In 2010 I devised and introduced the Mobius Strip Theory for MLB hitting line-ups, which presented a radical alternative to baseball’s traditional batting order template.
The Mobius Theory generated a lot of discussion and opinion. As the game evolves and the value of individual performance is better defined, the theory may appear more logical (but I admit it's still a dramatic leap).
I thought it would be interesting to apply the Mobius Strip Theory to the San Francisco Giants likely 2014 batting line-up (below), and continue the discussion. The traditional line-up may be one of the final untouchable strategic institutions inside the modern game.
Baseball’s offensive attack should be based on which configuration of hitters can potentially produce the highest number of runs in any given game; and average the most runs per game over a 162 game season.
In 2010 John Russell was about to start his third year as the Manager of the Pittsburgh Pirates. I wouldn’t really call Russell’s first two seasons in Pittsburgh “disastrous”... I think “catastrophic” is a much more accurate description: 62-99 in 2009, 67-95 in 2008.
So Russell decided to take a page from Tony La Russa’s playbook and at the end of Spring Training 2010, he announced that Pirate pitchers would bat 8th in the batting order throughout the entire season.
The idea was to generate more runs by adding the classic “second lead-off” hitter to the batting line-up. In this case shortstop Ronnie Cedeno batted in the 9th position, so when clean-up hitter Garrett Jones later walked up to the plate he might just find someone else on the field besides the opposition defense.
In the conservative world of baseball management even this modest experiment is the equivalent of going from analog to digital, or cutting rare steak from your diet and adding more fiber.
And if there’s one thing that the Major League Baseball establishment needs a lot more of, it’s fiber.
This fascinating subject is on the table only because La Russa, always an innovator, first batted his pitcher in the eighth slot of the order in 1998, his third year as manager of the St. Louis Cardinals.
La Russa stated that during his tenure as an American League manager with the DH, he was convinced that a “second lead-off” man batting ninth provided more opportunities for his number 3 and 4 batters to drive in runs.
Typically, the MLB establishment was out buying a corndog at the concession stands when this issue first came up, leaving the baseball saber and statistical community to crunch the numbers and properly analyze the phenomenon. And, as usual, they came through.
Specifically “The Book: Playing the Percentages in Baseball” by Tom Tango, Mitchel Lichtman, and Andrew Dolphin, researcher David Pinto, the legendary Cyril Morong and a number of other great researchers have thoroughly examined the impact of batting a position player 9th in the batting order (among many other batting order scenarios).
The hard research seems to point to a modest advantage for National League teams who hit their pitcher 8th: an increase from 4.50 runs per game to 4.59 runs per game, about 14.5 runs a year, which results in maybe two additional wins a year.
Thirty years ago authors Peter Palmer and John Thorn, in their classic book “The Hidden Game of Baseball”, determined that a team’s best hitter, rather than batting third in the order, should hit second. So in 2010 Bucs Manager Russell had his best hitter, center fielder Andrew McCutchen, bat in the two hole in the Pirate’s line-up.
It turns out the 2010 season didn't work out well for Manager John Russell as ownership and media pressure forced him to slowly abandon his tinkering with the Pirates line-up. So we really don't have a full season model to analyze. But five or ten years from now Russell and La Russa may be seen as early innovators in the redesign of the game's batting line-up.
The Linear Line-up
The traditional MLB batting lineup has always been seen as an up and down list of players with set offensive attributes that form a straight "building block" to create run production. Let's call it the Linear Line-up.
The Linear Line-up is viewed as continually starting and stopping, from lead-off to 9th in the order and then back again. To accommodate this idea of a predictably recurring batting order, set roles have been historically assigned to each spot on the Linear Lineup which are supposed to define and drive the offense:
> the lead-off man has a good on base percentage and is a fast runner;
> the second hitter can "move" the lead-off batter around the bases;
> the number three hitter is the best "pure" hitter in the line-up;
> the four hitter has the most power and is the primary RBI guy;
> the #5 hitter is the second best RBI power hitter;
> the #6 hitter has occasional power;
> the 7th, 8th, and 9th batters are, respectively, the worst hitters in the batting order.
But as research refines tradition, there is little about the performance aspects of Major League Baseball that hasn't been examined by a generation of baseball numerical scientists. It's time to reexamine the traditional Linear Line-up.
Let me emphasize that the goal of any hitting lineup analysis is to answer one question: how can a team restructure its batting order to create more runs? That is, how can a team put more runners on base so their best hitters can produce runs? And how can they develop more offensive opportunities per game to maximize the offensive situations that develop each game?
The Mobius Strip Theory
The instant the first pitch of a baseball game is tossed, the batting lineup, rather than being the repeating linear list we are all familiar with, actually becomes a potentially unending circular directory without beginnings or endings.
