Stat Chat: Playing Time And The 7 Body Problem

If you’ve heard of the Three Body Problem, you know that while it is possible to model the movement of two objects orbiting each other in space, it is impossible to accurately model the movement of three (or more) objects orbiting each other in space

Modeling a baseball lineup over the course of a 162 games has the same problem.  In an ideal world, you would have 8 starters for each non-pitcher position that all stay healthy all season, but that is obviously not the case. Players are injured, players are promoted/demoted, players switch positions, and teams make hundreds of changes and roll out hundreds of different lineups each year. In fact, the average non-catcher position uses on average 7 different players over the course of the season. So playing time projection isn’t a three body problem, it’s a 7 body problem orbiting around a bunch of other 7 body problems.

Taking a random example, the Tampa Bay Ray’s 2B playing time was projected to be (per steamer):

• Brandon Lowe – 530 PA
• José Caballero – 296 PA
• Taylor Walls – 258 PA
• Niko Goodrum – 47 PA

The reality was:

• Brandon Lowe – 222 PA
• Richie Palacios – 126 PA
• Christopher Morel – 89 PA
• José Caballero – 73 PA
• Curtis Mead – 73 PA
• Amed Rosario – 72 PA
• Jonathan Aranda – 19 PA
• Niko Goodrum – 3 PA

Even in a world where we measure how quickly Juinor Caminero’s left thigh twitches on a high fastball to predict his season wRC+, accurately predicting how many plate appearances Christopher Morel or Taylor Walls might try to eat away is where you can personally gain an edge. Gaps in playing time projection especially occur with young players whose promotions to the majors are not a certainty in February/March.

Consider a big league prospect whose possibility to be promoted is around 60%. A statistician will take this information and simply say their projected playing time is (Full Season worth of PA) * ~60% = 200~399 PA. However, if you think a prospect is good enough to make the team, it wouldn’t make sense that he would only get 200~400 PA, that’s more like what a defensive or platoon player gets over a full season. For some real life examples from the past 3 seasons, look at examples of young players that were projected 200~399 PA (at the Major League level) and how many PA they actually ended up getting that season:

At a playing time level these players were being projected at 50~70% of their value due to uncertainty about their playing time. This is why it’s important to export projections and make rankings and adjustments based on your own personal judgement. If you think a player isn’t good enough you should push them down the ranks, and you should bring their value up to a full season’s workload if you think they are good enough, but no half-measures.

Here are a few examples of players with potential underprojected playing time going into the 2025 season:

A final note: This works both ways, too. If there’s a veteran caretaker player whose position is vulnerable to a hyped prospect, their playing time should be less than a full season’s worth. An example last season was JD Davis, who was projected to have +500 PA with the 2024 A’s despite there being a list of players with whom he was going to be competing for playing time (Davis was ultimately DFA’d on June 18).

So knowing playing time is not an exact science, do not fear dabbling in the art of modeling your own 7 body planetary systems