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March 29, 2007
The Price of Contentment
"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."
"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."
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%.
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.
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 (WX
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 WX
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.
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