If you are reading this, you probably know that Chris Carpenter will reportedly miss his Opening Day start for the Cardinals. No length of time missed has been mentioned yet, but this obviously hurts St. Louis. You may or may not have heard that Roy Halladay is Chris Carpenter’s friend, but I am sure players all over the league are concerned about a loveable guy like “Carp. [Heard this: Zack Greinke is organizing a fruit basket with donations from other National League Central players.]

Despite losing Albert Pujols, the Cardinals actually had a pretty nice off-season, with Lance Berkman re-signing and Carlos Beltran being added to the outfield. Losing Albert Pujols hurts, but the National League Central is not exactly the American League East. While it is a mistake to note one change from year-to-year and hold everything else constant, it is worth remembering that the Cardinals won the World Series with an even better pitcher — Adam Wainwright — out the whole season with injury.

Everyone agrees, of course, at that the Carpenter injury is worrisome for the Cardinals. But just how much will it hurt the team? Sabermetrically-oriented analysts will (or should) point out that these things matter less than some think they do. Why is that? Rather than giving a complete rundown of all the reasons, or a full primer on replacement level, let’s use this Carpenter situation as an opportunity to go over replacement level (among other things).

There are so many good primers on “advanced” stats and metrics that I do not feel I can make a decent contribution by doing another one, so this is simply an illustration of one way they can be applied. For those curious about replacement level and related concepts, here is one good place to start (scroll down to the end for links), but it is not the only one out there.

Let’s begin with the basic question we want answered: how many games will Carpenter being out cost the Cardinals? Well, obviously the first thing we need to know is how long he will be out. Without pretending that I know anything about injuries, let’s hypothetically speculate that Carpenter, 37 years old next month, will miss the whole season. I am sure someone somewhere will say that the Cardinals cannot make the playoffs if that happens. Again, that is clearly wrong — they made the playoffs without Wainwright last season (and Pujols having his career worst year, which rarely gets mentioned — I mean “bad” by Pujols standards, i.e., the only year of his career that would not be part of a a Hall of Fame peak), who projected prior to last season better than Carpenter going into this year.

The Wainwright point is more rhetorical than substantive, since, again, last season is not a constant. How good is Carpenter expected to be this season? Some people do not like projections, and, well, I can’t help you if you are one of those, at least not in this post. In 2011 he was as good as ever, putting up 5.0 fWAR and having a 3.45 ERA and 3.06 FIP. What does it mean to say that he was worth five “wins” above replacement, though?

A replacement-level player is sort of a heuristic idea of a “freely available” player that can be acquired for nothing; a typical Triple-A journeyman. Such a baseline is needed because a) a “zero” baseline is unuseable in a practical sense, as there are, e.g., terrible pitchers who are worse than worthless who can still get outs; and b) “average” does not work as the baseline (at least in the baseball market) because average major-league players are far from freely available, and are actually pretty difficult to develop.

Many studies have been done about what a replacement-level “team” might be, and thus what the correct replacement level for pitchers and non-pitchers would be. Replacement level also varies from era to era. Again, we are keeping it simple. Various sites like FanGarphs, Baseball Prospectus, and Baseball Reference use different formulas for calculating of replacement level (it should be noted that replacement level for pitchers is debated more than for position players) and WAR in general. While I personally use a more involved formula, an easy one that gets pretty close for the sake of making today’s point sets replacement level for starting pitchers at 128% of league average ERA (or FIP, which is scaled to ERA — actually, we should use something scaled to Runs Allowed if we wanted to be more precise).

In 2011, the National League’s average ERA was 3.94, which would make replacement level 5.04. Assuming a similar run environment for 2012, and ZiPS projection of a 3.40 ERA for Carpenter over 200 innings, that would make him worth about 36 projected runs above replacement, or almost four wins (we are also fudging the runs-to-wins conversion, something I will discuss in an upcoming post, for the sake of simplicity).

Four wins over a full season is significant, but it is not the total season-killer some would make it out to be. If Carpenter only pitchers half the season, that is just two projected wins, which is significant in terms of projections, but a small swing of randomness can cancel those out. This is why injuries to key players are not as bad as it seems. Thus, for example, if Ryan Braun’s 50-game suspension had gone through, even if you think he is a six-win true talent player, it probably would only have cost the Brewers about two games in the standings.

But back to Carpenter and the Cardinals: at the moment the Cardinals are reportedly looking to move Lance Lynn into the rotation. Now, due to the nature of rotation slots, skipped starts, and workload restrictions, I doubt Lynn would get all 200 of Carpenter’s innings. However, for the sake of argument, let’s pretend he does. ZiPS projects Lynn for a 3.88 ERA, although part of that projection is based on his work as a reliever last season. Without getting into the deeper analysis needed for this particular situation, as a general rule analysts say that a reliever will have an ERA one run worse. Since ZiPS takes both the minors and majors into account, let’s be a bit more generous with Lynn and call it 0.7 runs, for a projected 4.58 ERA as a starter.

Over 200 innings, that would make Lynn about a one win pitcher, or two or three wins worse than Carpenter. That is not my personal projection for Lynn, but serves to illustrate the point. Even with a replacement level pitcher, the Cardinals would not be doomed by losing Carpenter. Lance Lynn probably is not going to be a star starter, but he is also probably better than replacement level. Moreover, we simply assumed that Lynn will get all of Carpenter’s innings, which is unlikely in the extreme, as Lynn will be in the back of the rotation and will probably get skipped relatively often.

Losing Chris Carpenter would hurt any team. Like Zack Greinke, I mourn the absence of such a class act from the mound. But with the aid of replacement level (and Lance Lynn), we can see that it the injury by itself is unlikely to cost the Cardinals their shot at the playoffs.

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