An Even Newer Way of Looking at Depth

Last year, David Appelman and I set about injuring a ton of players. Wait, that doesn’t sound right. Let’s try this again. Last year, David Appelman and I developed a method to use our depth charts projections to simulate how much injuries to the league’s top players might affect each of the teams in baseball. Today, we’re updating that article for the 2025 season. I’ll also present some research I’ve done into how these injury-aware depth charts compare to actual historical seasons.

First, a review of the methodology is in order. If you don’t need an update, or if you simply want to get right to the data, you can skip ahead; the results section is clearly labeled below. We decided to simulate depth by first removing the top X players from a team’s depth chart and then reallocating playing time to fill in the missing plate appearances or innings pitched. We then created a number of rules to make sure that these new depth charts were generated in a reasonable way, at least to the greatest extent possible.

Let’s use the 2025 Phillies as an example. As of the time of our run on April 7, we projected the Phillies for a .545 winning percentage against league average opposition. That projection comes from allocating playing time to each Phillies player according to our depth charts, using blended projections from ZiPS and Steamer to estimate the talent level of those players, and then plugging those projections into the BaseRuns formula to estimate runs scored and runs allowed. But those projections have an obvious weakness: they’re static.

Before the season, we marked Zack Wheeler down for 202 innings pitched. Wheeler is about as durable as they come, but he’s probably not going to pitch exactly 202 innings every year. In the past four seasons, he’s thrown 213.1, 153, 192, and 200 innings respectively. That’s even without missing any time with a catastrophic injury – plenty of star pitchers miss whole years. Our depth charts reflect a perfect-health world, more or less, and real life doesn’t always work out that way.

To account for the possibility of injury, we simply deleted Wheeler from Philadelphia’s depth chart. That leaves them with a 202-inning shortfall, which we start handing to other pitchers. First, we add as many innings as possible to the next pitcher on the depth chart. But uh, that’s Aaron Nola, and adding 202 innings to his projected 188 would result in a 390 inning projection, hardly reasonable. We add a cap at 20% of a team’s games started, which means that the vast majority of Wheeler’s innings pitched would have to be picked up by someone other than Nola.

Those innings cascade down the depth chart. First, Cristopher Sánchez sees his projected innings pitched increase by about 18 to get him up to a full workload. Then we just head down the list, with a few exceptions I’ll note below. Jesús Luzardo sees an uptick in projected starts. Then comes Taijuan Walker, and finally we’ve gotten to a pitcher who can take the vast majority of Wheeler’s innings. Thus, we recalculate the Phillies’ winning percentage against neutral opposition with a new team composition: no Wheeler, but extra playing time for his backups.

You’ll notice that I left out a few players when adding innings. Specifically, I omitted Ranger Suárez and Andrew Painter. That’s because we have an exception to the playing time waterfall rule: Players who are currently injured are excluded from any increase in plate appearances or innings pitched. That keeps a starter rehabbing from TJ or a hitter currently nursing a broken foot from ending up with an impossible projection.

Continuing with the Phillies as an example, we next look at how the team would look without its two best players. In this case, that means simulating Philadelphia without Bryce Harper, which conveniently lets me show you how this works on offense. Harper had a preseason projected playing time of 665 plate appearances. Those flow to the players behind him on the depth chart at first base, with some similar rules for realistic projections.

First up as a backup? Alec Bohm. Our playing time waterfall method hands him all 665 plate appearances. Unfortunately, that gives him a projected total of 1,281 plate appearances, which is clearly unrealistic. Thus, we cap playing time at 700 plate appearances for non-catchers and 640 for catchers. Maxing Bohm out at 700 leaves 581 plate appearances still to be assigned. Next up comes Weston Wilson, but alas, he’s currently injured and thus ineligible for any playing time increase. The next rung down the first base depth chart is Kody Clemens, and given that he only projected for 49 PAs with the team at full strength, he can take all 581 remaining. It’s slightly more complicated than that in practice because Harper had a few games of DH in our preseason projections, and those get allocated down the DH depth chart instead of first base, but you get the idea: We remove a player, then hand the playing time out to his backups, in order, respecting maximum workloads and injury restrictions.

The rebuilt Phillies are, unsurprisingly, worse than the full-strength Phillies. Specifically, when we consider Philadelphia’s full team without Wheeler and Harper, it projects for a .522 winning percentage against league average opposition, down from .545 at full strength. That’s roughly four games over a full season. It’s less of a decline than you’d get by simply adding Wheeler’s and Harper’s WAR, but that makes sense. They’re not getting replaced with replacement level players, because some of the other regulars can pick up slack first.

