How many starting pitchers will the Cardinals need in 2016?

If you weren't aware, the last several years Fangraphs writer Jeff Zimmeran has done some great work projecting injury risk. While he does this for all players, today we'll concentrate on Cardinals starting pitchers. Craig looked at what the Cardinals' starters were projected for a few weeks ago, but I wanted to play a little bit more with the numbers to see what we could expect.

To start off, here's each individual pitcher's projections:

No surprise seeing Jaime on top, or Waino in second. Prior injuries are a big part of predicting future injuries, and Adam Wainwright of course missed most of last year with his Achilles injury, and Jaime Garcia is pretty much always injured. Zimmerman says that pitchers who threw 120 innings or more in the previous season have on average about a 40% chance of a DL trip, so El Gallo, Leake, and Wacha all have a less than average chance of getting hurt.

First, I wanted to look at what a missed DL trip would mean in terms of missed WAR, as well as using the injury projections to figure out on average, how much each pitcher's injury risk will cost them in WAR. Steamer's projections include Games Started, which allowed me to find a projected IP/GS stat. Combine that with Zimmerman's calculation that the average DL trip for pitchers lasts 66.3 days, and I can get an average innings missed figure from taking the expected production from 13 missed turns in the rotation. I also rolled in Zips' projections on a rate basis with Steamer to get an average projection between the two systems. Here's the results:

So, Jaime's health on average will cost the Cardinals the most WAR of any starter, a factor of his high injury projection and high level of performance on a rate basis. Wainwright is right behind, due to the same factors, but also due to the fact that he goes deeper into the game than any other Cardinal starter.

But, from the perspective of the entire rotation, its hard to get a good idea for how many injuries the Cardinals could be dealing with. There's certainly a large variation in terms of what could happen, but where's the middle ground?  How likely are we to go the entire year with just one injury to the starting rotation? What's the chances everyone gets hurt? What about in between?  I used an excel sheet along with these numbers and made a bunch of calculations to find out a few things.

Basically, I went through every combination of the Cardinals' five starters. For instance, the chances Waino and Jaime get hurt, but no one else does, is 6.5%. I did that for every way it could possibly work. I didn't include pitchers passed the 5th spot because that would make things a bit more complicated. But according to Zimmerman, Marco Gonzales has 34.9% chance of a DL stint, Tim Cooney is at 36.1%, and Tyler Lyons is at 43.7%. Though I believe Lyons should be and will be in the bullpen,  hypothetically he could stretch out as a starter if enough injuries occurred early on.

On each of these, I also used the missed WAR/DL stat to calculate averages for how much WAR the team would miss out on in each of these scenarios. For now, these numbers do not include the fact that the replacements for these pitchers would be above replacement level.

Here's the results:

Remember, the average DL stint for starting pitchers is 66.3 days. That's every type of pitcher injury from something that lasts all year like Tommy John Surgery, to trips where the pitcher only spends the minimum 15 days on the DL. Most likely, the Cardinals will sustain 1-3 trips to the DL. A whopping 83.5% of the time the Cardinals will be in that range.

Compared to average

Let's add some more context. How do these numbers compare to what a staff with average injury risk? I used the same equation, but input 40% for each pitcher. Here's the same chart, but with the average staff alongside it for comparison:

The differences are fairly small. The Cardinals have a 35.4% chance that three or more of their opening day rotation will hit the DL at some point, the average team sits at 31.7%. Using a weighted average of these scenarios, the Cardinals project for 2.1 DL trips compared to 2 for the average staff.

Memphis Reinforcements

As mentioned earlier, the Cardinals would not be replacing their starters with replacement level pitchers, so just using WAR limits us in nailing down the value lost from injuries. Tim Cooney and Marco Gonzales would be first up. For them, I again used Steamer's projected GS and IP totals to calculate a IP/GS metric, and then used Steamer and Zips' averaged projections for their rate stats. From there, I calculated the value these two would provide over 13 starts, the average DL stint:

Relating just to performance, Cooney projects better, though the playing time projection implies that Marco would be more likely to fill in. Based on these computations, Cooney would be able to replace (on average) about half the value that the Cardinals missed out on from a rotation injury. Gonzales would be able to replace about a third of the value.

In the event of two starting pitchers being injured at the same time, Cooney and Gonzales on average would be able to recoup about 45% of the lost value. If the two injuries overlapped for 13 turns in the rotation, the average difference between Cooney and Gonzales and the injured starters would be about a win and a half. Considering 13 turns in the rotation is a third of the year, that doesn't sound all that bad. One and half wins is of course important at the Cardinals' spot on the win curve, but without running the numbers I'd bet most teams would suffer a bigger hit than that.

Three simultaneous injuries and we'll probably see the Cards make some type of move. Stretching Lyons back out to start is one option. Because Lyons' projection is based largely on him getting most his time as a reliever (where pitchers give up less runs) it's not possible to give a similar projection for Lyons. But, being that Steamer projects a 3.16 FIP and Zips a 3.90, he's fairly likely to at least be as good as Cooney.

Consider him just as good as Cooney, and with three injuries to the original rotation, Cooney, Gonzales, and Lyons would project to recoup about 49% of the lost value during that time frame. Working with the 13 starts, that's a loss of a little more than two wins. Though that wouldn't factor in the cost of removing Lyons from the bullpen, which would make those numbers look a little worse.

If it gets worse than that, well, maybe it's not the Cardinals' year. Reyes and Weaver don't currently project as great, and even if you're not a numbers guy, I think the scout guys will agree with that sentiment right now. These two could make an impact in the future, but expecting it to happen this year wouldn't be prudent. There absolutely is some chance that either of these two take a step forward though, and act as insurance against even more injuries.

Now of course, the error bars are a bit large for this. Even when we're specifying how many injuries could occur, we've just been working with the average DL time of 66.3 days. And we're only assuming an average distribution based on each individuals' injury risk.

Losing Jaime, Waino, and El Gallo to Tommy John Surgery early in the year is a lot different than Carlos Martinez, Michael Wacha, and Mike Leake missing just the minimum of 15 days at separate parts of the year. One would require just 6-9 starts from the Cardinals' best backup starter, the other would require Cooney, Lyons, and Gonzales to be in the rotation for the rest of the year. One would cost the team less than one win, the other would cost more than five. And that's just the projections, which have error bars themselves.

Even when breaking things down as much as I have, we always have to keep in mind that we're just talking about the average situation. But with that in mind, I think it's interesting to look at the numbers a little differently in order to get a picture. I hope you agree.