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April 20, 2006

Schrodinger's Bat

Baserunning, in Two Acts

by Dan Fox

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"We really want to concentrate on being better baserunners and more aggressive baserunners. We've got to find more ways to score more runs."
--Mariners Manager Mike Hargrove, April 3, 2006

As I write this on April 19, the Mariners are tenth in the AL in runs scored per game to go along with their 6-8 record. Last season, they were 22nd in run scoring in all of baseball, and 13th in the American League, sandwiched nicely between those offensive juggernauts, the Royals and Twins. So what Hargrove is saying about needing more runs is certainly true, but is a more aggressive baserunning style an avenue to improvement?

This week I'll take a quick look at that question in my first act, followed by a brief foray into the world of rundowns in the second.

Act I: Aggression on the Bases

Some readers may be aware that James Click and I both did some work on quantifying baserunning in the last couple of years. For my part, the theoretical framework was discussed in a series of articles on The Hardball Times last season.

Simply put, the methodology I employed looks at the value of baserunner advancement 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

After totaling each player's opportunities and results in these scenarios, we then control for the 24 base/out situations, and assign a value for each opportunity based on the increase or decrease in run expectancy in the scenario, with the exception that runners who advanced only the standard number of bases (one for a single and two for a double) were given no credit. Additional context is also taken into account, including the handedness of the batter, the position of the fielder who fielded the ball, and the ballpark.

The result is a framework that produces a number of Incremental Runs (IR) that the baserunner added to his team through his baserunning. Like Click's Equivalent Baserunning Runs (EqBR), a positive value indicates that the player's baserunning was on the whole beneficial to his team, while a negative value indicates that he was a liability. We also calculate a rate statistic, Incremental Run Percentage (IRP) that is not weighted by the number of opportunities and can therefore be used for comparison.

Given that we do have a quantitative way to look at the question, we should probably first ask whether the Mariners have much room for improvement, keeping Hargrove's emphasis on baserunning in mind.

To determine how much improvement is possible it follows that there are two related concepts to look at. First, by examining the distribution of IR across all teams, what you consistently find (at least going back to 2000) is that the difference between the best and worst teams in IR is roughly 30 runs in a given season, centered on 0. For example, in 2005 the best baserunning team, the Tampa Bay Devil Rays, gained 13.08 runs; the Phillies were the worst at -15.85 runs. The spread for that season was 28.92 runs.

When using the rule that approximately ten runs is equivalent to a win, that spread is therefore equivalent to about three wins. In other words, even if the Mariners went from the worst to first in 2006, the most they could expect to improve their bottom line by is three wins.

The second related concept is just how much room the Mariners have for improvement. It turns out that the answer is 'not much.' In 2005, they ranked 8th in all of baseball by posting a very respectable 5.38 Incremental Runs. In addition, their IRP was 1.04--in other words they gained 4% more runs than would have been expected given their opportunities--which placed them 4th. The following table shows the results for all teams where OA is the number of times runners were thrown out advancing and BRR the total number of Baserunner Runs.

             Opp      OA     BRR      IR     IRP
TBA          447       6   81.15   13.08    1.04
OAK          478       3   85.70   11.10    1.05
ATL          392       4   68.14    8.65    1.02
KCA          453       7   70.94    7.79    1.03
NYN          372       5   56.37    7.03    1.05
COL          449       7   80.32    6.86    1.03
CHN          422       8   64.82    6.01    1.01
SEA          403       5   58.13    5.38    1.04
CLE          437       7   68.60    3.92    1.01
TEX          402       6   67.03    3.28    1.02
TOR          453      10   58.83    3.09    1.00
DET          445       5   62.32    2.76    1.01
CHA          420      11   62.30    2.54    1.01
SLN          409       6   63.71    1.42    1.01
ANA          474      10   74.23    1.22    1.01
NYA          485      11   62.59    0.49    1.02
SFN          440       8   63.09    0.05    1.00
CIN          377       8   51.44    0.02    1.00
MIN          449       7   59.34   -0.73    0.98
MIL          383      12   53.93   -1.86    0.99
ARI          393       6   52.60   -3.47    0.98
WAS          392       7   55.85   -4.37    0.98
HOU          413      11   58.37   -4.96    0.98
PIT          458      13   67.57   -5.11    0.97
BAL          436      11   61.16   -5.45    0.98
SDN          427      13   64.31   -5.95    0.97
LAN          396      12   44.34   -8.75    0.95
FLO          447      10   55.74   -8.94    0.98
BOS          501       7   57.97  -12.09    0.96
PHI          447      18   52.78  -15.85    0.94
Note: Readers of The Hardball Times Baseball Annual 2006 will note that these values differ slightly from those in the article describing the system. This is because a tweak was made after the publication of the book to take into account advancement during the play when a batter singles with a runner on first. Formerly the run values calculated when the runner scored did not take into consideration that the runner could have stopped at third base rather than taken the standard advancement.