This methodology can get a bit funky when you’re replacing 10 players. Imagine the Phillies without Wheeler, Harper, Trea Turner, Nola, Bryson Stott, Sánchez, Bohm, Brandon Marsh, Suárez, and Kyle Schwarber. Assigning all that playing time is necessarily going to have some error bars. Luckily, it doesn’t matter much, because by the time you’re looking for 3,000 plate appearances, the marginal last plate appearance is going to one of a variety of players with fairly similar projections. Does it matter if Cal Stevenson or Gabriel Rincones Jr. gets 50 of Schwarber’s PAs? Probably not; they’re both roughly replacement level.

We repeated this process for the top 10 players on every team. Is 10 a reasonable number of top players to miss the entire season? As I’ll get into later in this article, it is not. But consider this a proof of concept: We don’t have to lop off all those players from the depth charts to see how a team might fare when facing injuries, but it’s nice to know that we’re capable of doing it. The most important part of the forthcoming tables is the first couple of rows. How a team would perform without its top two players is a useful examination of depth. How it would perform without its top 10? Probably not relevant, but again, it’s nice to know that we can measure it.

Results

Without further ado, here’s an enormous table with all of our depth-aware projections. It’s sortable in case you have a particular question you’d like answered:

Broadly speaking, there are two ways of looking at these results. First, who’s most affected by the loss of top players? The best teams, of course. It’s not that they don’t have depth; sticking with the Phillies, their projected winning percentage without their top seven players is the fourth-best in baseball. In other words, if you lopped the top seven players off of every team in the league, the Phillies would still be one of the best groups around. That sounds like depth to me. But they also have the fourth-largest decline in projections from removing those top seven players. I don’t care how good your backups are; removing Wheeler, Harper, and company is more damaging than, say, the White Sox losing Luis Robert Jr. and a bunch of fringe major leaguers.

I like to think of these tables as showing a mix of two things: depth and top-heaviness. Depth is how good you are without your best players. The best team in baseball, if everyone had to play without their 10 best players, would be the Orioles. The Rays aren’t far behind. The Cardinals are right in the mix despite lackluster full-strength projections. Quite simply, if your backups are good, you have good depth.

Top-heaviness is something else entirely. It doesn’t matter how good your backups are; they’re a lot worse than Wheeler, or Aaron Judge, or any of the game’s best players. Teams with a large decline in projected winning percentage are top-heavy because a disproportionate amount of their strength comes from their top few stars. Take a look at this table of the projected winning percentages with the top three players removed from every team’s depth chart, as well as the change in projections from the full-strength version:

You can be top-heavy and deep, like the Phillies. They have the sixth-largest decline in projections, quite top-heavy. They also have the third-best projected winning percentage, quite deep. You can be top-heavy but not deep, like the Royals, who fall from a .500 team to a .450 team without their top three players. Bobby Witt Jr. – pretty good! You can be deep but not top-heavy; we have the Giants down as the 15th-best team in baseball at full strength, but they have an enviable array of backups, and thus see their neutral-opponent winning percentage decline by only 24 points, the sixth-smallest gap in baseball. And of course, you can be neither top-heavy nor deep like the Rockies, who lose essentially no winning percentage when you remove their best three options, and yet project as the second-worst team in baseball anyway because neither the starters nor the backups move the needle.

At the bottom of this article, I’ve included an appendix of extra tables that break the data up by the number of players removed from the depth chart as well as by division. But first, I’d like to present a new piece of research to add to the puzzle. In a vacuum, this method doesn’t tell us a lot. Sure, I can tell you how good the Dodgers would be if they were missing their top eight players, but how likely is that to happen? Can’t be very likely. Heck, last year’s Braves had one of the worst runs of injury luck you can imagine, and that didn’t work out to much more than their top two players missing time.

To connect our theoretical injury-aware depth charts to real-life team strength, I looked to the past. I noted the top 10 projected players for each team and each season starting in 2015, excluding the 2020 season. Then, I noted how those players’ actual playing time compared to their projected number. I converted that to WAR, using the player’s preseason projection for WAR/PA or WAR/IP as appropriate. Let’s use last year’s Braves as an example: Ronald Acuña Jr. was projected for 696 plate appearances but played only 222. He was projected for 7.3 WAR in those plate appearances, so to calculate Atlanta’s injury-based shortfall, I used this formula: (696 – 222) * (7.3 / 696). That gave me a result of 4.97 WAR; in other words, Acuña’s limited availability cost the Braves roughly 5 WAR worth of projected wins, which they had to fill in with backups.

