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The Mathematically Optimal Batting Order

In this era of advanced baseball stats, lineups are continually evolving. Some of baseball’s unwritten rules of lineup creation have been challenged.

In 2021, Kyle Schwarber batted lead-off 27 times despite having minimal speed threat (career-best four steals in a season) and just a .340 career on-base percentage. Similarly, the Atlanta Braves won the World Series in some part due to putting Jorge Soler at the top of their lineup. Soler only has eight more steals than World Series rings, and he has a career on-base percentage of .329.

Leading off with Schwarber or Soler is not exactly mathematically ideal, but at least it is objectively fun to watch them golf home runs into the next area code. Schwarber transformed into prime Barry Bonds when batting lead-off, and Soler became the first player in World Series history to lead off the series with a home run.

However, let’s optimize.

Batting First

The prototypical lead-off hitter does two things well. First, they get on base a lot. Second, they run the bases well. Currently, Ronald Acuna Jr. hits these criteria to a tee. In his first 1,510 plate appearances as a lead-off hitter, he has a .387 on-base percentage. In games played as a lead-off hitter, he has 83 steals under his belt, pacing for 40 steals per 162 games.

Power is also helpful here, but it is not a requirement. The goal of a good lead-off hitter is to get on base for the upcoming slots in the lineup.

Batting Second

Styles of two-hole hitters have changed in recent decades. The three most-tenured two-hole hitters are defense-first middle infielders with below-average bats. Nellie Fox logged more than 1,700 games as a two-hole hitter in the 1950s and 1960s. Similarly, both Omar Vizquel and Ozzie Smith played over 1,500 games in the two-hole while manning shortstop.

Modern two-hole hitters come in the mold of power-discipline types. Through May 30, Freddie Freeman, Aaron Judge, Matt Olson, Juan Soto, and Rafael Devers have played at least 40 games in the two-hole. They are the best of both worlds between the lead-off hitter and the clean-up hitter.

Batting Third

The three-hole is one of the most appreciated roles in a traditional lineup. Many times, this hitter is the best hitter on the team. The likes of Stan Musial, Albert Pujols, Willie Mays, and Henry Aaron logged more than 1,800 games in this spot.

However, this is a spot that teams routinely put the wrong hitter in. To maximize run-scoring, players such as Jose Ramirez should bat first, second, or fourth rather than third. Of the 30 best ways to organize the most common Cleveland Guardians lineup, Ramirez’s spread is 15 two-hole appearances, 13 four-hole appearances, and two five-hole appearances. He is overqualified to be in this role.

The three-hole might be earlier in the lineup, but it has less of an influence on run production than the top two spots and the next two spots. To use a strange analogy, the top two spots study for the test while the four and five spots take the test. The three-hole is the bus ride to the testing facility. It can’t be a disaster spot, but it is more important to have a difference-maker in the five spot.

Batting Fourth

Most teams get this spot right. They place their thumpers here. Of the top-five four-hole hitters by games played, two are in the 500 home-run club and two have exactly 493 home runs. The other is Honus Wagner who led MLB in slugging three times.

In 2022, the most common four-hole hitters are Pete Alonso and Christian Walker. Both players are among the NL leaders in home runs. Nick Castellanos is third with his 18 extra-base hits. Yordan Alvarez, C.J. Cron, and Giancarlo Stanton have also each launched double-digit home runs out of the four-hole.

Batting Fifth

The five-hole is comparatively undervalued in run production. Only two players have played more than 1,000 games in the five-hole: Hall of Famer Harry Heilmann and Stuffy McInnis. The five-hole occupies a weird spot in the lineup because it is the buffer between the good hitters and the not-as-good hitters.

The five-hole hitter should function as what people think of the three-hole hitter. They can be more slug-focused than earlier spots in the lineup as there is usually a drop in on-base qualities in the bottom half of the order. In 2022, Rowdy Tellez has been an excellent five-hole hitter. He has seven home runs and five doubles.

Batting Sixth

In general, the six spot is the beginning of the lineup where players are in for their defense. Lineups with better depth can use this spot as a serious hitter (such as Kyle Tucker on the Houston Astros). Historically, the likes of Graig Nettles, Brooks Robinson, and Yadier Molina have been heavily-used six-spot hitters. They were good enough hitters to warrant a spot, but they were still glove-first.

Six-hole hitters come in a variety of styles. Some are high-volatility players with big strikeout and home run numbers (such as Joey Gallo). Others are players with a high-contact approach without the desired walks or extra-base power to hit higher in the order (such as 2022 Dylan Carlson).

Some lineup matrices put a team’s worst hitter in this spot. This train of thought turns the seven-hole into a mini-lead-off role with the one-hole hitter functioning as a secondary clean-up hitter.

Batting Seventh

Much of the six-spot logic applies here. Since 1961, many of the most common seven-hole hitters are defense-first players, usually catchers. Some players are wildly overqualified such as Robinson Cano, Andruw Jones, and Javy Lopez, but they played on excellent teams with deep lineups.

Hitters do not exactly strive to be future seven-hole hitters. The most common seven-hole hitters in 2022 include a resurgent Cody Bellinger, a bevy of Gold Glovers, and top prospects.

Batting Eighth and Ninth

If MLB operated under NFL rules with separate offenses and defenses, these players would likely not be asked to play offense. Conventional wisdom states these two hitters are the worst in the lineup.

Until 2022, many nine-hole plate appearances went to pitchers, but with the universal designated hitter in effect, the nine-hole will likely be occupied by the likes of Martin Maldonado, Andrew Velazquez, and Cristian Pache. All three are exceptional fielders, but they bring next to nothing as hitters. Through May 30, Velazquez is the only one of the three to have an OPS of even .500 as a nine-hole hitter in 2022.

One new age thought is to treat the nine spot as a secondary lead-off man. In 2022, Gavin Lux and Dansby Swanson have been .750 OPS nine-hole hitters. Nicky Lopez has been effective at getting on base (.356 OBP), and the likes of Victor Robles (four steals) and Jorge Mateo (seven steals) are stressing the basepaths.

The second lead-off man helps the top part of the lineup while the worst hitter in a lineup moves to the eight-hole. Joe Maddon occasionally employed this strategy, batting the pitcher eighth when he was the Chicago Cubs manager.

The underlying mathematics says that the second lead-off hitter is more beneficial to run production and batting the worst hitter eighth is the best strategy. This change could occur faster at the MLB level now that pitchers no longer hit.


It is unlikely to ever be a perfectly optimized lineup. A bevy of factors goes into an individual lineup card from player psychology to the opposing pitcher(s) to the ballpark. The lineup card itself is sometimes a self-fulfilling prophecy as players are asked to perform certain tasks because they occupy a certain position in the lineup.

Main image credit Embed from Getty Images

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