Batting order (baseball)
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The batting order, or batting lineup, in baseball is the sequence in which the nine members of the offense take their turns in batting against the pitcher. The batting order is the main component of a team's offensive strategy. The batting order is set by the manager before the game begins (although substitutions may subsequently take place). If a team bats out of order, it is a violation of baseball's rules and subject to penalty. When the player who led off the inning makes a second plate appearance, it is called "batting around."
In modern American baseball, some batting positions have nicknames: "leadoff" for first, "cleanup" for fourth, and "last" for ninth. Others are known by the ordinal numbers or the term #-hole (3rd place hitter would be 3-hole).
At the start of each inning, the batting order resumes where it left off in the previous inning, rather than resetting to start with the #1 hitter again. While this ensures that the players all bat roughly the same number of times, the game will almost always end before the last cycle is complete, so that the #1 hitter (for example) almost always has one plate appearance more than the #9 hitter, which is a significant enough difference to affect tactical decisions.
Positions in the lineup 
The first player in the batting order is the leadoff hitter. Generally, the leadoff batter is the fastest baserunner on the team. He bats more often than anyone else in the lineup. His goal is to ensure the team has baserunners on base when the later, more powerful hitters come to bat. His need for a high on base percentage (OBP) exceeds that of the other lineup spots. Because leadoff hitters are selected primarily for their speed and ability to reach base, they are typically not power hitters. Leadoff hitters typically hit mostly singles and doubles and draw walks to get on base. However, speed is not essential, as was shown by Wade Boggs, but it is highly desired among leadoff hitters. Once on base, his main goal is to get into scoring position (that is, 2nd or 3rd base) as quickly as possible, either through steals, hit and run plays or intelligent baserunning decisions, and then on to score.
Examples of classic leadoff hitters are Phil Rizzutto, Richie Ashburn, Maury Wills, Lou Brock, Pete Rose, Rod Carew, Tim Raines, and Ichiro Suzuki, with some having somewhat more power (Lou Whitaker, Rickey Henderson, Paul Molitor, Derek Jeter).
The second batter, most often just referred to as in the two-hole, is usually a contact hitter with the ability to bunt a baserunner over or get a hit. His main goal is to move the leadoff man into scoring position. Often, these hitters are fairly quick, competent baserunners and tend to avoid grounding into double plays. Managers often like to have a left-handed hitter bat second because of the potential gap in the infield defense caused by the first baseman holding the leadoff batter. On a very good team this batter can have characteristics of both a leadoff hitter and a power hitter (Curt Flood, Joe Morgan, Robin Yount, Alan Trammell).
The third batter, in the three-hole, is generally the best all-around hitter on the team, often hitting for a high batting average but not necessarily very fast. Part of his job is to reach base for the cleanup hitter, and part of it is to help drive in baserunners himself. Third-place hitters are best known for "keeping the inning alive". However in recent years, some managers have tended to put their best slugger in this position.
Typically the greatest hitters for a combination of power and OBP on their teams bat third, as is shown by the use of such hitters as Babe Ruth, Mel Ott, Ted Williams, Willie Mays, Barry Bonds, Mickey Mantle, Carl Yastrzemski, Albert Pujols, Joey Votto, Miguel Cabrera, Josh Hamilton, Evan Longoria, José Bautista, and Hank Aaron in this position in the lineup. Even without the combination of extreme power (Yogi Berra, Al Kaline, George Brett) or high batting average (Ernie Banks, Harmon Killebrew, Johnny Bench, Mike Schmidt, Reggie Jackson) this batting position contains an inordinate number of hitters who eventually become members of the Baseball Hall of Fame.
The fourth player in the batting order is known as the cleanup hitter, and is almost always one of the best hitters on the team, often the one with the most power. Baseball managers tend to place hitters who are most likely to reach base ahead of the clean-up man, so that the fourth batter can "clean" the bases by driving these baserunners home to score runs. His main goal is to drive in runs, although he is expected to score runs as well. In fact, the fourth spot in the order has the luxury of being somewhat "protected" from bad situations early in the game: the batter only rarely faces a spot with two outs and no baserunners in the first time through the order—possible if, for example, one of the first three batters hits a home run and the other two make outs or following a home run by the #3 hitter. If nobody gets on base, the cleanup hitter has a chance to start a rally in the second inning by being the first batter, with zero outs. However, hitting cleanup also requires an exceptional level of talent, and the ability to deliver big hits in important situations (such as the bases loaded with two out). Examples of #4 hitters include Lou Gehrig, Eddie Mathews, Willie McCovey, Billy Williams, Tony Pérez, Eddie Murray, Alex Rodriguez, Prince Fielder, and David Ortiz
The theory behind the cleanup hitter concept is that at the beginning of the game, the first three batters will reach base with a single-base hit, walk, or equivalent, thereby loading the bases, and enabling the cleanup hitter a chance to hit a grand slam. But even without the grand slam, this batter can extend an inning with a high batting average and frequent walks.