As the cliché goes, baseball, unlike other pro sports, doesn’t have a clock, which means it ends only when one team offensively outscores the other and holds the lead. So a winning team not only needs to be able to maximize possible offensive opportunities as they come up each game, that team also needs to create those opportunities.
The actual batting order is a circular directory of hitters. Finding the correct location and orientation for the most accomplished batters is therefore logically best served by having them centered inside the circular directory, separated as far as possible from non-producing batters.
A Mobius strip has the mathematical property of being non-orienting, meaning there is no starting point or stopping point, only one side and only one boundary. The analogy to a baseball batting order is that, once the game has begun, there is no lead-off batter and no number 9 batter-- there is only a continually looping directory of players in random order depending on the location of outs made each inning.
Here is a condensed summary of the Mobius strip theory.
The three best hitters on a team bat 1 through 3 in the line-up, with the “best” hitter batting second. That would be the traditional #3 batter.
The 8th and 9th batters in the line-up would be the next two best hitters on the team. The players who contribute least to the offense, typically the pitcher and position players known more for their defensive skills (shortstops, catchers, etc.), are separated from the 1-3 hitters equally from either end of the lineup.
The central point here is to give the best run-producing hitters in a team's line-up the most opportunities to create runs by insulating them as much as possible in the batting order from the least productive hitters in a team's line-up. For as many innings as possible.
Here’s how the projected 2014 San Francisco Giants lineup looks using conventionally accepted linear batting order criteria:
1. Angel Pagan - CF Good OBP, fast runner, moves around bases well.
2. Marco Scutaro - 2B Contact hitter, moves lead-off batter into scoring position, great bat control.
3. Brandon Belt - 1B Best young hitter on the team, high OBP, emerging power.
4. Buster Posey - C Cleanup hitter; best pure power hitter on a team without power, RBI leader.
5. Pablo Sandoval - 3B Second best power hitter on team, "protects" #4 batter, second RBI leader.
6. Hunter Pence - RF Extra base hit power, RBI producer.
7. Michael Morse - LF More likely to create outs, occasional power.
8. Brandon Crawford - SS Contact hitter, possibly on base for top of the order, best spot in lineup for defensive players.
9. Pitcher - National League pitcher slot. Often American League "second lead-off" man spot.
And here’s how the same 2014 Giants lineup would look in a Mobius batting order configuration:
1. Marco Scutaro - 2B Second or third best pure hitter on the team.
2. Buster Posey - C Best hitter on the team (the #3 batter in most linear lineups).
3. Pablo Sandoval - 3B Second or third best pure hitter on the team.
4. Hunter Pence - RF First of two players with extra base hit potential, but lower OPS.
5. Michael Morse - LF Extra base hit potential, more likely to create outs.
6. Brandon Crawford - SS Second most likely hitter to create outs in the continuing directory of batters.
7. Pitcher - Most likely to create outs in the continuing directory of batters.
8. Brandon Belt - 1B Good OBP, fourth or fifth best hitter on the team.
9. Angel Pagan - CF Good OBP, fourth or fifth best hitter on the team.
Not only do the statistically best hitters, assigned 1-3 in the batting order, receive the most at-bats, the best hitter on the team (batting #2) will have the three batting order positions in front of him filled by the second or third best hitter on the team, and the fourth and fifth best hitters on the team. Which increases the potential to create runs.
Each ballgame “artificially” starts with the #1 hitter at the plate, in this case Marco Scutaro. But, after the pitcher’s #7 spot is passed the first time around in the order, the lineup becomes the continuing directory of a Mobius strip with the three best hitters up more often, and two quality hitters batting in front of those three players for the rest of the game.
The Mobuis Theory puts the hitters most likely to create outs as far away as possible from the top three hitters in the lineup tasked with creating runs throughout the game.
Several sidebar issues
First, “moneyball” considerations. Specific player on-base percentages, the ability to make contact with the ball and scoring runs without pounding out 45 home runs, etc. are as workable as any other definition of what a "preferred" hitter might be.
Each general manager and manager determines the criteria of what constitutes a “good hitter”; primary placement in a Mobius Strip lineup can include such considerations as which players are the best contact hitters, which hitters take a lot of pitches, and which players are most adept at moving around the bases, etc.
The manager still has the primary responsibility to put the right players inside the Mobius Strip lineup configuration, which would include platoons and the best hitter-pitcher match-ups.
Second, to the extent that pinch hitters are often used in National League games in the late innings to replace the pitcher, and pinch hitters are theoretically accomplished batters, their pinch-hit at-bats would only further support the overall effect of a Mobius line-up by continuing an already fully developed offensive configuration.
Obviously player talent level is relative for each team: the object here is to look at the concept, not at individual player names. Having Miguel Cabrera play first base rather than Brandon Belt would obviously make a difference. So each team has to work with the personnel it has on the 25 man roster-- the Mobius Strip line-up works with all levels of teams.
