Properly Valuing Hitters with Injury Risk

Editor’s Note: This is the fourth post of “Fantasy Baseball Preview Week!” For more info, click here.

Look at the Steamer projections for players like Giancarlo Stanton, Miguel Cabrera and Troy Tulowitzki and you’ll quickly see they’re not projected to play anywhere close to a full season. Certainly this is due to their increased likelihood of trip(s) to the disabled list. For fantasy players, most calculation systems convert those projected stat lines into rotisserie dollar values but don’t account for replacement level statistics accumulated when the injured player is on the DL.

In this article I’ll look at this adjustment using projections for the 2016 season.

Identifying the Players

I started this process with Steamer projections as of Feb. 1. Using a standings gain points approach, I then calculated dollar valuations for those players. I then scanned through that list and selected 13 players who appeared relatively high in value but who clearly had fewer projected plate appearances than those around them in the list. The unlucky players I selected are:

Assumptions Used

Before I get too far along, let me specify the assumptions I used in calculating the dollar values. These reflect a 12-team league using standard rotisserie rosters of 14 hitters, nine pitchers, and no bench. This means 168 hitters will be drafted. Teams are given a $260 budget and calculations reflect an allocation of 67 percent of the budget to hitting and 33 percent to pitching. I’ll also note that due to some issues with player IDs and missing projections, certain players like Byung-Ho Park and Hyung-Soo Kim were not included in this analysis.

Defining Replacement Level

Because projections are so volatile, and due to differences in opinion, it’s unrealistic to identify only one player as “replacement level.” Accordingly, I’ll use the average stat line for the first five undrafted players at each position to represent “replacement level.” For a 12-team league using the roster arrangements listed above, here’s what replacement level looks like:

And here are those same players aggregated into a per-game average:

You might be wondering why I left catcher out of the mix. Feel free argue this in the comments, but I saw two issues with including catchers:

• When I think about the actual logistics of how replacement level works, it goes something like this. Your player gets injured. You then go to the waiver wire, typically in search of a player you expect to receive regular playing time. For a 12-team league, if someone misses 30 games to the DL, you can probably find a replacement that will fill in for just about those same 30 games. I don’t believe that assumption holds true for catchers, particularly in the league setup I’m using for this analysis. In a two-catcher setup you’d be scraping the bottom of the catcher ranks for a replacement. These typically are not full-time players. If Buster Posey misses 30 games, you would be lucky to find a fill-in to play 20 games.
• The other issue with including catchers is deciphering how much of their projected playing time is reduced due to injury versus lost to normal days off. If a catcher is projected for 130 games, is that because of injury? Or is it because that’s how much he’d play in a full season without being injured?

Not to mention that the replacement level stats you would add back would be putrid!

There’s too much mud in the water with catchers. For these reasons I concluded to leave catchers out. This decision did have some interesting ramifications which I discuss at the very end of this article.

An Example

Let’s start with a simple example using Giancarlo Stanton. As you see above, Stanton is projected to play in 126 games. Assuming he’d lose some time to the DL and some time to regular days off, let’s add 29 games of replacement level outfielder stats. That would suggest 155 games, leaving seven rest or nagging injury days off that we could not replace. Here’s how his projection and dollar value calculation transforms:

Interesting. This adjustment was enough to move Stanton up from being the player with the 10th highest projected valuation to the second, behind only Mike Trout!

Not So Fast!

It would be a major error to do what I’m suggesting above with Stanton.

I can’t just do this for one player or even the small group of players who are “most likely to get injured.” Doing so would give those “adjusted players” an advantage not being offered to others and would result in artificially inflating their value. Yes, we want to incorporate the value of replacement level stats for the unlucky 13, but there are many other players who have lesser degrees of injury risk in their projection. To name a few: Freddie Freeman (140 projected games), Prince Fielder (144), Starling Marte (142), Justin Upton (144), Adam Jones (144), Nelson Cruz (140) and Joey Votto (138) are also projected to miss time. If we adjust only the unlucky 13 they’ll fly right past these other players in our rankings.

The highest projected games played I can find for any player in Steamer projections is 147 games played for Paul Goldschmidt, Jose Altuve and Evan Longoria. Seeing that makes my decision to bump Stanton up to a 155 game total look really poor. I’ve given him eight more games played than any other player AND he was originally projected for only 126.

