up to what amounts a pretty small difference in the end. One should keep in mind though that in calculating these metrics we've used a standard analytic approach based on comparing before and after "snapshots" based on the Run Expectancy matrix. Individual plays some readers probably well remember may indeed have cost their team an excellent or even certain chance of winning a particular game or games. For example, if Eric Munson of the Devil Rays gets gunned down at the plate in the bottom of the tenth with the score tied (as he was on June 28, 2005), that clearly has a large impact on that game. However, Run Expectancy only allows us to credit plays at the granularity of differences in average run scoring given particular base/out combinations, and the technique is inherently not quite so context-specific. In order to account for the context more fully we could instead use the Win Expectancy (WE) Framework, which allows us to quantify events by their impact not in terms of runs but in wins (or actually percentages of wins), therefore capturing the importance of that tenth-inning play. However, doing so puts us in danger of tipping too far in the other direction, and would skew the results if players happened to find themselves in an inordinate number of high- or low-impact situations.

In essence, what these metrics measure is not really the actual number of runs a team gained or lost by an advancement event but theoretically how the many decisions made throughout the course of the season in the aggregate put the team in more or less advantageous situations measured in terms of runs. If events in the real world always worked out exactly as our models tell us they should, the team would in reality gain or lose the number of runs calculated in these metrics. As we all know, the real world doesn't quite work like that, but in the end, this more theoretical perspective is what I think anyone interested in even these kinds of small advantages should be looking at. This philosophy, as hinted at by Mike Scioscia, was summed up nicely by former Dodgers GM and current Padres Special Assistant for Baseball Operations Paul DePodesta in an article penned a couple years ago, where he likened the philosophy to the house advantage enjoyed by casinos:

"I was on a quest to find relevant relationships. Usually it wasn't as simple as 'if X then Y.' I was looking for probabilistic relationships. I christened the new model in the front office: 'be the house.' Every season we play 162 games. Individual players amass over 600 plate appearances. Starting pitchers face 1,000 hitters. We have plenty of sample size. I encouraged everyone to think of the house advantage in everything we did. We may not always be right but we'd be right a lot more often than we'd be wrong. In baseball, if you win about 60% of your games, you're probably in the playoffs."

Teams that do well in these metrics can in some sense be said to have used their house advantage.

The second thing we can learn from the above lists, and what you probably noticed already, is although the difference between the top and bottom teams is similar in both metrics, those teams who do well in EqGAR don't necessarily fare well in EqAAR and vice versa. In fact, the correlation coefficient (the measure of the strength of the linear relationship between two sets of values with a perfect positive correlation equaling 1 and a perfect negative correlation at -1) between GA Rate and AA Rate for 2005 was actually negative. In other words, knowing a team's GA Rate tells you nothing about their AA Rate, and vice versa.

At first blush, this would seem counterintuitive. After all, it would seem that teams who have personnel who can take extra bases on ground balls should find themselves able to do so on balls hit in the air as well. There are two reasons why this otherwise reasonable expectation might not be the case. First, it just may be that the skills required to do well in one metric are not in fact the skills required for excellence in the other. Perhaps raw speed is more useful in obtaining a good EqGAR while judgment is more useful in EqAAR. That's certainly possible but in my mind what is more likely is that EqGAR has a higher skill component while EqAAR is more infused with randomness making them difficult to correlate.

If you look at teams across the six seasons we've been working with (2000-2005), what you find is that the correlation coefficient for GA Rate in the five pairs of seasons runs like so:

Correlation Coefficients for GA Rate
2000-2001  0.54
2001-2002  0.25
2002-2003  0.48
2003-2004  0.62
2004-2005  0.22

Here we can see some middling to weak positive correlations, which indicate that perhaps personnel or coaching or team philosophy may be influencing the repeatability of this metric, even given the turnover that teams deal with. On the other hand, the coefficients for AA Rate are as follows:

Correlation Coefficients for AA Rate
2000-2001   0.16
2001-2002  -0.04
2002-2003   0.14
2003-2004  -0.06
2004-2005  -0.04

As you can see, for air advancement there is no discernible correlation. One might speculate that the reason for this lies in the fact that for advancing on outs in the air there are both fewer opportunities, so our sample sizes are decreased (which increases the variability), and the success rates are so high that getting thrown out a few extra times is enough to send a team plummeting from the upper third to the bottom third. Individual plays have a greater relative impact on the aggregate outcome, so the uncharacteristically great throws by a Johnny Damon or Bernie Williams or an otherwise good runner getting a bad jump or being the victim of a bad call have large impacts on the outcomes, thus scrambling the results. We also haven't accounted for the outfielder's arms for each attempt, so it's possible that a team like the Giants--who scored poorly--just happened to test some good arms and failed when doing so.

You can take a look at some of the individual EqAAR results for 2005 for players with 25 or more opportunities on my blog and here for EqGAR.

Seasonal Leaders and Trailers

To round out this discussion of team performances, we'll leave you with plenty of numbers to chew on. We present the top and bottom five teams for both ground and air advancement for each of our other five seasons (2000-2004) sorted by our rate statistic.

