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Why Weeks Shouldn't Steal Second, but Gomez Should

EDITOR'S NOTE: I'm on the road today and in a hotel with crappy internet, so the Mug will be off Friday. Thanks to ecocd for submitting this post to help fill the vacancy. - KL

Since Roenicke was first named the new manager of the Brewers, we’ve been hearing about how he wants to be aggressive on the basepath. We’re also all very well aware that Macha was strictly a 27-Outs Manager. Given that the two approaches lie on the opposite ends of the spectrum, I decided to go looking for an answer as to which one would work best for the Brewers. Relying heavily on the work in Dan Levitt’s 2006 article "Empirical Analysis of Bunting," I believe the answer lies closer to Roenicke than Macha.

This post repurposes Levitt’s tables for stolen bases rather than bunting. It’s evolutionary, not revolutionary. I’ll do my best to make this post self-contained, but if you’re intrigued by what you read in this post, you’ll learn a lot from reading his original article. It’s dry and a bit long, but you’ll get a lot out of it.

 

Expected Run Tables and Breakpoints

 

Anyone who has been around Sabermetrics long enough knows about the Expected Run Table (ERT). There are 24 basic states of the game in terms of bases and outs. Levitt calculated the average runs scored for each of these states using data from 1977 to 1992:

TABLE 1 - Expected Run Table (1977-1992)

AL         0        1        2      NL        0        1        2
-----------------------------------------------------------------
---     .498     .266     .099     ---     .455     .239     .090
x--     .877     .522     .224     x--     .820     .490     .210
-x-    1.147     .693     .330     -x-    1.054     .650     .314
xx-    1.504     .922     .446     xx-    1.402     .863     .407
--x    1.373     .967     .385     --x    1.285     .907     .358
x-x    1.758    1.187     .507     x-x    1.650    1.123     .466
-xx    2.009    1.410     .592     -xx    1.864    1.320     .566
xxx    2.345    1.568     .775     xxx    2.188    1.487     .715

Where, for example, ‘xx-‘ means runners on first and second, third base empty. Thus if a team has runners on first and second with no outs, on average they will score 1.504 runs over the remainder of the half-inning; with one out, .922; and with two outs, .446.

Levitt makes the point that this table takes the generalizations too far. Using the table above to make a blanket statement about baseball strategy is almost pointless since the vast majority of baseball is situational.

The only calculation I use for this post is the breakpoint (a.k.a. breakeven point) of stolen base percentage at which point the baserunner is helping rather than hurting his team.

Breakpoint = (Current Expected Run State – Caught Stealing Expected Run State) / (Successful Steal Expected Run State – Caught Stealing Expected Run State).

In the NL, using the table above, a team with a runner on 1st with no outs can expect to score an average of 0.820 runs (henceforth "xR" for expected Runs). If that player is then thrown out trying to steal second (CS), his team is now in the state of Bases Clear, 1 out at 0.239 xR. A successful steal (SB) leaves his team in the 2nd base, 0 outs state at 1.054 xR

Breakpoint = (0.820 – 0.239) / (1.054 – 0.239) = 71.3%

The problem with breakpoints, which Levitt strains to emphasize, is that they simplify the situations too much. I’m going to save that conversation for the end of this post, but keep in mind that the generalized tables don’t take into account Gomez’ speed causing a throwing error to score from 1st base on a sacrifice bunt against the Chicago Cubs.

Levitt then produced the same ERTs split by batting order. Batting order serves as a proxy for the relative strength of each batter in a lineup and how their individual success rates will translate into expected runs. There are now 24 states for each of the 9 spots in the batting order for a total of 216 unique game states. I’ll use Levitt’s own words here:

Table 2 shows the expected runs based on lineup position for each league. For example, what does the expected runs table look like if the cleanup hitter is at bat? … To keep the data as pure as possible to reflect lineup position, appearances by pinch hitters in the identified lineup position are not included.

