Shawn Trewartha | August 12, 2026

The current & traditional lineup

On Tuesday, July 28th, while preparing for a game in San Diego, Warren Schaeffer posted a lineup that had become predictable over the previous couple of months of Rockies baseball. Michael King, a right-hander, was on the mound, which generally meant better production from the Rockies lineup. Against right-handed pitching, the Rockies were hitting to a .756 OPS compared to just .651 against lefties. 

With that in mind, Schaeffer once again deployed his lefty-dominant lineup, with McCarthy leading off, followed by Moniak, Goodman, and Rumfield. Carrigg, Johnston, Castro, and Julien followed, while Tovar rounded out the lineup in the ninth spot.

This had become the norm, and there really wasn’t anything surprising about it. From an offensive standpoint, however, the lineup was successful. While the Rockies ultimately lost that day in San Diego, the offense reached their “taco’s” threshold by scoring seven runs, two above their season average of 4.72.

Also looking at the lineup, it is one that any manager from the 1990s would slap together. It has all the trimmings of a stereotypical Major League lineup card. Complete with your speedster/get-on-base guy leading off, followed by your three best power bats in decreasing order of speed. Your five through eight hitters are filled with plug-and-play left-handed or switch-hitting bats for advantageous matchups. And your nine-hole guy is struggling to stay above the Mendoza Line, but needs to stay in the lineup because of his glove.

I don’t think there is anything inherently wrong with this approach, but during a transition year when wins can sometimes be hard to come by, I believe there is an opportunity to take a more data-driven approach and optimize the platoon lineups against right- and left-handed pitching.

The Markov approach to lineup construction

In an attempt to construct the ideal lineup, it is useful to simplify the game of baseball into a Markov process. Under this framework, the outcome of a given at-bat is assumed to be independent of what happened previously, conditional on the current state. In other words, the outcome depends on the batter’s underlying statistics and the current state of the game, defined by the number of outs and the arrangement of runners on base.

Assumptions are also necessary to simplify the algebra. For example, runners on first base will only ever advance one base on a single, while runners on second base will always advance two bases and score on a single. While this removes baserunner speed as a variable, it helps isolate the batter’s contribution to scoring runs, which is the primary goal of the analysis.

By using each player’s current and historical probabilities of outcomes such as singles, doubles, triples, and outs, the Markov process allows us to assign linear weights to each Rockies hitter. For this analysis, those weights represent how many runs a hitter is expected to create per plate appearance relative to the MLB average. This analysis can then be conducted twice: once against right-handed pitchers and once against left-handed pitchers.

Right-Handed Pitchers: Expected Runs Created Above MLB Average for Rockies Batters

Rockies Batter	Runs Above AVG / PA
Tj Rumfield	+0.0421
Mickey Moniak	+0.0337
Troy Johnston	+0.0297
Hunter Goodman	+0.0281
Cole Carrigg	+0.0143
Jake McCarthy	+0.0137
Kyle Karros	+0.0119
Willi Castro	+0.0093
Edouard Julien	+0.0023
Tyler Freeman	+0.0018
Brett Sullivan	-0.0083
Ezequiel Tovar	-0.0093
Jordan Beck	-0.0124
Braxton Fulford	-0.0235

Left-Handed Pitchers: Expected Runs Created Above MLB Average for Rockies Batters

Rockies Batter	Runs Above AVG / PA
Hunter Goodman	+0.0392
Jake McCarthy	+0.0289
Cole Carrigg	+0.0092
Willi Castro	+0.0048
Ezequiel Tovar	+0.0028
Jordan Beck	-0.0000
Kyle Karros	-0.0023
Tj Rumfield	-0.0026
Brett Sullivan	-0.0061
Edouard Julien	-0.0095
Braxton Fulford	-0.0100
Tyler Freeman	-0.0100
Mickey Moniak	-0.0149
Troy Johnston	-0.0188

Once these expected runs-created-per-plate-appearance values are calculated, we can begin constructing the ideal lineup by selecting the nine highest-valued hitters for each pitcher handedness and putting them through another Markov chain analysis. This allows us to determine the expected runs created over a nine-inning game and, ultimately, produce two mathematically optimized lineups: one against right-handed starting pitchers and one against left-handed starters.

The results suggest that Warren is doing the right thing by using a platoon-heavy starting lineup, but the order of the batters could be reimagined. Rather than following the traditional baseball orthodoxy that seems to guide his lineup construction, the Rockies could potentially squeeze more runs out of the same group of hitters by arranging them differently.

The Data-Driven Ideal Lineup

Against right-handed pitchers, the ideal lineup construction is expected to produce an average of 5.0 runs per game. TJ Rumfield (1B) would lead off, followed by Mickey Moniak (RF) and Jake McCarthy (LF), with Hunter Goodman (C) hitting cleanup. Willie Castro (SS), Edouard Julien (2B), and Kyle Karros (3B) would follow, with Cole Carrigg (CF) and Troy Johnston (DH) rounding out the order.

This lineup obviously excludes the struggling Ezequiel Tovar, who was calculated to have below-average expected runs created per plate appearance. Tyler Freeman is also left off, but would be a suitable replacement, as he is the last remaining Rockies batter with an above-average run-created value against right-handed pitchers.

Against left-handed pitchers, we see another surprise at the top of the lineup. With an average expected runs per game of 4.4, the ideal lineup would have Hunter Goodman (C) leading off, followed by Cole Carrigg (CF) and Ezequiel Tovar (SS), with Jordan Beck (RF) hitting cleanup. Brett Sullivan (DH) and TJ Rumfield (1B) would follow, along with Kyle Karros (3B), while Jake McCarthy (LF) and Willi Castro (2B) round out the order.

The same analysis was completed both before and after the Brenton Doyle trade. Before the trade, Doyle was included in the ideal lineup in place of Brett Sullivan, with the other eight hitters remaining unchanged. Following the trade, expected runs per game decreased from 4.43 to 4.38, equating to roughly eight fewer runs over a 162-game season.

Data Meets Decision-Making

These two lineups point to a trend that has been seen throughout the league in recent years: hit your best players first. Over a 162-game season, each spot lower in the lineup is expected to result in roughly 18 to 20 fewer plate appearances. With that in mind, not having your best hitters in the leadoff spot costs them potential at-bats and additional run-scoring opportunities. TJ Rumfield and Hunter Goodman have the highest expected runs created against right- and left-handed pitching, respectively, and the data makes a strong argument for having both hitters lead off in their respective platoon situations to maximize the Rockies’ run-scoring potential.

As with any analytical approach, there is a human element that the Rockies might rightfully take into account. Factors such as a player’s comfort and familiarity with a particular lineup position, the desire to give players rest or additional opportunities at the plate, and contract structures or a player’s long-term standing with the organization may all influence decisions that cannot be captured by the data alone. For example, after Mickey signed a two-year, $16 million extension, the Rockies may have a greater incentive to develop him into an everyday starter rather than continue using him primarily as a right-handed platoon outfielder.

My approach, however, is intentionally driven solely by the data. This allows the analysis to evaluate lineup construction objectively, without the subjective considerations and organizational factors that may influence real-world decisions.

Written by Shawn Trewartha.