Having proposed the Mobius Strip Theory, it is important to note that professional sabermetricians (whose knowledge certainly exceeds my own) have conducted countless scenarios which consist of placing different categories of hitters in different slots in the batting order to see how run production might be affected.
So far, although no agreed upon “perfect” lineup has emerged, a great deal of interesting and valuable information has been developed. Some amount of this research runs contrary to the Mobius Theory. For example, some scenarios show batting the pitcher 8th in the order can increase runs scored, while batting the pitcher 7th does not.
As the corners of baseball’s sabermetric universe continue to be explored and expanded, the everyday batting lineup will always be a focal point of discussion and theory. And that's the first step in challenging unexamined and conventionally less productive ways of achieving success.
Not to distract from the Mobius discussion, which I find quite interesting, just wanted to add that this blog reminded me of another type of line-up that I have seen used by mangers of softball teams where the #1 power hitter bats 4th, and the #2 power hitter bats 8th, with the three top on-base batters batting 1, 2, 3, and the last three guys (not counting pitcher) batting 5, 6, 7.
It's certainly an interesting way to look at a baseball line-up and the writer obviously has done a bit of research. The theory would be sound if one thing were true: That the line-up, once ordered from 1-9, is then started from a random position at the beginning of the game, not from the 1st spot every time. Yes, once the game begins, the line-up is a bit like a mobius strip. The problem is that this particular mobius strip starts from the same point (the first batter) every game. Imagine if you drew a line across a mobius strip and then traced your finger around the entire thing until you reached the line again. Let's say you do this 3 times to simulate the shortest possible MLB game (the line = the 9 hitters in the line-up, so traced 3 times = 27 outs). Obviously, most games don't end with a team getting 27 outs straight, so I'm going to stray from the analogy for a second, hopefully this still makes sense. In a baseball game, when someone gets a hit or a walk, the game continues on to the next batter without an out being recorded (obvious again, I know, bear with me). Say there's only one hit or walk (or error) allowing a runner from the Giants to get on base. So now the opposing team will have allowed 28 PA's to the Giants, and who gets to come up again in that 28th PA? The very first batter. If we get 2 runners on base, then the 1st 2 batters get 1 more PA apiece. Etc. I don't have the #'s in front of me, but someone once calculated over the course of an entire season the amount of PA's each spot in the line-up receives. You will not be surprised to find out the 1st batter gets the most over a season, the 2nd batter the 2nd most, the 3rd batter the 3rd most, etc. on to the 9th batter, who gets the least amount of PA's. This is largely what a sabermetric line-up is based on: You want your highest OBP guy coming up to bat first because he is going to see the most PA's over the entire season. You want someone on base every time the line-up restarts for the guys behind him. You want your best hitter second because he will get the 2nd-most PA's and there is a high likelihood that someone will be on base when he gets his hits/walks. Obviously you want your best hitter getting the most PA's possible, but you'd also like at least one person on base in case he cranks out a HR/triple/double. The problem with the mobius strip theory and the batting-the-pitcher-8th theory is that over the course of a season, you are giving more PA's to worse hitters and therefore wasting them. Batting a pitcher 8th is less egregious because there isn't a massive difference in the amount of PA's between the 8th and 9th spots, but you're still giving some PA's to a worse hitter. If we bat weak hitters in the 6th and 7th spots, over the course of a season, we are giving a lot of PA's to inferior hitters. This is counter-productive to the goal of winning the most games possible. It's a good attempt to shake up the line-up and obviously the writer knows a bit about sabermetrics, but this theory put into practice would cost the Giants runs. He's right that we want to clump our best hitters together - that's why we do that at the top of the order. If an MLB line-up is indeed a mobius strip, then it doesn't matter if we put 2 of our best hitters at the end of the line-up and 2 of them at the beginning or if we put them all at the beginning. Except for that fact that if we clump as many of them as possible at the beginning of the line-up, then they will receive the most PA's possible over the course of a season, which is what we want our best hitters to see.
These two line-up are the same after the second or third inning. The only thing yours did was give the opposing team an advantage the first time through the order. The Mobius line-up has the same three guys ahead of Posey and the same five after as the linear line-up.
Doesn't this approach assume a wide gap between the players? Let's say Scutaro, Posey, Sandoval and Belt are all identical players. Isn't it a mistake to give up a lot of ABs for Belt to gain a few ABs for the other three? In that case, don't you put Belt in the top 4, move Pence and Morse down 1 and drop Crawford to 8th?
So true. When I was a player/manager on a local softball league team I tinkered with various line-up schemes for several years.