Given that the Mariners were already in the top half of the league, it would appear that the most Hargrove could expect to squeak out is about ten more runs, or one additional win over the course of the season.

Broken down at the player level we get the following results for the Mariners.

Name                     Opp      OA     BRR      IR     IRP
Michael Morse             23       0    5.38    1.62    1.14
Jeremy Reed               31       0    6.49    1.57    1.12
Ichiro Suzuki             63       1    8.56    1.28    1.06
Willie Bloomquist         22       0    2.69    1.26    1.16
Randy Winn                28       0    3.84    0.91    1.03
Yuniesky Betancourt       12       0    1.67    0.65    1.15
Yorvit Torrealba           9       0    1.38    0.64    1.26
Pat Borders                8       0    2.87    0.59    1.10
Dave Hansen                4       0    0.74    0.28    1.03
Wilson Valdez              7       0    1.58    0.26    1.14
Chris Snelling             2       0    0.25    0.21    1.22
Raul Ibanez               46       1    7.72    0.20    1.01
Bret Boone                25       0    3.49    0.19    1.03
Ramon Santiago             2       0    0.37    0.19    1.08
Aaron Sele                 1       0    0.74    0.17    1.20
Jamal Strong               2       0    0.74    0.14    0.95
Jaime Bubela               3       0    0.26    0.09    1.08
Shin-Soo Choo              2       0    0.74    0.04    0.95
Dan Wilson                 2       0    0.00   -0.03    0.91
Greg Dobbs                13       1    1.67   -0.09    0.80
Miguel Ojeda               2       0    0.00   -0.12    0.78
Miguel Olivo               8       0    0.31   -0.13    1.00
Adrian Beltre             35       0    4.39   -0.19    1.05
Wiki Gonzalez              7       0    0.07   -0.41    0.90
Jamie Moyer                1       0    0.00   -0.54    0.81
Jose Lopez                 8       1    0.89   -1.01    0.84
Richie Sexson             31       0    2.19   -1.09    0.93
Rene Rivera                6       1   -0.92   -1.31    0.64
As you can see, the Mariners didn't have anyone who was particularly exceptional in either IR or IRP. Willie Bloomquist led the team with an IRP of 1.16 (in over 20 opportunities, he had 22) which was 70th in baseball. Michael Morse led in IR with 1.62, which was 50th in baseball. Overall, however, the Mariners avoided having any one player like a Luis Gonzalez (-5.33) or Pat Burrell (-5.48) that really weighs a team down. But most importantly for their overall performance, as a team they were thrown out just five times, which tied them for third-fewest with Detroit and the Mets and trailed only the A's (3) and Braves (4).

That final point is the one to emphasize.

Using the run expectancy table for 2005, we can see that the cost of getting thrown out at third with nobody out is, on average, .97 runs (.54, which is the run expectancy with a runner on first and one out minus 1.50, the run expectancy with runners on first and second with nobody out). With one out, the cost is .69 runs, and with two out .45 runs. This is what you'd expect, since the probability of actually scoring the runner goes down as the number of outs increases. At the same time, the incremental benefit of making it to third goes down as well with a gain of .26 runs with zero outs, .25 runs with one out, and .05 runs with two outs.

Incidentally, the difference between the latter value and the others makes the case of the Rockies' Danny Ardoin getting thrown out at third with two outs, which erased a run in their one-run loss on April 12th, even more frustrating for Rockies fans despite the fortuitous bounce that Luis Gonzalez received. I should also add that Matt Holliday was benched the next night as a result of manager Clint Hurdle's new tough-love policy, since Holliday failed to run through home plate. Todd Helton was reportedly not amused.

But getting back to the run expectancy tables, what this means is that the cost of getting thrown out in this scenario is 3 to 9 times higher, depending on the number of outs, than the benefit of advancing the extra bases. As a result, getting thrown out is the quickest way to sink you or your team's IR and IRP.

Interestingly, you'll note that unlike the other teams at the bottom of the list, Boston was thrown out just seven times. This indicates that their performance can be attributed to overly conservative running and not getting thrown out all over the diamond, as opposed to how the Phillies did it, in part by getting caught 19 times.

To go back to the Mariners, in a Cactus League game this year, Jeremy Reed singled and Yuniesky Betancourt followed by hitting a dying quail to right. Reed then turned too aggressively at second and was seemingly hung out to dry with Vladimir Guerrero loading up to nail him at third. Reed decided to head to third, and was safe when Guerrero's throw went wide.

After the game Hargrove referenced the play and noted:

"Your stomach turns and flip-flops some, but it worked and led to some runs. I've said it before. We're going to run into outs, and some of them are going to look really ugly…But for every ugly one, we'll have five good ones, and I'll take that ratio."

If that's the case, then Hargrove should hope those ugly outs come at the right times since the break-even success rate on a single with a man on first ranges from 38% if the runner attempts to score with two outs, to 90% when a runner attempts to take third with two outs.