The #3 and #4 hitters can often be switched in roles. For example, the 2011 Detroit Tigers had Miguel Cabrera as their #4 hitter but moved him to the #3 hitter after acquiring Prince Fielder as a free agent before the 2012 season.
#5, #6 
The fifth and sixth (and sometimes seventh) batters have traditionally been RBI men, with the main goal of driving runners home, especially with sacrifice flies. The 3rd, 4th and 5th hitters in the lineup are called the "heart of the order", signifying their collective ability to get on base, hit for power and drive in runs. Modern sabermetric baseball theory suggests that even the 5th and 6th batters should have high on-base percentages, though this approach has not been universally adopted. The fifth batter is usually a team's second-best power hitter, and his purpose is often to "protect" the clean-up hitter in the batting order. He is expected to pose enough of a threat that the opposing team refrains from intentionally walking the clean-up hitter in potential scoring situations. The sixth hitter serves as a backup to the fifth hitter in case he fails to score runs or to drive more in himself if another scoring opportunity presents itself.
#7, #8 
The seventh and eighth batters are often not as powerful as the earlier batters, and do not have as high a batting average. They are often players who are in the lineup more because of their defensive ability (typically catcher, second baseman or shortstop) than their ability as hitters. They are still expected to produce (as is the case for any regular starter), but they have less pressure in those spots. The main pressure on the eighth hitter comes when there are two outs: in this case, he must battle the pitcher to get on base so that the ninth hitter can come up. That way, even if the ninth hitter gets out, the top of the order comes up next. Very often the #7 hitter is a catcher, commonly the slowest baserunner on a team whose lack of speed would contribute to a large number of double plays higher in the order even if he is a good hitter (Bill Freehan). The eighth batter is often a good contact hitter, and can be used as a back-up #2 hitter. In leagues without designated hitters (DHs), the catcher often bats eighth, as they are often employed for their defensive skills and handling of the pitching staff, and tend to have a relatively low batting average. However, this is by no means always the case. In a situation where the pitcher is batting in the #9 slot, #8 hitters are sometimes intentionally walked to get to the pitcher's spot in the #9 hole; however, with two outs the opposing pitcher is expected to battle the #8 hitter, so in the event of an out the pitcher leads off the following inning.
In the presence of the designated hitter, the ninth batter is often like the second leadoff. Nine-hitters tend to be fast, and have a decent on base percentage like the leadoff hitter.
In leagues where the DH rule is not in effect, the starting pitcher almost always fills the ninth spot, although relief pitchers may occupy a different spot due to a double switch. If there is a man on first or second base with fewer than two outs when the ninth hitter is up, he almost always bunts. However, a notable alternative exists to this, in which the pitcher or weakest hitter actually bats in the 8th slot, and another player with decent OBP and speed bats in the 9th slot, thus creating a kind of second leadoff hitter, at the bottom of the lineup, that loops to the top of the order afterwards. This has been used sparingly in the major leagues, but was notably employed by St. Louis Cardinals manager Tony La Russa in the second half of the 1998 baseball season, and again in August 2007 and in 2008, and by Milwaukee Brewers manager Ned Yost in 2008. Former New York Mets manager Bobby Valentine occasionally employed this technique, having Rickey Henderson hit leadoff and Roger Cedeño bat ninth.
Bragan's Brainstorm 
In 1957 major league manager Bobby Bragan placed his best hitter in the leadoff position and the remainder of his lineup in descending batting average order. Earnshaw Cook in his 1966 book, Percentage Baseball, claimed that, using a computer, Bragan's lineup would result in 1 to 2 more wins per season. A recent computer simulation demonstrates the superiority of Bragan's lineup.
- MLB.com La Russa shakes up lineup. August 4, 2007. Retrieved January 17, 2008.
- The Official Site of The St. Louis Cardinals: News: Notes: La Russa to bat pitcher eighth