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March 29, 2007

Schrodinger's Bat

The Price of Contentment

by Dan Fox

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"He told me the rule book doesn't specifically cover that situation. He said you've seen one of the most unusual plays in baseball."
--Official scorer Randy Minkoff, recounting his conversation with Seymour Siwoff about the Cardinals "quadruple steal" in August of 1985, as recorded by Retrosheet

"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible."
--Aristotle

On the first day of August in 1985, the Cardinals and Cubs were set to complete a three-game midweek series at Wrigley Field. Having split the first two games, the Cardinals were holding on to a two-game lead in the National League East over the Mets, while the Cubs (on the heels of their surprising 1984 campaign) were a disappointing 8.5 games out, and just five games over .500.

To start the first inning, Cubs starter Scott Sanderson gave up a leadoff single to would-be Rookie of the Year Vince Coleman, and then walked eventual batting champion and MVP Willie McGee. In the full spirit of Whiteyball, both Coleman and McGee promptly took off with Tom Herr at the plate. Although both runners were safe, Coleman overslid third base, so he immediately leaped up and started towards home, saying later that "I knew I couldn't get back to the bag. I was still in no-man's land. So my reaction was to go to the next base." It worked--the Cubs had him in a rundown, but apparently neither Sanderson nor first baseman Leon Durham covered the plate. Coleman scored as McGee hustled around second and beat the throw to third.

The Retrosheet play-by-play log notes that Elias' Seymour Siwoff was then consulted by official scorer Randy Minkoff, and as a result each runner was credited with two stolen bases on the play--a quadruple steal, if you will. With those two bags giving Coleman 74 SB, he broke the rookie record of 72 set by Juan Samuel just the year before. The rest of the game wasn't bad either, as the Cubs pulled out a 9-8 thriller on a Larry Bowa bunt single with the bases loaded in the bottom of the 14th inning in a game that would take over five hours.

When reader Bert Dalmer called my attention to this play after last week's column on double steals, I'll admit I was at first stumped, since I knew that this play would have turned up in the final section of that piece where the twelve successful triple steals in the data set that stretches back to 1970 were mentioned.

Upon further review it turns out that the Retrosheet game log records what in actuality was one continuous play as two separate and consecutive events. As a result, when I credited Whitey Herzog with 13 successful double steals in 19 attempts in 1985, and 112 of 141 during his managerial career those numbers should really have been 12 of 18 and 111 of 140. And herein lies a lesson--the codes used in play by play data files, as wonderful as they are (I just re-read the essay "How is Project Scoresheet Doing?" in the 1986 Baseball Abstract wherein Bill James proudly reports that every game of the 1985 season was recorded), are not always granular enough to tell the entire story.

This week we'll investigate a larger instance of that general rule, and then move from Run Expectancy to Win Expectancy.

The Two-Out Dilemma

As coincidence would have it a reader raised the underlying issue in my March 16th chat:

Valentine (Boston): Hi Dan! I've enjoyed your series on baserunning value, yet your ability to answer certain questions appears limited by the traditional scoring rules. If you could rewrite the scoring system for baserunning plays, what would it look like?

I noted that it would be nice to know in a consistent fashion when runners were moving with the pitch, so that we could more easily separate hit and runs from stolen base attempts. It turns out that this is also the root cause of my consternation last week. After reviewing the success percentages for double steal attempts in light of what a strategic assessment using the Run Expectancy matrix might say, I wrote:

What is perhaps the most interesting point in these two tables is the fact that the success rate is so much higher when there are two outs as opposed to zero or one out. At first glance it is not obvious why this should be the case although I'm sure our enlightened readers will provide some clues.

To be more precise, in my data set there are 5,276 double steal attempts with a success rate of 67.2%. Of those, 1,244 occurred with two outs and were successful at a rate of 91.1%. The difference of 59.9% with zero or one out, and over 90% with two outs should have caused me to look a little deeper, but alas our intrepid readers did indeed quickly set me straight. As mentioned last week, if on a double steal attempt one runner is caught stealing the other runner does not get credit for a stolen base per rule 10.08(d).