Overall, the numbers in the first table above indicate that a good baserunning team sees successful outcomes around 99 times out of 100, while even bad baserunning teams like the 2005 Phillies were thrown out under five percent of the time. This suggests that there simply aren't that many opportunities where an aggressive team could take the extra base, since the vast majority of those chances have outcomes that are virtually certain, which explains why the spread in IR between good and bad baserunning teams is relatively small. So, we can pretty confidently conclude that aggressiveness on the bases certainly is beneficial, but if that style results in even a few more runners being thrown out, the cost quickly outweighs the benefit.

There are three elements that this analysis misses, however.

First, there may in fact be a psychological benefit to a more aggressive style. Increased aggressiveness may breed increased confidence and a better team attitude, resulting in an unquantifiable advantage that just may translate to on-field performance. Game theory also suggests that if opposing teams are aware of the Mariners' new style of play, they may be more inclined to pitch out, hold runners, and play the defense differently, all of which could give the Mariners slight advantages in certain situations.

Second, this analysis is based on run expectancy, not win expectancy. As such, it doesn't consider the score, the inning, or the run environment of the situations in which the baserunning events occurred. While we would mostly expect that run expectancy and win expectancy would even out in the long run, there may in fact be some players or teams that are more judicious in their decision making regarding baserunning. Evaluating these scenarios in terms of the Win Expectancy (WX) Framework is certainly more complex, but would allow us to tease these tendencies out.

Finally, one of Hargrove's initiatives is also to be more aggressive in terms of stolen bases. Last month I took a look at Whitey Herzog's Cardinals team of 1985, and using a similar methodology found that their 314 stolen bases resulted in a net gain of 31.1 runs, or about three wins, which was their margin of victory over the second-place Mets. However, Dayn Perry did a nice analysis of postseason teams in his book Winners, and shows that on average, even those that reach the postseason experience a net loss from stolen base attempts. The 2005 Mariners stole 102 bases, good for fourth in the league, but were caught 47 times, a percentage beneath the break-even rate, which put them on the negative side of the ledger.

As a result, many more stolen bases (say 150)--swiped at a much higher success rate--would be needed to eke out even a few more runs from this aspect of the running game for Hargrove's Mariners.

Act II: The Cost of Over-Aggressiveness

Each of the last three springs, my friend Ron and I have traveled to Arizona to soak up the sun and take in a few Cactus League games. As we observe the various minor league workouts, it never fails to amaze me how hard the minor leaguers work at rundowns. Invariably, each morning before batting practice the pitchers, catchers, and middle infielders will man their positions as outfielders take turns pretending to try and avoid the tag. An endless procession of rundowns commence between third and home, and then between each of the bases.

photo of baserunning drill

After seeing these drills run again and again this spring, one wonders if they are worth the investment in time and effort. After all, something that's practiced so assiduously would hopefully pay off in the long run.

It turns out that isolating rundowns using play-by-play data is not as straightforward as one might think. However, we can identify those plays where there were two consecutive throws by the defense without an error that did not originate from the outfield (to avoid counting simple relays) or where there were more than two consecutive throws. Yes, this does not count the optimum rundown from a defensive perspective that consists of a single throw, nor does it count when an error is made on the first or second throw. So sue me.

That said, in 2005 there were 341 such plays. But of those, 206 occurred on pickoffs or during a stolen base attempt, and in 111 of the pickoffs the runner simply put his head down and made a bee line for the next base without attempting to entangle himself in a rundown.

As near as I can tell, that leaves us with 230 rundowns of some length, or one every 21 games per team. And how many times did the defense commit an error causing the runner to be safe?

Exactly twice.

So, just over 99% of the time the runner is eventually put out when he gets himself in a rundown. It looks like all that work may actually pay off after all. Of course, the other way to look at it is that given the low frequency and the possibility that rundowns are an easy enough play that continued repetition doesn't buy any added benefit, and you come to the conclusion that perhaps all that drilling does not confer much of a benefit.

For the curious, the longest rundown of 2005 occurred on September 22nd, when Gustavo Chacin of the Blue Jays picked Mariner Yuniesky Betancourt off of first base in the top of the first inning in a play that went 1-3-6-3-6-1. Was Betancourt perhaps being too aggressive with his lead? If so, he's lucky that he has a manager who may not be that concerned.


A correction to last week's article: At the end of last week's column, I noted that in the chapter on platoon splits in The Book, the authors say that a right-handed hitter's measured platoon split should be regressed to the mean by weighting the league average by 2200 plate appearances, while for lefties you would weight by 1000 PA. What I failed to say is that in both cases the weighted league average would be combined with the measured platoon split weighted by the number of plate appearances versus left-handed pitchers in order to calculate the estimated platoon split. The implication in the original article was that you would weight the platoon split by total plate appearances, which is not the case.

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