The traditional MLB batting lineup has always been imagined as a linear list consisting of players with set offensive attributes. This linear list is viewed as continually starting and stopping, from lead-off to 9th then back again. Roles have been historically assigned to each spot on the linear lineup list which are supposed to define the offense; the lead-off man has a good on base percentage and is fast, the number four hitter has the most power, the worst hitter bats ninth, and so on. But as research refines tradition, there is little about the performace aspects of Major League Baseball that has been unexamined by a generation of baseball scientists who have also redefined the boundries of research.

The baseball establishment often tries to marginalize this serious work by dismissing it as the irrevelent mathematical ramblings of stat wonks who don’t appreciate the “real” game. But during the past ten years, a number of stubbornly conventional baseball organizations have found themselves left behind and desperately trying to catch the sabermetric train after it has left the station.

Baseball social politics aside, let me emphasize that the goal of all this hitting lineup analysis is to answer a question: can a team restructure its hitting lineup to create more runs scored. To put more runners on base when your best hitters come up to the plate, to develop more offensive opportunities during a game, to maximize offensive situations that develop during a game, and basically to put crooked numbers up on the scoreboard.

The instant the first pitch of a baseball game is tossed, the batting lineup, rather than being the repeating linear list we are familiar with, actually becomes a potentially unending circular directory (though almost always terminated in the 9th inning). As the cliché goes, unlike any other major sport, baseball doesn’t have a clock, which means it ends only when one team offensively outscores the other and holds the lead. Given the circular directory, finding the correct location and orientation for the most accomplished hitters is logically best served by having them centered in the circular directory, and separated from out producing batters.

A Mobius strip has the mathematical property of being non-orientable, 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 a condensed summary of the Mobius strip theory, the three best hitters on a team bat 1-3 in the order, with the “best” hitter batting second; the 8th and 9th batters in the line-up would be the next two best hitters on the team. The players who contribute the least to the offense, typically the pitcher and players known more for their extraordinary defensive skills, are separated from the 1-3 hitters equally from either end of the lineup.

Here’s how the 2010 San Francisco Giants lineup looks using conventionally accepted linear batting order criteria (please ignore currently injured players, and players whose talent does not perfectly match the specific slot criteria):

1. Aaron Rowand – CF  High OBP, fast runner, moves around bases well.
2. Freddie Sanchez – 2B  Contact hitter, moves lead-off batter into scoring position, can bunt well.
3. Pablo Sandoval – 3B  Best all around hitter on the team, high BA, high OBP, on base for cleanup hitter.
4. Aubrey Huff – 1B  Cleanup hitter; best pure power hitter, RBI leader.
5. Mark DeRosa – LF  Second best power hitter, “protects”  #4 batter, second RBI leader.
6. Bengie Molina – C  Extra base hit power, RBI producer.
7. John Bowker – RF  More likely to create outs, lineup spot for defensive standouts.
8. Edgar Renteria – SS  Contact hitter, possibly on base for top of the order, second spot in lineup for defensive players.
9. pitcher – P  National League pitcher slot; often American League “second lead-off” man.

And here’s how the same 2010 Giants lineup would look in a Mobius batting order configuration:

1. Mark DeRosa – LF  Second or third best pure hitter on the team.
2. Pablo Sandoval – 3B  Best hitter on the team (the #3 batter in a linear lineup).
3. Aubrey Huff – 1B  Second or third best hitter on the team.
4. Bengie Molina – C  First of two players with extra base hit potential, lower OBP and BA.
5. Aaron Rowand – CF  Extra base hit potential, lower OBP and BA.
6. John Bowker – RF  Second most likey to create outs in the continuing directory of batters.
7. pitcher – P  Most likely to create outs in the continuing directory of batters.
8. Edgar Renteria – SS  Good OBP, fourth or fifth best hitter on the team.
9. Freddie Sanchez – 2B  Good OBP, fourth or fifth best hitter on the team.

Not only do the statistically best hitters, placed the 1-3  in the order, receive the most at-bats, the best hitter on the team (batting #2) has the three lineup positions in front of him filled by two of the next three best hitters on the team.

Each ballgame “artificially” starts with the #1 hitter at the plate, in this case Mark DeRosa. 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 from the top three hitters in the lineup as possible throughout the entire game.

Several sidebar issues. First, “moneyball” considerations of player on-base percentages, making 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”; so primary placement in a Mobuis 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. The manager still has the primary responsibility to put the right players in whatever lineup configuration is used.

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 likely to be accomplished batters, their at-bats would only further support the overall effect of a Mobius 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 Alex Rodriguez playing third base rather than Pedro Feliz will obviously make a difference, but each team has to work with the personnel it has (and I mean no disrespect to Houston third baseman Pedro Feliz, who has, by the way, a World Series ring).

Having proposed the Mobius lineup theory, it is important to note that serious professional sabermetricians (who know more on Tuesday than I do all year) 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, the every day batting lineup will always be a focal point of discussion and theory. Which is the first step in challenging unexamined and conventionally less productive ways of doing business.