The one that seemed to be particularly productive was replicating the linear line-up twice within the same batting order. That is, batting the three best OBP hitters 1-3 followed by the best power hitter on the team at #4. Then, three more good OBP batters follow at 5-7, capped off by the second best power bat on the team in the #8 slot.
Great analysis, clear and on point. [I will concede, as you did, that you also have done "a bit" of research and know "a bit" about sabermetrics.]
Two points. First, there is no handicap inherent in the Mobius Strip line-up at the start of the 1st inning.
In the 1st inning, teams using a Mobius line-up are guaranteed to have the three best hitters in their line-up come to the plate. As opposed to the linear line-up where, if the lead-off and #2 hitters make outs, potentially only one of the team's best three hitters gets an AB in the 1st inning (many teams bat their best hitters 3-4-5).
And I have no problem starting every game of the season that way.
Think about it. Pretty much by definition, the top three hitters on any MLB team will likely have the best on-base percentage numbers on the team. The Giants traditional lead-off hitter, Angel Pagan, had a .338 OBP in 2012, and a .334 OBP in 2013. But in those same years Marco Scutaro went .385/.357, Buster Posey .408/.371, and Pablo Sandoval .342/.341. So nothing is lost in terms of ABs and OBP by not having the traditional linear lead-off hitter batting first in the line-up.
In fact, Mobius provides an improvement to the customary linear line-up in the very first inning.
As far as pitcher ABs in the 7th spot of the order with Mobius there are two factors.
First, it's rare for a pitcher to have even three (and often two) ABs in a game unless they're pitching extremely well. Last season in 30 GS Matt Cain had 52 ABs-- 1.733 ABs per game; Bumgarner had 56 ABs in 29 GS-- 1.93 ABs per game; and Barry Zito had 34 ABs in 29 GS-- 1.172 per game.
So the #7 slot in a Mobius line-up (just like the #9 slot in a traditional line-up) is not filled by a pitcher the entire game. With the bullpen revolution over the past twenty-five years and starter pitch counts, pinch hitters abound and complete games have disappeared faster than Dennis Rodman's integrity.
Second, the point of a Mobius line-up is to configure a team's batting line-up to maximize runs forward. Which takes suspending and questioning what we've accepted over the years. I think the long-accepted "rules" of the traditional MLB line-up are a barrier to exploiting run production and won't stand up to being vetted against new ideas.
In looking at the Mobius model it's helpful to forget player names-- this is more about constructing a hitting attack that surrounds a team's most productive two hitters on a team with the team's third, fourth and fifth best hitters.
On most teams the so-called "best" hitter is in the third slot. The Giants can't do that because only two players (Posey and Sandoval) have consistent power, so Posey hits 4th and Sandoval 5th. In a better constructed line-up Posey would bat third.
Look at the traditional linear line-up: in the first inning the #3 hitter has just two batters ahead of him. But for almost the rest of the game the worst hitter in the line-up, the pitcher batting 9th, is only two batters away from the #3 batter. And the second worst hitter in the line-up, the 8th place hitter, is only three batters away from the #3 batter.
One of the ideas central to Mobius is to get the two most unproductive hitters in the line-up as far away as possible from the most productive hitters in the line-up, for as many innings as possible.
So in the Mobius model, the best hitter, batting in the #2 slot, now has three of the team's best hitters in front of him throughout the rest of the game (or until late in the game when pinch hitters might be used).
On the back side, the best hitter now has the second best hitter in the line-up batting behind him at #3, followed by two potential run-producing hitters at #4 and #5. Then the weakest hitter and the pitcher bat, and the cycle starts again.
The central point here is to give the best run-producing hitters in a team's line-up the most opportunities to create runs by insulating them as much as possible in the batting order from hitters more likely to consistently make outs.
[I'm going to drop a sentence from this into the blog-- your on-point comment prodded me to explain the goal more clearly.]
Noah-- The Mobius line-up doesn't require a wide difference between the batters. Certainly the player roles for offensive-rich teams like Detroit, the Dodgers, St. Louis or Boston are more clearly identified. But that same reasoning applies to the traditional line-up format.
Even in a haphazardly constructed hitting line-up like the Giants have, I think there's plenty of difference between, say, Buster Posey and every other hitter. He is by far their best offensive piece.
For precise line-up teams like Oakland and Tampa Bay, Mobius should make their approach even more productive.
And Sandoval and Belt are pretty far apart as players-- Belt tending to a higher OBP and lots of walks while Sandoval is more of a free swinger. Plus, Sandoval has the second best power bat on the team after Posey (something the Giants can't squander in their line-ups).
To your point about maybe putting different players in different slots than I did in my Mobius/Giants example-- I agree. Pagan could bat 8th, and Belt and Pence could switch. But the odd thing is, I think the Mobius line-up works just as well for poor run producing teams like San Francisco as well as it does for the big run producing teams I listed above.