       Ground Advancement              Air Advancement
Year   Team  GA Opps   EqGAR GA Rate   Team   AA Opps   EqAAR AA Rate
2000   COL       315    5.35    1.22   MIN        276    4.62    1.16
2000   MON       361    5.03    1.17   MIL        237    4.39    1.16
2000   ANA       290    3.59    1.17   CIN        295    4.49    1.14
2000   SFN       279    2.57    1.14   SDN        253    3.87    1.14
2000   KCA       326    2.68    1.11   SEA        305    4.35    1.13

2000   NYA       269   -4.12    0.75   ANA        299   -6.10    0.81
2000   BAL       293   -3.54    0.82   CLE        290   -6.41    0.82
2000   LAN       287   -2.94    0.83   PHI        262   -4.24    0.83
2000   TEX       318   -3.59    0.84   DET        307   -5.32    0.85
2000   CLE       280   -1.67    0.91   BOS        324   -3.86    0.88
---------------------------------------------------------------------
2001   ANA       268    3.81    1.19   TEX        305    4.24    1.12
2001   PIT       299    3.61    1.17   PHI        294    3.97    1.11
2001   MIL       269    2.41    1.13   CHA        260    3.08    1.10
2001   CHA       283    2.70    1.13   OAK        275    2.58    1.08
2001   FLO       311    2.40    1.12   NYA        287    1.76    1.07

2001   SDN       255   -3.07    0.83   NYN        297   -8.34    0.70
2001   NYA       282   -3.82    0.83   PIT        255   -4.43    0.82
2001   TEX       252   -1.33    0.92   CLE        287   -5.20    0.86
2001   NYN       259   -1.16    0.93   SFN        281   -4.68    0.87
2001   LAN       274   -0.99    0.94   BOS        249   -3.03    0.90
---------------------------------------------------------------------
2002   SFN       295    2.77    1.14   OAK        273    2.36    1.11
2002   TEX       271    2.61    1.13   DET        251    3.27    1.10
2002   COL       287    2.38    1.12   MON        246    2.47    1.10
2002   SLN       296    2.45    1.11   MIN        271    2.79    1.09
2002   NYN       324    2.60    1.10   CLE        228    1.75    1.07

2002   OAK       247   -3.38    0.80   MIL        241   -4.92    0.81
2002   PHI       323   -4.40    0.80   SDN        254   -3.91    0.85
2002   HOU       268   -2.49    0.86   NYN        233   -3.02    0.85
2002   NYA       270   -2.79    0.86   SLN        302   -3.13    0.91
2002   CLE       292   -2.45    0.87   CHA        307   -3.35    0.91
---------------------------------------------------------------------
2003   ANA       300    4.62    1.21   DET        253    4.90    1.20
2003   SLN       325    2.96    1.13   BOS        318    5.07    1.13
2003   MIL       297    2.45    1.11   CIN        242    2.24    1.13
2003   FLO       313    2.81    1.11   NYN        240    3.29    1.13
2003   NYN       322    2.14    1.09   MIN        280    2.88    1.10

2003   BOS       260   -4.72    0.77   LAN        241   -2.85    0.87
2003   NYA       282   -2.80    0.84   SDN        292   -3.84    0.87
2003   TBA       296   -3.59    0.84   BAL        288   -2.97    0.89
2003   CLE       274   -2.84    0.87   CHA        264   -2.68    0.90
2003   OAK       289   -2.49    0.89   PIT        264   -2.47    0.90
---------------------------------------------------------------------
2004   ANA       325    5.08    1.20   ATL        228    4.52    1.18
2004   SDN       315    3.39    1.15   CHA        270    4.21    1.17
2004   CHA       270    2.59    1.13   MIL        223    3.28    1.15
2004   PIT       330    2.56    1.12   PIT        230    3.39    1.15
2004   SLN       319    2.59    1.11   SLN        282    4.46    1.13

2004   BOS       255   -4.67    0.74   MON        236   -5.13    0.81
2004   OAK       269   -3.88    0.79   CIN        227   -3.01    0.85
2004   CHN       307   -3.19    0.86   KCA        280   -3.82    0.85
2004   NYN       320   -2.19    0.91   LAN        243   -2.93    0.87
2004   CLE       326   -2.08    0.92   ARI        240   -2.65    0.90

As mentioned previously, you can see even from these partial lists that some teams seem to do well in ground advancement year after year, while others do poorly. For example, the Angels are among the leaders in four of the five seasons, and actually led in three of those (2001, 2004-2005). Meanwhile, Cleveland is among the bottom teams in four of the five seasons. Could this be the result of coaching or a team philosophy? Well, there is anecdotal evidence anyway that for the Angels the latter might indeed by the case.

To get a better handle on the influence of individual coaches, however, we would need data on just which first and third base coaches were employed by what teams over what span of time. We'd also want to expand the scenarios we look at, to not only include advancing on outs but also doing so on hits as well, as taking into consideration events such as pickoffs, which a base coach might influence. Although I have nothing to report on that score yet, there is work under way with a fellow SABR member to collect the requisite data and begin to analyze it. Stay tuned.

Finally, because I know someone will ask if I don't, here are the top and bottom teams over the course of the last six seasons. Note that almost all of the Mets -8.72 EqAAR came in 2001 when they recorded the lowest total at -8.34 by virtue of getting thrown out 12 times and being credited with negative runs in 76 of their 297 opportunities.

Ground Advancement                      Air Advancement
Team     GA Opps   EqGAR GA Rate        Team     AA Opps   EqAAR AA Rate
ANA         1810   25.33    1.18        SLN         1681    7.88    1.05
SLN         1882   13.67    1.10        DET         1617    7.80    1.04
PIT         1825   12.02    1.09        TOR         1647    8.41    1.04
SFN         1819    9.36    1.08        ATL         1569    6.59    1.04
MON         1704   10.32    1.08        TEX         1766    5.78    1.04

NYA         1659  -16.25    0.85        NYN         1531   -8.72    0.93
BOS         1598  -15.78    0.87        PIT         1567   -9.18    0.94
OAK         1584  -14.21    0.87        MON         1222   -7.64    0.94
CLE         1768  -10.18    0.92        ANA         1813  -11.41    0.94
LAN         1839   -8.82    0.93        PHI         1657   -7.01    0.95

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