I specifically tailored this method to focus on availability rather than results. If you wanted to make a different metric, you could include how Acuña actually played in those 222 plate appearances. But we’re not looking for under- or over-performing players here; we’re specifically interested in whether players missed time. Thus, I only used preseason projections in calculating the WAR shortfall for each player whose playing time was lower than expected.

I did this for the 10 Braves with the highest preseason WAR projections. Adding them all up, the Braves lost out on a projected 14.15 WAR due to injury; Acuña was the largest hit, but Spencer Strider (184 projected IP, 5.0 projected WAR, nine innings in real life) wasn’t far behind. Then I set out to translate that 14.15 WAR into our depth chart methodology. This wasn’t hard to do; I just had to see how many WAR the Braves’ top X players projected to earn, for a variety of X’s. The Braves’ top two players, Acuña and Strider, projected for a combined 12.3 WAR. Add in Austin Riley, the third name, and we get up to 16.3 WAR. So in terms of actual games missed by their projected top players, the Braves came in somewhere between “all the playing time of our top two players” and “all the playing time of our top three players.”

I repeated this method for every team in every year. I rounded to the nearest half player’s worth of WAR; for example, I marked the Braves down as a 2.5-best-player-missing team. I ended up with the following distribution of availability shortfall relative to our projections of full strength:

That’s a satisfyingly reasonable shape. It’s quite rare for a team to have no injury issues at all among their top 10 players. It’s equally rare for a team to have huge injury problems, missing the equivalent of more than their top two players. The vast majority of teams fell somewhere between 0.5 and 1.5 top player equivalents of missed time.

In tech terms, I’d say that this historical calibration is still in beta. I haven’t finalized my methodology yet, and I still have some things to work out. I haven’t decided how to handle trades or benchings, or whether I should even specifically address them. I have some ideas for how to better account for teams with one incredibly good player and not much behind them, which makes for some weird results. But broadly speaking, I can comfortably say that we don’t need the entire 10-scenario grid to figure out how much playing time teams need to fill in with backups in the real world.

At some point, I’m hoping to connect this output to our playoff odds. For each simulated season, we’d load the grid of different talent levels at different levels of injury, randomly select how close to full strength each team was, and use that to set their opponent-neutral win percentage. We’re not there yet, both because we haven’t figured out how to fold that into our infrastructure and because we haven’t finalized the methodology for estimating likelihood of various injury scenarios, but I feel that the overall plan is sound.

In the meantime, here’s one other way of thinking about it. Instead of using a Monte Carlo simulation, I just weighted each team’s winning percentages from the table above with the likelihood of each bucket of time lost to injuries. For the increments of 0.5, I just took halfway between the two – this is more art than science, obviously. That gives me this modified measure of team strength, accounting for likelihood of injury:

You should care more about the relative placement of each team than the raw numbers. In a world where every team’s projection is too high, “league average opponent strength” doesn’t make a lot of sense. The average of our 30 teams worth of winning percentage is .486; naturally, if you remove good players from every team but still make them play full-strength theoretical opposition, that’s going to be the case.

Takeaways? Well, our odds are probably overstating the playoff likelihood of teams with superstar players, and underestimating the likelihood that deep teams like the Cardinals, Twins, Giants, and Rangers will play into October. On the other hand, we already know that our odds are probably a bit light on great teams due to the way we project fixed plate appearances, so to some extent the lack of accounting for injuries is useful and offsetting.

Also useful to know: The variation across the league in injury resilience is relatively minor. The Mets take the biggest hit to their expected winning percentage after accounting for depth at 24 points of winning percentage, with the league average drop being 14 points. The least affected? That’s the Rockies, thanks to their lack of high-end talent. Their expected winning percentage against neutral opponents drops by only a single point after accounting for the chance of injury. That gap of 23 points is less than four games across a full season.

Is that worth measuring? Obviously. But it’s nice to know that based on historical data, the difference between a team with elite backups and one with a relatively weak bench is on the order of low single digits. Depth matters. Measuring playoff odds more precisely is an admirable goal. It’s reassuring that, as best as I can tell, we’re both heading in the right direction and not far off already.

Appendix: Some Tables
Interested in seeing the tables from up above rotated in new and hopefully helpful ways? Let’s get going. First, here are winning percentages for various levels of depth, organized by division:

Next, here’s how much worse each team projects to be after losing their top one or two players:

Here’s three and four players:

Five and six:

Seven and eight:

And finally, nine and 10:

If you can think of any other ways to slice this up, well, there’s always space to add to this appendix. Let me know in the comments!