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Constructing an Optimal Lineup

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Is it safe to come out? Is Beane done? Well, now that we (maybe?) have a complete set of batters, we need an order to bat them in. Sure, there's a well-established conventional wisdom to this, but is it accurate? Is it really what's best for scoring runs? The introduction of heavy statistics into baseball has reversed and shaped countless managerial decisions in the last decade or so. Can it find an optimal lineup that gives us the best chance at scoring more runs? I'm sure a lot of you already know what I'm going to say in this post, but I'm going to take a stab at bringing the less sabermetrically inclined of us up to speed, keeping it simple and easy to understand. All figures come from The Book, by Tango, Lichtman, and Dolphin.

Before I start, though, I have to address one thing. The batting order really doesn't make as much of a difference in a team's offense as you might think. Assuming that we stay in the realm of reality and throw out any obviously ridiculous lineups that will never happen (batting Holliday and Pujols 8th and 9th, for example), the difference between a bad lineup and a good lineup is only about a handful of runs over the course of the entire season. That being said, why not try and squeeze all of the runs we can get out of the players we have? Unlike most other tweaks to a team, changing a batting order doesn't cost a dime. So why not have it be the best that it can be?

 

Plate Appearances

The first item we have to consider is a relatively simple one. In our lineup, we'd want the best hitters to come up more often, and we'd want our poor hitters to come up less. If every game was a perfectly pitched game, all members of the lineup would get exactly three plate appearances per game, and every batter would come up to bat the same amount of times. Of course, that isn't the case, and most games end with a batter other than the ninth one making the final out, "robbing" some players of the chance to bat. Over the course of a season, the leadoff man tends to come up to bat 4.8 times per game, and the figures decline gradually by batter. The ninth batter comes up only 3.9 times per game. That's a big difference, and so of course, we'd want our better hitters clustered up at the top of the order, with our lesser hitters "hidden" near the bottom.

 

Men on Base

Let's imagine that it's three years in the future, and Chris Carter is everything we had hoped for and more. If baseball allowed us to move batters around whenever we felt like instead of sticking to a strict order, when would you put Carter in? The best thing to do would be to use him when we've got two or three guys on base, waiting for that big hit to come home. We can't change the batting order on the fly, unfortunately, but instead, we can try and put our best hitters in a slot that tends to come up when men happen to be on base. Well, it turns out that the slot that comes up with men on base most often is the fourth spot.

Lineup Slot

1

2

3

4

5

6

7

8

9

PA's with Men on Base

36%

44%

48%

51%

48%

46%

47%

46%

45%

 

Outs

Let's go back to our hypothetical Chris Carter and our fluid batting order. If men on base weren't an issue, what other factors would you take into consideration when choosing when to bring Carter up? To get the best production out of the guy, you'd want to put him in when there's no outs in the inning. Putting Carter in would be kind of a waste if you waited for a two out scenario. Of course, we can't actually put batters in whenever we wanted, but like before, we can see which slots tend to come up with no outs.

Lineup Slot

1

2

3

4

5

6

7

8

9

PA's with No Outs

48%

33%

28%

34%

35%

33%

33%

34%

34%

 

The Final Results

If we put everything together, we can find a set of run expectancy figures for each batting order. This next table is a summary of run expectancies for each slot in the lineup, including everything I mentioned previously. The total line sums up the potential damage a batter can do in that slot--the bigger, the better.

Lineup Slot

1

2

3

4

5

6

7

8

9

Single

0.515

0.515

0.493

0.517

0.513

0.482

0.464

0.451

0.436

Double

0.806

0.799

0.779

0.822

0.809

0.763

0.738

0.714

0.689

Triple

1.121

1.100

1.064

1.117

1.106

1.050

1.014

0.980

0.948

Home Run

1.421

1.450

1.453

1.472

1.438

1.376

1.336

1.293

1.249

Walk

0.385

0.366

0.335

0.345

0.348

0.336

0.323

0.312

0.302

Total

4.248

4.230

4.124

4.273

4.214

4.007

3.875

3.750

3.624

 

From this table, we can define a set of general guidelines that any manager should follow for an optimal lineup. The batters in slots 1, 2, and 4 have the highest chance of scoring runs. Conventional wisdom has the third hitter as the best--these numbers clearly disagree. If you were to rank your batters in order of quality, your top three hitters should be in slots 1, 2, and 4. The next two batters in quality should sit in slots 3 and 5, with the rest in the lower slots in descending order. Between the top three hitters on the team, ideally, the best home run threat would go in the fourth slot, and the most patient hitter would lead off. Between the guys slotted third and fifth, the player with a higher slugging percentage would bat third, with a higher contact guy in the fifth position.

With all of this in mind, I propose the following lineup, with 2010 CHONE projections following each name.

 

1B Barton (.261/.366/.413)

RF Sweeney (.286/.350/.409)

3B Kouzmanoff (.259/.304/.431)

DH Cust (.235/.370/.441)

C Suzuki (.275/.335/.405)

CF Davis (.270/.329/.375)

LF Crisp (.254/.330/.370)

2B Ellis (.248/.312/.386)

SS Pennington (.243/.325/.341)

 

Odds and Ends

  • This article is long enough already, but I know I'm going to get questions about not having the prototypical speedy basestealer up at the top. I won't go into the details, but The Book comes to the conclusion that rather than stacking speed up at the top, you should put a basestealer in front of a singles hitter who doesn't strikeout a lot. But this rule should only be followed if you don't violate the higher priority rules above.
  • Wow, those CHONE projections are sobering.
  • Of the top ten CHONE-projected hitters under Oakland's control, only five are slated to be starters. In order (by wOBA): Jack Cust, Daric Barton, Ryan Sweeney, Travis Buck, Jake Fox, Michael Taylor, Kurt Suzuki, Gabe Gross, Kevin Kouzmanoff, and Chris Carter.
  • Eric Sogard is projected to be a little under three runs better than Pennington over the course of a full season. In the major leagues.