In order to catch those scenarios, my software was looking for advancement by trailing runners when leading runners were caught stealing. But as several readers gently reminded me, with two outs the scorers probably would not typically record the trailing runner's advancement, as they would be forced to do with less than two outs, since the inning is effectively over with the caught stealing.

Still, scorers do occasionally do this (115 times anyway) and that's what led to my comment above. Over half of the 115 occurrences are double steal attempts, often delayed double steals, with a runner on third and where that runner scored before the trailing runner was put out. Most the remainder involve rundowns where the trail runner had already advanced before the lead runner was thrown out. These plays, few though they are, are also problematic since it is not clear whether the trailing runner was really off with the pitch.

Such is the state of the data, and that state makes it impossible to definitively answer the question of whether double steal attempts with two outs are generally successful from a strategic perspective. But let's not be disheartened, and instead take Aristotle's advice and be satisfied with the approximation we have, imperfect as it is.

Winners and Losers

Keeping the limitations in mind, other readers wondered how double steals stack up from a Win Expectancy (WX) standpoint. In an effort to not disappoint, using the same definitions of successes and failures outlined in the first section of last week's column and including all the two out data we have, the following table lists the top and bottom 20 managerial seasons in terms of aggregate change in WX. This takes into account the score, inning, base situation, number of outs, and run environment.

Year     Team    Manager           Succ     Att     WX
1989     MIL     Tom Trebelhorn      13      17   0.812
1983     OAK     Steve Boros         13      15   0.794
1978     PIT     Chuck Tanner        13      16   0.703
1991     NYN     Bud Harrelson        9      10   0.651
                 Mike Cubbage         9      10   0.651
1982     OAK     Billy Martin        17      21   0.604
1976     OAK     Chuck Tanner        16      19   0.536
1980     BAL     Earl Weaver          7       7   0.512
1980     MON     Dick Williams       12      14   0.500
1976     NYA     Billy Martin         8       8   0.459
1985     CHN     Jim Frey            10      14   0.453
1978     KCA     Whitey Herzog        9      10   0.451
1998     FLO     Jim Leyland          6       9   0.433
1988     MIL     Tom Trebelhorn       8       9   0.433
1985     CIN     Pete Rose            6       6   0.416
1988     NYA     Billy Martin        11      12   0.411
                 Lou Pinella         11      12   0.411
1971     CIN     Sparky Anderson      3       3   0.401
1982     DET     Sparky Anderson      7       8   0.399
1989     MIN     Tom Kelly           10      12   0.392
-------------------------------------------------------
1991     MON     Buck Rodgers         6      15  -0.645
                 Tom Runnells         6      15  -0.645
1997     ATL     Bobby Cox            1       5  -0.569
1993     CAL     Buck Rodgers         5      14  -0.547
1988     MON     Buck Rodgers         7      12  -0.540
2000     SEA     Lou Pinella          7      11  -0.522
1986     MON     Buck Rodgers         9      16  -0.521
1989     SFN     Roger Craig          0       4  -0.491
1989     LAN     Tommy Lasorda        3       8  -0.478
1997     NYA     Joe Torre            4      10  -0.425
1987     SFN     Roger Craig          3       9  -0.418
2006     WAS     Frank Robinson       4       7  -0.396
1997     SLN     Tony LaRussa        10      17  -0.395
1986     TEX     Bobby Valentine      4      10  -0.395
1976     CLE     Frank Robinson       2       8  -0.382
1990     CHN     Don Zimmer           6      10  -0.379
2002     SDN     Bruce Bochy          6       8  -0.359
1989     MON     Buck Rodgers         8      17  -0.352
1987     MIL     Tom Trebelhorn       4      11  -0.347
1986     KCA     Mike Ferraro         1       4  -0.343

Interestingly, Tom Trebelhorn finds himself in the top spot with his 1989 Brewers at +0.812 wins, and also 14th with the 1988 Brewers (+0.433), but then 19th from the bottom at -0.347 with his 1987 squad.