TABLE 2 - ERT by Lineup Position

AL                                          NL
  1          0        1       2               1          0        1       2
---       .553     .291    .100             ---       .542     .294    .102
x--       .951     .567    .210             x--       .911     .530    .213
-x-      1.263     .753    .323             -x-      1.130     .720    .342
xx-      1.614     .966    .428             xx-      1.526     .868    .418
--x      1.395     .976    .399             --x      1.319    1.003    .399
x-x      1.840    1.242    .527             x-x      1.786    1.107    .506
-xx      2.182    1.456    .623             -xx      1.978    1.336    .621
xxx      2.365    1.621    .773             xxx      2.081    1.480    .722
  2         0         1       2               2          0        1       2
---       .543     .297    .113             ---       .530     .286    .104
x--       .966     .576    .253             x--       .977     .611    .251
-x-      1.214     .752    .346             -x-      1.180     .723    .333
xx-      1.599    1.028    .453             xx-      1.583     .979    .450
--x      1.435    1.012    .432             --x      1.368     .971    .394
x-x      1.865    1.286    .531             x-x      1.778    1.211    .523
-xx      2.100    1.487    .609             -xx      2.068    1.375    .570
xxx      2.434    1.685    .822             xxx      2.398    1.473    .732
  3          0        1       2               3          0        1       2
---       .536     .305    .117             ---       .517     .297    .118
x--       .945     .581    .268             x--       .928     .582    .278
-x-      1.192     .740    .385             -x-      1.129     .735    .395
xx-      1.609    1.002    .522             xx-      1.607    1.007    .518
--x      1.422    1.017    .400             --x      1.337     .993    .401
x-x      1.820    1.249    .574             x-x      1.831    1.266    .562
-xx      2.052    1.534    .674             -xx      2.031    1.518    .715
xxx      2.468    1.699    .867             xxx      2.402    1.720    .817
  4          0        1       2               4          0        1       2
---       .488     .293    .118             ---       .442     .274    .115
x--       .885     .567    .252             x--       .849     .553    .261
-x-      1.160     .711    .343             -x-      1.098     .719    .350
xx-      1.501     .962    .488             xx-      1.488     .961    .532
--x      1.318     .972    .412             --x      1.308     .958    .390
x-x      1.816    1.230    .530             x-x      1.741    1.247    .559
-xx      1.950    1.445    .644             -xx      1.864    1.426    .596
xxx      2.345    1.616    .863             xxx      2.457    1.615    .867
  5          0        1       2               5          0        1       2
---       .452     .254    .107             ---       .403     .224    .103
x--       .835     .537    .245             x--       .757     .494    .220
-x-      1.110     .706    .339             -x-       .925     .648    .340
xx-      1.453     .930    .463             xx-      1.336     .913    .452
--x      1.223     .946    .373             --x      1.159     .942    .389
x-x      1.674    1.200    .529             x-x      1.579    1.163    .496
-xx      1.900    1.353    .550             -xx      1.881    1.356    .607
xxx      2.301    1.601    .795             xxx      2.284    1.588    .775
  6          0        1       2               6          0        1       2
---       .446     .231    .094             ---       .370     .191    .079
x--       .791     .464    .220             x--       .725     .430    .210
-x-      1.059     .646    .336             -x-       .941     .585    .309
xx-      1.415     .905    .459             xx-      1.311     .851    .404
--x      1.328     .951    .367             --x      1.095     .829    .342
x-x      1.712    1.129    .518             x-x      1.435    1.106    .452
-xx      2.016    1.340    .581             -xx      1.764    1.336    .531
xxx      2.200    1.532    .755             xxx      1.997    1.536    .726
  7          0        1       2               7          0        1       2
---       .439     .225    .083             ---       .363     .183    .061
x--       .800     .438    .201             x--       .652     .388    .176
-x-      1.076     .617    .310             -x-       .913     .540    .261
xx-      1.408     .836    .419             xx-      1.293     .756    .385
--x      1.230     .888    .354             --x      1.242     .749    .327
x-x      1.625    1.107    .453             x-x      1.507    1.036    .419
-xx      1.852    1.360    .570             -xx      1.718    1.220    .469
xxx      2.337    1.480    .753             xxx      2.062    1.450    .717
  8          0        1       2               8          0        1       2
---       .474     .226    .077             ---       .397     .172    .054
x--       .798     .461    .179             x--       .678     .375    .127
-x-      1.039     .609    .283             -x-       .923     .485    .230
xx-      1.431     .804    .410             xx-      1.179     .694    .321
--x      1.419     .919    .347             --x      1.212     .782    .274
x-x      1.674    1.105    .444             x-x      1.514     .945    .429
-xx      1.962    1.322    .561             -xx      1.620    1.157    .495
xxx      2.289    1.465    .686             xxx      1.994    1.315    .661
  9          0        1       2               9          0        1       2
---       .519     .263    .081             ---       .450     .194    .050
x--       .852     .480    .182             x--       .739     .362    .125
-x-      1.128     .641    .293             -x-      1.022     .542    .181
xx-      1.475     .927    .382             xx-      1.238     .705    .230
--x      1.423     .947    .341             --x      1.281     .753    .236
x-x      1.725    1.145    .457             x-x      1.466     .891    .269
-xx      2.108    1.396    .513             -xx      1.730    1.048    .387
xxx      2.386    1.533    .709             xxx      1.930    1.219    .470

He splits it by AL/NL for obvious reasons and this BrewCrewBall.com post will focus on the NL for equally obvious reasons. The quality of the players at the plate matters a lot. A typical leadoff hitter in a typical 9-man batting order is worth 0.542 xR before he even steps into the batter's box in the 1st inning. If the 6th spot is up in the order to start the 2nd inning, that hitter is worth 32% less at 0.370 xR.