Picking and choosing the individual players to adjust for opens us up to bias. To be fair and accurate, I should run this same exercise on all players and push them all to an equivalent number of games played.

A Better Example

In this example I pushed most players to 147 games played, using replacement level stats to get them to 147. For example, Mike Trout‘s original projection shows 143 games played. I added four games of replacement level outfield performance to his totals.

You might ask why I concluded to do this for Trout. If he’s only four games less than 147 it doesn’t represent a true DL stint and I couldn’t replace him. Right?

My reasoning goes back to the way projections work. We know they’re a weighted average calculation of all possibilities. Maybe there’s a 20 percent chance Trout plays in 160 games, but there’s also likely a 20 percent chance he ends up on the DL for 30 days. When you mash all those outcomes together into one projection, you might come out with 143 games. And again, I can’t ignore Trout and make adjustments to all other players.

Yes, Trout’s only four games from the 147 mark while some are more than 15 games, or a full-DL stint, away. But Trout’s 143 reflects the possibility of DL stints too. They’re just less likely to happen. So I’ll still adjust for the four games.

There’s still one significant elephant in the room. And that is how to deal with players who simply are not “full-time” starters. Matt Adams is projected for 92 games played, Ryan Zimmerman 97. Zimmerman’s projection is likely due to potential injury. Adams’ is likely due to injury and some platooning. Giving him the full credit for 147 games wouldn’t be appropriate. I’ll discuss this more in a bit. But for this example I decided to proceed with the 147.

After making this 147-game adjustment to players (except catchers), here’s Giancarlo Stanton‘s revised dollar value:

To summarize, his original unadjusted value was $29.55. My faulty calculation put him at $37.22. And my next iteration put him at $35.97. He still goes up when we add his replacement stats. But not by as much when we include the effects of on all players.

What Happens to the Rest of the Unlucky 13?

Let’s take a closer look at all the players I singled out earlier. Each player’s original, or unadjusted, value is presented in the “$ORIG” column. The “$ADJ” column represents the player’s value after the entire player population gets replacement level adjustments.

Well, that’s interesting. Most players went up, but not all. And not by similar amounts. Cain actually lost value because he was passed by players projected to play fewer games than him, Carlos Gomez and Ben Revere, and therefore received less of a bonus than those around him.

Let’s Think About the Dynamics

To understand the full situation, I should also tell you that Mike Trout‘s value went from $42.44 in the unadjusted scenario to $47.28 after the adjustment. For giving him credit for only four more games? How could that be?!? Replacement level drives everything when calculating dollar values.

Do you remember the names on the replacement level list much earlier in this article? Logan Morrison, Brett Lawrie, Jose Reyes, David Wright, Devon Travis…. Notice anything about them? They’re all injury-prone themselves.

There’s a circular calculation effect that I should probably think more about. But these players also received the bonus we’re talking about. By adding replacement level stats to these players, replacement level rises.

When replacement level rises, there are fewer resources (runs, homers, stolen bases, etc.) to divide the league budget over.This means more of the league budget gets allocated to the top players. Even if I take the four replacement level games away from Trout, his value still rises to nearly $46.

Before an adjustment, replacement level was full of players who are fairly productive when they play, but injury prone. After adjustment, replacement level looks more like players who just aren’t productive and do play a fair amount. For example, some notable players who fell below replacement level are Joe Mauer, Starlin Castro, Alcides Escobar, Trevor Plouffe, Chase Headley, Nick Markakis and Nori Aoki.

You might also be wondering why most of the outfielders in the unlucky 13 didn’t change significantly in value. This again goes back to replacement level. After the adjustment, replacement level for outfielders is noticeably higher than it is for any other position. It appears this happened because a number of outfielders benefited greatly from the adjustment. Michael Brantley, Jarrod Dyson (not an injury risk, so we’ll revisit him later), Avisail Garcia, Corey Dickerson, Rusney Castillo, Hanley Ramirez and Byron Buxton all moved up over 20 places. You can see these are very productive players who have been riddled with injuries.

The same can’t really be said about a position like first base, where most of the interesting players are already owned and there aren’t as many injury risks toward the bottom of the rankings. Bumping Justin Smoak, Mike Napoli and Yonder Alonso to 147 games played doesn’t really get intriguing.

