As baseball fans, we are fortunate to have multiple high quality player projections such as ZiPS and Steamer publicly available to help shape out understanding of moves and expectations. Likewise, these get aggregated into team level forecasts such as the FanGraphs Depth Charts to provide insight into how teams stack up against each other.
One issue with both as analytical tools is that they are presented as single numbers. That is, they are point projections that represent a central expectation, be it a weighted average or median/50th percentile expectation. But that is only half the equation: when it comes to forecasting, the average is important, but so the uncertainty or shape of the distribution of expected or possible outcomes.
This is especially the case when the underlying distributions are not symmetric. Total production is a function of productivity and playing time. If a regular is projected for 140 games as the base case, there’s very little possible upside but a significant or major injury means major potential downside on the other tail. For established players, productivity risk skews somewhat to the downside, for high upside prospects there’s more uncertainty and a sjew to the upside.
For that reason, before the 2018 season, I took a stab at creating distributions for each starting position (hitters, starters) by projecting playing time and productivity on a five point scale. That combined into 25 different outcomes for each player which were then smoothed into a distribution. It’s rudimentary, since it ignores correlation between the two variables, but it gives a reasonable idea. Those can then be rolled up with additional components and integrated into a team level distribution.
With 2021 marking the first full season of contending posture since then, it’s once again a worthwhile exercise. To achieve a finer distribution, I’ve expanded to a seven point scale on each dimension to create a 7x7 matrix of 49 outcomes, roughly double the 25 from the 5x5 matrix. The seven points roughly correspond to the 5th/20th/35th/50th/65th/80th/95th percentile outcomes on each dimension. I’ve used the projection system to guide the inputs, but also incorporating my own expectations (biases).
We’ll start today with catcher and DH, before looking at the infield, outfield, and stating pitching, and then finishing with by bringing all that and more into the overall team level projection.
The distribution for Jansen is almost perfectly symmetric, and also with one of the most compact with small tails. I think this makes sense given his profile. His playing time ranges are relatively narrow, capped by the fact that catchers max out these days at 110-120 games played regardless, and even if supplanted by one of the other catchers still figures to get a good amount of playing time.
In terms of productivity, his career to date likely suggests a pretty high floor based on his strong defensive ability, and good eye at the plate. I’m less bullish than the projections on his batted balls, so my base case is closer to 90 wRC+, but if one is more bullish inclined on his offensive profile, there might be a rightward shift to the distribution and slightly longer tail on the upside (again, the limited playing time for catchers limits the ability to pile up WAR).
Even if Tellez doesn’t win an Opening Day job, he figures to get a good amount of playing time, but even on the higher end unlikely to play truly everyday unless he mashes out of the gate (which is reflected in the short right tail).
Given the high offensive bar at 1B/DH, even if most of the gains he showed in 2020 carry over, the WAR totals are limited. The central mass between 0.5 and 2.0 is a combination of scenarios where he retains a good portion of the gains and is a solid regular, really productive in a platoon role, or where he doesn’t get a full season.
Kirk is a wild card in terms of projecting at this point since it’s unclear if he’ll even start the season with the Jays or what exactly his role will be. Nonetheless, one way or another and perhaps splitting time between catcher and DH I think he’ll get a fair bit of playing time so it’s worth taking a stab.
The distribution centres on a lower WAR total as a result of combinations of scenarios involving low or lower paying time, not being very good at the plate, and being a solid-to-solid hitter but mostly at DH where the offensie bar is very high limiting the credit received.
There is a substantial left tail or poor productivity which is appropriate given how little track record he has and thus high uncertainty. On the flip side, there is a long right tail representing scenarios where he’s ready to contribute at the MLB level. In any event though, it’s hard to fathom a scenario where he gets above 4 WAR, either because of not playing everyday behind the plate, or playing more frequently at DH.