The first big assumption I’m making is using the above tables. We know the Brewers offense is most definitely better at the top of the order than a typical NL lineup. Using the above tables isn’t going to be entirely reflective of the Brewers. Even if I had the data and the experience to create ERTs specifically for each Brewer the sample sizes would be too small, so I’m just gritting my teeth.

I’ve calculated breakpoints for the solo man-on-base situations for all 9 batting order spots and you can see them on a Google spreadsheet here. I’ll hit the high points in this post.

 

When Rickie Weeks Should be Stealing

 

Coming into 2011, Rickie Weeks carries 91 career SB with 20 CS for a SB% of 82%. Take note that this is overall SB% and does not split his SB% between stealing 2nd base and stealing 3rd base. I talk a little more about how stealing 3rd base is different than stealing 2nd base later.

Let’s say Weeks gets on base to lead off the game. With the 2nd spot in the batting order up, he’s in one of two game states, runner on 1st, no outs or runner on 2nd no outs. Here are his breakpoints:

#2 hitter

Gain xR

Loss xR

breakpoint

0 outs man on 1st

0.203

-0.691

77%

0 outs man on 2nd

0.188

-0.894

83%

When Weeks is on base to lead off the game, he should pretty much be staying put. The guys behind him are going to be getting him home without the extra base. The situation changes, however, when the pitcher led off the inning with an out and Weeks gets on base:

#2 hitter

Gain xR

Loss xR

breakpoint

1 out man on 1st

0.112

-0.507

82%

1 out man on 2nd

0.248

-0.619

71%

With 1 out, Weeks should be staying put on 1st base, but could actually be fairly aggressive in taking 3rd base. Finally, let’s say Yuni grounds out weakly to the shortstop, Marcum strikes out and Weeks gets on base with two outs:

#2 hitter

Gain xR

Loss xR

breakpoint

2 outs man on 1st

0.082

-0.251

75%

2 outs man on 2nd

0.061

-0.333

85%

 

The adage, "never make the 3rd out at 3rd base" shines through bright and clear. Weeks can take his chances at swiping 2nd, but he should pitch a tent once he gets there.

For the most part, each of these percentages drop as you get later in the order. That is, a team should be more aggressive late in batting order than at the top.

 

When Carlos Gomez Should be Running

 

In his career, Carlos Gomez has posted a 76% SB% with 77 SB and 24 CS.

Let’s say Gomez is hitting in the 6 slot and gets a hit to lead off the 2nd inning.

#7 hitter

Gain xR

Loss xR

breakpoint

0 outs man on 1st

0.261

-0.469

64%

0 outs man on 2nd

0.329

-0.73

69%

Gomez should pretty much have a green light regardless getting a single or double. If he steals 2nd then he should be looking for another good running count to steal 3rd. And if he gets on with 1 out?

#7 hitter

Gain xR

Loss xR

breakpoint

1 out man on 1st

0.152

-0.327

68%

1 out man on 2nd

0.209

-0.479

70%

Again, he should be running at pretty much any good opportunity. How about in Bizarro World where Fielder and McGehee made outs, but Gomez gets on:

#7 hitter

Gain xR

Loss xR

breakpoint

2 outs man on 1st

0.085

-0.176

67%

2 outs man on 2nd

0.066

-0.261

80%

He’s more than welcome to take 2nd, however, even in the best batting order scenario, Gomez shouldn’t have designs on stealing 3rd with 2 outs.

 

Throwing Errors

 

The above tables are most definitely simplified situations and that’s no clearer than with the pitcher’s spot up, 2 outs and a man on 1st. In this case, the ERT gives a breakpoint of 55%! No manager in his right mind would risk having his pitcher lead off the following inning because a guy got thrown out trying to steal 2nd or 3rd base. That’s just stupid.

