Those who are familiar with the Pyramid Rating System’s All-Time team series are aware of the depth charts and subsequent lineups I produce for each team. I do this in part to add a degree of realism to the series, but also to try to understand better who these players were and what made them unique.

For the past few months, I’ve been trying to take this same approach toward historical teams that actually took the field. Traditionally, starting lineups for historical teams at sites like Baseball Reference have been presented in order of whoever played the most games at each position. While this is effective in most cases, it leaves out a lot of crucial information that the Pyramid Rating Model presents in a condensed matter, elements that will give more depth and a better understanding of the types of lineups teams employed.

Highlighting Versatility

To accurately show how the lineup system I have developed works, I’ll use real examples of historical teams. I’ll start with the 2018 Chicago Cubs. Their starting lineup going by the traditional system reads as follows:

Here’s how the lineup system used by the Pyramid Rating System would have it:

Pyramid Rating Lineup System vs RHP vs LHP Pos Name Pos Name C Willson Contreras C Willson Contreras 1B Anthony Rizzo 1B Anthony Rizzo 2B Ben Zobrist 2B Ben Zobrist 3B Kris Bryant 3B Javier Báez SS Javier Báez SS Addison Russell LF Kyle Schwarber LF Ian Happ CF Ian Happ CF Albert Almora Jr. RF Jason Heyward RF Jason Heyward

A few differences jump out right away, the main one being how Javier Báez’s use differs. The traditional model has him as the Cubs’ regular starting second baseman. This designation makes sense considering Báez played 102 games at second, which not only led the team but was also the position where he played the most.

The system I have chooses to move him around in a platoon role at third base and shortstop, while Ben Zobrist gets the second base job outright. Why is it that way? To explain, we must first delve into what the lineup system is trying to maximize, which isn’t the number of defensive games played at each position, but rather the total number of plate appearances in the lineup. Allow me to demonstrate.

2018 Cubs Lineups Name Positions Available to Play PA’s vs RHP PA’s vs LHP Total PA’s Anthony Rizzo 1B 500 165 665 Javier Báez 2B, 3B, SS 500 145 645 Willson Contreras C 410 134 544 Ben Zobrist 2B, LF, RF 385 135 520 Kyle Schwarber LF 419 91 510 Jason Heyward CF, RF 388 101 489 Albert Almora Jr. CF 335 144 479 Addison Russell SS 342 123 465 Ian Happ 3B, LF, CF, RF 345 117 462 Kris Bryant 3B, LF, RF 361 96 457

The chart above shows how I assess teams when coming up with lineups for my system. The positions a player is able to play is the same method on which I base positional availability on all-time historical teams. A player must play at least 10 percent of his games at that position to be eligible at that position on the chart.

2018 Cubs vs. RHP Name Positions Available to Play PA vs RHP Anthony Rizzo 1B 500 Javier Báez 2B, 3B, SS 500 Kyle Schwarber LF 419 Willson Contreras C 410 Jason Heyward CF, RF 388 Ben Zobrist 2B, LF, RF 385 Kris Bryant 3B, LF, RF 361 Ian Happ 3B, LF, CF, RF 345 Addison Russell SS 342 Albert Almora Jr. CF 335

If we isolate the total number of plate appearances Cubs players had against righties and try to build our lineup starting from the top to the bottom, we can see how this comes together. As Zobrist is the only player besides Báez who can play second base, having spent 63 games there, he becomes our starting second baseman against right-handed pitching.

If you go back to the traditional model, you will notice that Zobrist is not listed despite being fourth on the team in terms of plate appearances with 520. That’s because Zobrist didn’t lead the team in games played at any position. However, with 63 games played at second base, 43 in left field, and 61 in right field, it’s safe to say that Zobrist was a mainstay of the Cubs starting lineup even if his position wasn’t always the same.

Báez’s movement between third base and shortstop reflects how the Cubs accounted for injury issues with Kris Bryant and with Kyle Schwarber’s use as a platoon player. Zobrist’s inclusion in the everyday lineup is an infrequent one going off the traditional maximizing game model, but it does occur.

Here are some historical examples of players who are not featured in the starting lineup under this model, but can easily be accounted for once the primary emphasis is on plate appearances.

Better Accounting of late-season pickups

We all know how huge a late-season pickup can be for a team, but it rarely shows up in a traditional lineup model. Take how the 2015 New York Mets look in the conventional model…

…versus the one presented by the Pyramid Rating System.

2015 Mets, Pyramid Rating Lineup System vs RHP vs LHP Pos Name Pos Name C Kevin Plawecki C Travis d’Arnaud 1B Lucas Duda 1B Lucas Duda 2B Daniel Murphy 2B Daniel Murphy 3B Rubén Tejada 3B Juan Uribe SS Wilmer Flores SS Wilmer Flores LF Yoenis Céspedes LF Yoenis Céspedes CF Juan Lagares CF Juan Lagares RF Curtis Granderson RF Curtis Granderson

The most glaring difference is including deadline pickup Yoenis Céspedes, who overnight became the best bat the Mets had and helped lead them to a World Series appearance. How is Céspedes added to this team based on a maximum plate appearance model, when he had only 249 PA with the Mets?