I Said I Wouldn’t Single Players Out, But…

Let’s revisit the topic of platoon players and those who otherwise would not reach 147 games played, even if healthy. Instead of applying a blanket limit of 147 games, I could spend forever refining this model for each player. “I think Matt Adams will sit 20 games against tough lefties, Billy Burns 25, and I think Javier Baez will only play 115 games in a utility role….”

Another point to ponder is that not all injuries or injury-prone players are created equal. Take Yasiel Puig for example. The incredibly useful Pro Sports Transactions suggests Puig missed as many as 13 games in 2015 with “day-to-day” injuries. Peruse Troy Tulowitzki‘s recent history and you’ll see a similar story (granted, that rib injury in 2015 would have put him on the DL had it occurred outside of September). Day-to-day injuries like this don’t fit neatly into our “you replace the player with a free agent or waiver wire claim” scenario. If the player doesn’t hit the DL, there’s no mechanism to replace him with another player.

Some playing time projections are low because of DL risk. Some are because of platooning, days off, and projected “nagging” injuries. These can’t be replaced.

It’s all about balance. I shouldn’t adjust only Giancarlo Stanton. And I also should assume everyone plays the same number of games. Ideally, one would think more critically about the actual circumstances of each player and adjust only for games missed that can be replaced according to your league’s rules.

Use Caution, Apply Your League’s Rules

Speaking of league rules: I am relying on a significant underlying assumption for this analysis. That assumption is that your league rules allow you to freely and easily replace a DL-ed player. Any experienced fantasy baseball player knows this is not always the case. With the rising frequency of injuries in major league baseball, fantasy leagues that only offer one or two DL spots don’t necessarily offer this luxury.

With that said, the players most likely to benefit from the exercise of adding in these replacement level stats are higher valued players like the unlucky 13 above. If the 150th best player in the league is injured, you’re not that upset if you have to cut him to land a replacement.

Conclusions

As with anything complicated, it’s difficult to pull out broad generalizations that can be applied to everyone. There are a lot of moving parts to this analysis. Here are the main points I’d like to remind you of as you head away.

• You can’t treat individual players to the replacement level bonus. You need to attempt to apply it globally and then adjust where it doesn’t make sense (Seth Smith’s missed games aren’t going to all be due to injury, meaning you can’t bump him up to the same level of games played).
• It’s really hard to draw conclusions from how this would affect your league. You would need to calculate dollar values and playing time adjustments based on your league’s rules, settings, and DL limitations. These settings could have a dramatic effect on how your player values change. Those factors would adjust who the replacement players are, how freely you can replace injured players, and if replacement level players are likely to be full-time players (in an AL- or NL-only league you can’t assume you can replace 30 days on the DL with someone from the waiver wire).
• The best and most valuable players can benefit from this adjustment even if they’re not injury prone! Don’t just assume those suffering injuries get a bump here.
• I didn’t point this out above, but catchers received a huge bump in value even though I didn’t adjust them. That’s because the catcher replacement level stayed the same while it rose for all other positions. The same reason Mike Trout’s value increased is why catchers rose even higher in value. Every catcher’s “SGP over replacement level” stayed the same while all other player’s fell.
• All of these points keep going back to how important replacement level is in calculating a player’s value. Player value is determined by how much better a player is than the replacement level player at his position. Value changes when a player’s production changes (if you add replacement level stats) AND when replacement level changes. Catchers become more valuable in this scenario because the position is so weak. It has a compounding effect.
• There are other applications to this analysis. The most notable example would be minor league players. Take Kris Bryant or Byron Buxton during the 2015 season. There was a lot of speculation about when they would be promoted. If your league rules allow for you to freely replace minor leaguers, adding replacement level stats to their projections would have been warranted.
• Players like Jarrod Dyson and C.J. Cron benefited immensely from this adjustment. These are guys that are destined not to see full-time action, but are more productive than average when they do play. You don’t want to clog your bench up with players like this, but their value increases dramatically at the hint of them seeing increased playing time.
• I noticed a similar phenomenon with Michael Brantley. I like knowing that Brantley is likely to miss the beginning of the season. This allows you access to the waiver wire early in the year, when the quality of players there may be its highest. This is due to playing time battles shaking out and an increased likelihood someone will make a mistake and drop a player of value after a slow start.
• As you might expect, the players who decline in value and fall down the rankings are the “compilers” who aren’t highly productive but earn their value by staying healthy and playing full-time.