Billy Martin makes the top 20 three separate times (sharing the 1988 result with Lou Pinella, who managed 93 of the Yankees' 161 games). Along with Trebelhorn, Chuck Tanner finds his way into the list twice, as does Sparky Anderson. On the negative side of the ledger, Buck Rodgers appears no less than five times, including the 1981 season split with Tom Runnells, who managed most of the season.

Both Frank Robinson and Roger Craig, mentioned last week as the two lowest-percentage managers with over 40 attempts, appear twice in the list. Last week's list of top percentages for a single season found Terry Collins' 1996 Astros on the top with a 20 of 23 performance. However, in terms of WX it rated as a -0.027, since the three caught stealing were especially impactful at -0.295, and five of the successful double steals occurred when the batter actually struck out--and so resulted in a net negative change in WX.

Noting Rodgers' difficulties brings us to the career WX list with the top and bottom 20 listed below.

Name                  Succ     Att      WX
Whitey Herzog          112     141    2.452
Chuck Tanner            72     103    2.138
Billy Martin           102     151    1.589
Art Howe                46      68    1.436
Tony LaRussa           160     219    1.433
Sparky Anderson        125     170    1.404
Mike Hargrove           87     124    1.274
Pete Rose               41      48    1.033
Danny Ozark             41      50    0.997
Tom Trebelhorn          47      75    0.929
Dick Williams           68      95    0.927
Darrell Johnson         24      44    0.876
Earl Weaver             49      79    0.832
Tom Kelly               75     111    0.782
Dave Garcia             23      30    0.673
Charlie Fox             20      24    0.659
Mike Cubbage             9      10    0.651
Steve Boros             18      24    0.636
Jim Frey                19      27    0.620
Mike Scioscia           43      48    0.616
-------------------------------------------
Buck Rodgers            76     145   -2.751
Frank Robinson          46      92   -1.505
Roger Craig             29      66   -1.449
Bobby Valentine         45      82   -1.395
Jeff Torborg            44      85   -1.146
Tommy Lasorda           91     151   -1.108
Bob Lillis               7      15   -0.829
Joe Torre              111     165   -0.819
Tom Runnells             9      20   -0.762
Cal Ripken               8      21   -0.667
Dallas Green            24      40   -0.563
Gene Michael             1       8   -0.551
Jack McKeon             58      85   -0.537
Buck Showalter          18      29   -0.534
Dusty Baker             27      45   -0.497
Terry Bevington          7      14   -0.450
Russ Nixon              13      23   -0.428
Buck Martinez            5      10   -0.420
Ralph Houk               7      11   -0.416
John Felske              7      12   -0.411

Whitey Herzog (still counting the quadruple steal as two events) and Chuck Tanner both are credited with over two theoretical wins, while Buck Rodgers is more than a win worse at -2.75 than his closest competitors in Frank Robinson and Roger Craig. It should be noted that Mike Cubbage is credited with the performance of the 1991 Mets, when in reality he managed only seven games while Bud Harrelson skippered the remainder.

What these small gains and losses over so many seasons hint at is that the success rate tracks pretty closely with the break-even percentage (discussed below) and so in the end attempted double steals are a bit of a wash. In fact, taking all 5,276 attempts together the total change in WX is +13.3 wins. Since we know we have data problems with two-out attempts excluding those yields a total of -36.2 wins. That's not a large difference over the course of over 35 years.

Before we leave managers behind, it's also interesting to consider which managers got the biggest bang for the buck in terms of positive WX per double steal attempt. The top 10 are listed below without additional comment.

Name                  Succ     Att      WX   WX/Att
Pete Rose               41      48    1.033   0.022
Art Howe                46      68    1.436   0.021
Chuck Tanner            72     103    2.138   0.021
Danny Ozark             41      50    0.997   0.020
Darrell Johnson         24      44    0.876   0.020
Whitey Herzog          112     141    2.452   0.017
Mike Scioscia           43      48    0.616   0.013
Tom Trebelhorn          47      75    0.929   0.012
Jim Fregosi             33      45    0.546   0.012
Cito Gaston             36      43    0.500   0.012