The answer refers to how plate appearances are calculated in the new model. Céspedes may have had only 57 games with the Mets, but he played in 159 games on the year. His estimated number of plate appearances takes the average number of plate appearances per game he had with the Mets (249/57) and multiplies it by the total number of games he played in that year (159) to give us a pro-rated total of 659 plate appearances on the year. That’s significantly higher than the 408 plate appearances put up by Michael Cuddyer.

Had Céspedes been with the Mets from Opening Day, it’s doubtful he would have either played in 159 games or gotten to 659 plate appearances, but it’s unlikely Cuddyer would have reached his previous totals either. Because I cannot determine who to deduct plate appearances from, I don’t subtract plate appearances from either player.

Another example is in the Mets’ third base situation, where Juan Uribe gets in via platoon while Eric Campbell and his 206 plate appearances are left entirely out of the starting lineup in the Pyramid Rating System model.

In addition to Céspedes now being featured in the 2015 Mets lineup, the same approach also allows Scott Rolen to crack the 2002 Cardinals lineup, Justin Upton to break the 2017 Angels lineup and many other late-season pickups who played a significant role to be represented.

Tracking Platoons

In a lot of instances it’s hard to tell if that .300 hitter who played in 100 games with 400 plate appearances was a platoon player or just someone going through injury issues. Each answer gives a different perspective as to what type of player someone was. To know the difference, we have to look at the number of plate appearances a player had against right-handed and left-handed pitching.

Notable Platoons Players Since 1977 Name Handedness # of Seasons as a Platoon Starter Career PA’s vs. LHP Career PA’s vs. RHP Ernie Whitt L 10 572 3699 Frank Catalanotto L 9 409 3883 Dave Martinez L 9 987 5483 Harold Baines L 9 2619 8473 Paul Sorrento L 8 541 3349 Dickie Thon R 7 2062 2809 Ryan Raburn R 7 1313 1421 Candy Maldanado R 7 1884 2706

These players all spent a significant portion of their career in platoons, and if you examine the number of plate appearances they had against either left-handed or right-handed pitchers, you will see the figures in every case are all heavily skewed toward facing one type of pitcher.

With Frank Catalanotto, we see that roughly only one in every 10 plate appearances came against a lefty, helping to explain why this perennial .300 hitter qualified for the batting title only twice in his 14-year career. On the flip side is Ryan Raburn, who has an almost equal number of plate appearances against lefties and righties. Although it may be a 50/50 chance that Raburn will be in the lineup with a righty starting, you can all but guarantee he would be starting against a lefty.

Because of the plate appearance model, this allows players to platoon at multiple positions, and in conjunction with utility players, can better explain how managers were likely to set their lineups.

Determining Rotation Order

Like starting lineups and batting orders, a rotation order is ever-changing throughout the season. In a lot of cases, there is no such thing as an “average” rotation order a team used.

The traditional model used goes mainly by the number of innings pitched to determine the rotation order, but the Pyramid Rating System model instead uses the number of innings pitched per start. This is to better account for pitchers who were dominating throughout the season but may have missed a handful of starts. A look at the 2016 Los Angeles Dodgers illustrates this point.

2016 Los Angeles Dodgers Lineup Name Traditional Order Pyramid Rating System Rotation Order IP GS IP/GS WAR Kenta Maeda #1 #3 175.2 32 5.49 3.3 Clayton Kershaw #2 #1 149 21 7.1 6.5 Scott Kazmir #3 #4 136.1 26 5.24 1.2 Ross Stripling #4 N/A 100 14 5.4 1.1 Julio Urías #5 #5 77 20 4.62 1.8 Rich Hill N/A #2 110.1 21 5.52 3.8

Even though Clayton Kershaw missed 10 starts on the year, it is evident that he was the Dodgers’ workhorse that year, pitching more than a full extra inning compared to everyone else in the rotation. Rich Hill, who came over in a midseason trade, is included as the number two starter, with his entire season accounted for as if he pitched for the Dodgers from day one. Kenta Maeda was the most consistent Dodger starter for 2016, but his listing as a number three starter is very much in line with what you expect him to be in the rotation based on both his WAR and his durability in starts.

Given the frequency of pitchers missing starts in today’s game, I believe that innings pitched per start gives a much better read on where pitchers were in the rotation, as opposed to just innings thrown.

Conclusions

While the traditional lineup model has been useful in presenting data, I believe it’s time to move on to a more complex model that can better explain how managers constructed their lineups. By switching to a model that is based more on total plate appearances than games played at a position, and also accounts for midseason pickups and platoons, we get a much more comprehensive presentation of the types of lineups teams fielded.

The main thing to keep in mind with any system like this is that given how frequently teams change their rosters during the season, and the roles players play, no model can account for everything. If we refer back to our first example, this new lineup system will not show that Báez was primarily a second baseman last year. Nor does it show the impact players who left midseason had.

But overall I do believe this is a superior and more in-depth lineup system that provides insights the traditional model cannot weed out.