The above tables also fail to take into account throwing errors. To make the point, I’m going to say that 7% of all stolen base attempts, result in a 1-base throwing error from the catcher (this is about Total Catcher Errors / Total SB Attempts over the last 3 years).

Weeks’ breakpoint for 1st base, no outs drops 1.2%, whereas his 2nd base, no outs breakpoint drops only 0.3%. The small possibility of moving to 3rd base on an errant throw, means he can take more risks in getting to 2nd base. He’s so likely to score from 3rd base with no outs that a throwing error when going from 2nd to 3rd doesn’t have a big enough impact on the expected runs to justify being more aggressive on trying to swipe 3rd. If we use the same throwing error rate for Gomez with 2 outs, his breakpoint on stealing 3rd drops down to 75% - near to the point of not getting an earful from Roenicke if he gets caught.

 

Scoring Only One Run

 

In a point I won’t address in as much detail, Levitt creates another set of tables that lay out the probability of scoring at least one run from a given game state. This is the classic 8th or 9th inning situation. Your team is down by one or tied and you don’t care about the possibility of putting up a 4-spot anymore; you just need one run to bring it even or close it out.

If Weeks gets a lead off single, he’s going to score about 50% of the time. When he opens with a double, that jumps to 66%. His breakpoints change dramatically when the team only needs to score a single run:

#2 hitter

Gain (prob)

Loss (prob)

breakpoint

0 outs man on 1st

0.162

-0.326

67%

0 outs man on 2nd

0.187

-0.488

72%

He’s gone from practically never trying to steal a base with no outs to almost always taking advantage of a good opportunity to steal a base.

 

Situations Make All the Difference

 

Levitt gives strong empirical evidence that managers know how to evaluate advantageous game states beyond the simple batting order ERTs. He shows that teams routinely beat the "expected runs" on bunting decisions.

There are actually hundreds of thousands of game states, if not more, and they all have some impact on the expected run state for a given action. Does the hitter at the plate hit a HR 5% of his AB? 10% of his AB? Does he only hit singles? Are you facing a ground ball pitcher? Where are the outfielders situated? These all have some impact on the expected run state. Levitt demonstrates that managers well outperform a simple 216 cell ERT in bunting situations and I’m sure the same would be shown for stolen base decisions if someone were to bother to do the work to make the calculations.

Stealing 3rd Base

 

One could write an entire article about stealing 3rd base and Tim Kurkjian did just that last year. He notes that the number of stolen base attempts at 3rd base has been increasing over the past few years. In 2009, the Texas Rangers accounted for one-third of all MLB stolen base attempts at third, converting on 32 of 35 attempts for a very impressive 91.4% success rate. Compare that rate to the above tables and one could nearly always green light a steal of 3rd base even with 2 outs. It once again, however, comes down to situational baseball.

While the catcher has a shorter distance to throw the ball, the base stealer will get a much larger lead. Kurkjian quotes Larry Bowa

"It is much easier to steal third [base] against a left-hander. When a runner gets a good lead off second, the pitcher has to literally turn his head all the way around to see him."

I’ll encourage everyone to read the full article, because I have a feeling the Brewers could be amongst the league leaders this year. An attentive Brewers fan at a game might be able to call a steal of 3rd before it happens thereby winning a friendly wager and earning a free beer from his mystified friends.

 

Conclusion

 

In summary, it should come as no surprise that there are smart times to run and there are dumb times to run. I think Roenicke’s aggressive behavior will pay off over the course of the entire season. The breakpoints I calculated are based on generalized game states and in reality, all of the breakpoints are probably a little smaller. The players and managers are going to be choosing to steal in better run states than the generalized tables cover.

I believe the batting order ERTs are still instructive in that we have empirical evidence that each player can have a different SB%, but still be considered successful on the basepaths. So don’t be surprised if Weeks isn’t running very often, despite his speed and impressive career SB%. On the other hand, don’t throw up your hands when Gomez only posts a 71% SB% while hitting in the bottom half of the order. And I’m going to have to learn not to swear at Hart every time he tries to stretch a single into a double this year.

 

Bonus Material!

 

Here’s one final fun fact for you boys and girls. The typical #7 and #8 hitters are so poor that the numbers say when one of them steps into the batter’s box with a man on 3rd base and 2 outs and the team only needs to score 1 run, the baserunner should attempt to steal home if he can make it 75% of the time! If a team were only to attempt it once (maybe twice) in a season, I believe someone with amazing speed like Carlos Gomez could achieve a theoretical 75% success rate. Make it and he’s a hero. Get caught and he’s an idiot. Either way, he probably made the right call to try it.

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