In terms of bang for the buck the largest single change in WX for any double steal attempt in our data set occurred on September 13, 1971 in a game where the Reds were hosting the Braves. With the score tied 1-1 in the bottom of the 13th inning with two outs, the Reds had Lee May on first and Pete Rose on second with Johnny Bench at the plate. The runners took off and were both safe, but the throw hit the third base bag, allowing Rose to score the winning run while the unlucky Braves third baseman Gil Garrido was charged with an error for being late to cover the bag. The Reds WX before the play was 62.9%--afterwards it was of course 100% for a change of 37.1%. From a strategic perspective, as you might imagine, the play made little sense since with two outs Rose would likely have scored from second on a hit. This is reflected in the fact that the break-even percentage, as described below, for this play was almost exactly 100%.

Strategy Revisited

In addition to simply adding up the total change in WX for all attempted double steals, we can also employ WX to calculate a break-even percentage for each individual attempt. In other words, we can calculate the threshold percentage at which a manager might decide whether attempting a double steal is in the team's best interests. For example, if the break-even percentage in a given scenario is 66%, then a manager should elect to steal if he believes the play at that time has a greater than 66% chance of succeeding. By calculating the break-even percentage for every double steal attempt, and averaging those for each manager, we should then be able to determine which managers chose the most appropriate times to steal.

In order to calculate the break-even percentages for double steal attempts we'll follow a notation similar to that used by Keith Woolner in his Baseball Prospectus 2006 essay "Adventures in Win Expectancy," in which he used the same approach to determine which individual baserunners were choosing the best situations in which to try and steal.

Calculating the break-even percentage for the situation where a team has runners on first and second with nobody out can be illustrated as shown in the flowchart below.

image 1

Here, a manager is presented with a situation where runners on first on second, represented by B(12x), with nobody out shown as O(0). The manager then may elect to attempt to steal. If he doesn't elect to steal, his Win Expectancy (WXc, or WX Current) is calculated as that with the same base and out state, B(12x):O(0), as well as the same score S(n), inning I(y), and run environment RE(z). However, if the manager attempts to steal and is successful (WXs or WX Success), then the base state changes to B(x23):O(0), with the same additional context denoted as S(n):I(y):RE(z). If the play is unsuccessful, the model assumes the lead runner is caught, and the Win Expectancy (WXf or WX Failure) changes to a single runner on second base, B(x2x) with one out O(1) and the additional context the same.

Finally, in order to calculate the break-even percentage we subtract the WX for a failed attempt from the WX of the status quo, and divide the result by the WX when successful minus the WX that results from a failure. In this case, as in others, there are actually multiple states that can result from a caught stealing (the trailing runner could be cut down instead, for example). So, to be more accurate we should calculate the WXf for each outcome, and then weight them according to their probability of occurrence. This was not done for this article--instead we use the failure scenario that was the most costly and reasonably likely (I didn't use the outcome where both runners are caught for instance). This has the effect of raising the break-even percentage a little over what it would otherwise be if all the possible outcomes were considered.

Creating a similar model for each of the four base states where a double steal is possible and applying that model to the additional context of each double steal attempt allows us to calculate the break-even percentage for each event.

When applied to managers we can now produce the following table that shows the top and bottom managers in terms of average break-even percentage by attempt:

Manager               Succ     Att   Avg BE      WX
Davey Johnson           52      73    0.629   0.559
Bob Boone               34      47    0.629   0.481
Gene Mauch              43      74    0.629   0.303
Del Crandall            32      54    0.630   0.249
Darrell Johnson         24      44    0.630   0.876
Don Zimmer              52      88    0.634   0.047
Bobby Valentine         45      82    0.634  -1.395
John McNamara           29      43    0.636   0.141
Don Baylor              49      77    0.636   0.449
Doug Rader              26      41    0.637   0.213
---------------------------------------------------
Mike Scioscia           43      48    0.736   0.616
Terry Collins           40      52    0.713  -0.268
Walter Alston           30      44    0.701  -0.049
Pete Rose               41      48    0.694   1.033
Cito Gaston             36      43    0.690   0.500
Billy Martin           102     151    0.685   1.589
Jeff Torborg            44      85    0.680  -1.146
Bobby Cox               61      92    0.680  -0.288
Buck Rodgers            76     145    0.678  -2.751
Frank Lucchesi          29      45    0.677  -0.074

