A Lineup Construction Experiment by Chris Russo March 11, 2021 Who should bat second? This question has been debated quite a bit in recent years, as the modern approach has become to slot the best hitter in the 2-hole to increase their total plate appearances in a season. Others argue that the second hitter, like the leadoff man, should be a table-setter and the goal should be to get the best hitters to the plate with runners on base. So which is more valuable: getting your best hitter to the plate with men on or getting them to the plate more often? A simple experiment suggests that we are wasting a lot of energy arguing either side, and it would be time better spent thinking about other elements of lineup construction. Overview I created nine fictional players that will be referred to by position. I arbitrarily provided probabilities for the players based on seven possible plate appearance outcomes: single, double, triple, homer, walk, hit by pitch, and out. To simulate the lineup playing a game, I used a simple base-to-base style (the runners on base move up the same number of bases as the batter). An oversimplification of play to be sure, but the goal is to get an approximation of potential lineups relative to each other. Each lineup “plays” 100,000 nine-inning games so that the run distribution is virtually identical on multiple simulations. Players Instead of listing all of the probabilities, here are the resulting slash lines to get an idea of the types of players in the lineup: C: .237/.290/.387 1B: .348/.400/.576 2B: .337/.350/.388 3B: .307/.390/.443 SS: .247/.300/.312 LF: .272/.330/.424 CF: .258/.310/.366 RF: .309/.350/.521 DH: .315/.370/.609 Lineups We will compare three lineups. The first takes the modern approach and bats the best hitter (1B) second, while the second takes a more traditional approach and bats a singles hitter (2B) second. The lineups are otherwise similar: Lineup 1: 3B – 1B – DH – RF – 2B – LF – CF – C – SS Lineup 2: 3B – 2B – 1B – DH – RF – LF – CF – C – SS The third order is used as a reference to see what happens when we deliberately create a “bad” lineup: Lineup 3: C – SS – CF – LF – 2B – RF – 3B – DH – 1B Results Lineups 1 and 2 performed nearly identically, with Lineup 1 producing an average of 4.279 runs and Lineup 2 producing an average of 4.283. Basically, in this case the extra at-bats for the best hitters in the first lineup were perfectly balanced out by the extra runners on base for those batters in the second. The third lineup was clearly worse, putting up 4.122 runs per game. However, despite a definite difference, .161 fewer runs per game amounts to just 26 fewer runs in a 162-game season when designing the worst possible lineup. The shape of the distribution of runs is also similar across all three lineups: The plot does show some differences between Lineups 1 and 2 in terms of the relative frequency of certain values, and this may be a result of the particular lineup or a result of random variance. However, the similar shape of the distributions suggests that the average is a good metric to use to compare. We could also compare other batting orders, but by testing two of the most sensible lineups and one illogical lineup, we have basically defined the range of possible outcomes roughly between 4.1-4.3 runs per game for these nine players. Discussion The implications of this simple experiment relate exclusively to run production in the long run. When the performance of batters is static, the order in which they bat is not that important. In particular, while there was a slight difference when trying to form a bad lineup, the two reasonable lineups yielded the same results in a large sample. Thus, when trying to optimize a lineup, the emphasis should be placed on gaining advantages with particular batter-versus-pitcher matchups — the goal of which would be to maximize the performance of each player rather than worry about who goes to the plate the most often. Interestingly, though maybe not surprisingly, we saw this strategy on full display with how the Rays manipulated their lineups in the 2020 postseason. Not only did Tampa Bay utilize platoons at many positions, manager Kevin Cash was quick to pinch-hit for his platoon players when an opposite-arm reliever entered the game. Though these moves were not discussed as much as his pitching changes, there was one particular instance of note in the sixth inning of the instant-classic World Series Game 4. After Randy Arozarena managed a mere single to lead off the inning, Cash pinch-hit for Mike Brosseau with Ji-Man Choi in the third spot in the order. Righty Blake Treinen had entered the game in relief of lefty Julio Urías, so it was a simple platoon pinch-hit. However, I remember this moment because the announcers noted how rare it was that a manager would pinch-hit for his 3-hole hitter in the middle innings. The thing is, to the Rays, Brosseau was not the 3-hole hitter, as he was a batter in their lineup who they consistently pinch-hit for. Whether he was batting lower in the order or leading off (both of which he did in 2020), he was in the lineup to face lefties. This occurrence underscores the idea that the Rays were focused on the smaller matchup battles as opposed to the larger lineup considerations like who to bat first. The Rays are a special case considering few of their players are considered “everyday” players. Another example of effective lineup construction strategy was displayed by the 2020 Phillies. In an interview, manager Joe Girardi discussed batting Bryce Harper between righties Rhys Hoskins and J.T. Realmuto. With the three-batter-minimum rule in place, this meant that if the opposing team wanted to bring in a lefty for Harper, they would likely have to face either Hoskins or Realmuto, both of whom were much better against lefties in 2020. While Harper’s overall numbers are much better than Hoskins’, batting Hoskins before Harper allows for a more optimal performance by Hoskins. Ironically, Girardi discussed this well-executed strategy while slamming the three-batter rule. The lineup construction implications are a perfect illustration of why the three-batter rule can actually add to the strategy, contrary to what many opponents of the rule claim. To illustrate the benefit of increasing batters’ production in this manner — even slightly — I ran one final simulation of the team where each player manages one extra single per 100 plate appearances. Using Lineup 1, this team produced 4.553 runs per game — about 44 runs per 162 games better than the initial team. This change is already more effective than changing the batting order, without considering a potential increase in doubles, homers, etc. We can continue to manipulate the probabilities in this manner, but since this is a general approximation, the takeaway should be that the best way to optimize a lineup is to maximize the performance of the batters in it without worrying about whether the best hitter should bat second or third.