These lists are interesting since they indicate that while some managers may generally pick good times to run, their success rates indicate that they chose poor personnel with which to run. Conversely, some managers may seemingly have the odds stacked against them, yet they still do well. Bobby Valentine is an example of the former, and Mike Scioscia the latter. In the case of Scioscia, his break-even percentage was high, since 25 of his 48 attempts came when his team had a lead of two or more runs, which tends to drive up the break-even percentage, while only five attempts occurred with his team trailing. This is also a reason why, despite his excellent percentage, he doesn't score better in terms of total WX. When compared to other managers (Darrell Johnson for example), Scoscia's successes simply didn't raise the probability of his team winning by very much.

From an overall perspective we can now create a table that shows the success rates for the various categories of double steals broken down by number of outs:

Base     Outs    Succ      Att  Percent  Avg BE
12x         0     643     1127   57.1    0.587
12x         1    1595     2258   70.6    0.667
12x         2     772      776   99.5    0.831
1x3         0      21       70   30.0    0.728
1x3         1     147      478   30.8    0.590
1x3         2     350      457   76.6    0.597
x23         0       2        4   50.0    0.717
x23         1       2       51    3.9    0.633
x23         2       4        4  100.0    0.727
123         0       0        5    0.0    0.544
123         1       5       39   12.8    0.524
123         2       7        7  100.0    0.798
Total            3548     5276   67.2    0.661

Here we see that, overall, managers do a pretty good job on the double steal with runners on first and second, a not very good job with runners on first and third, and a pretty horrendous job with runners on second and third or with the bases loaded. The overall success rate looks pretty good when compared to the average break-even percentage, but keep in mind that this table includes attempts with two outs which we know are incomplete, and it's missing attempts that were not successful. Taking those out of the equation, the success rate goes down to 59.9%, and the break-even rate down to 63.5%, which tracks with the -36 run total when looking at attempts with less than two outs. Although it's very close, in the end managers probably call for the double steal a tad more often than they should.

The Runners

Thus far our discussion of double steals has been conspicuous for its lack of any discussion of the individual runners themselves. To close out this subject, we'll take a quick look at the runners involved in double steals since 1970. First, here are the top ten runners in terms of attempts as a part of a double steal. This includes only stolen bases and caught stealing that were officially recorded and so a trailing runner on a play where the lead runner was caught is not included.

Name                 SB     Att   Percent
Rickey Henderson     91     101    90.1
Paul Molitor         51      52    98.1
Craig Biggio         46      52    88.5
Barry Larkin         47      50    94.0
Vince Coleman        45      50    90.0
Ozzie Smith          42      44    95.5
Tim Raines           33      39    84.6
Omar Vizquel         35      37    94.6
Willie McGee         30      36    83.3
Davey Lopes          29      36    80.6

Rickey Henderson's 101 attempts included 72 successful steals of third in 82 attempts, while Vince Coleman's included 42 steals of third in 46 attempts. Ken Griffey Jr. had the most steals of second with 22, with Henderson was far and away the leader of swipes of third, and Paul Molitor led with nine steals of home in as many attempts. Interestingly, Molitor stole home ten times in his career, but nine of these were recorded as double steals, with the trail runner stealing second eight times and third once. On two other occasions Molitor did not get credit for a stolen base, but did score from third when the trail runner was caught in a rundown.

From a percentage perspective, the top ten with 25 or more attempts make for interesting reading:

Name                 SB     Att   Percent
Derek Jeter          32      32    100.0
Larry Bowa           31      31    100.0
Paul Molitor         51      52     98.1
Roberto Alomar       33      34     97.1
Kirk Gibson          30      31     96.8
Willie Randolph      26      27     96.3
Jeff Bagwell         25      26     96.2
Ozzie Smith          42      44     95.5
Omar Vizquel         35      37     94.6
Barry Larkin         47      50     94.0

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