In which Nate Silver writes what might be his most-cited baseball article, or might not be, who really knows.

The Injury Nexus
February 26, 2003

Abstract: Nate and Will Carroll collaborate to confirm, with more precision, a hypothesis that had been floating around sabermetric circles (credited, in another Silver piece, to “Ron Shandler and other analysts”): that young pitchers in a so-called “injury nexus” are more prone to catastrophic injury than other pitchers. They find that the hypothesis is not only true, but that the injury nexus is more concentrated in younger pitchers than had previously been recognized. Specifically, established major-league starters 22 or younger were more than twice as likely to suffer a catastrophic injury than established major-league starters aged 24 or 25.

Key quote: “Even for a successful, established pitcher, the risk of catastrophic injury is meaningfully high throughout his career, almost certainly at least 10 percent in any given season. However, the risk does appear to be to some degree dependent on a pitcher's age.”

Notable: Tucked in at the end of the piece is an aside that suggests a lot of fantasy players have probably been using the injury nexus concusions all wrong:

From what specific data we do have available, it appears that fatigue-based injuries are more likely to afflict older pitchers. According to MLB data, while the risk of tears and fractures decreases with age, the risk of strain and inflammation increases. So too does the risk of injury to body parts that are secondary to a pitcher's motion, such as his back, knee, and hamstrings. Fatigue-based injuries such as these may account for the gradual slope upward in injury risk after the age of 25.

The injury nexus suggests that 22-year-old pitchers are far more likely to suffer the sort of injury that ends or severely disrupts a career, but if older pitchers are more likely to suffer the sorts of injuries that interrupt or alter single seasons, then there’s maybe not much reason to take this into account when you’re drafting in non-keeper leagues. The injury nexus is important to teams, to agents, to insurance companies. Probably not as important as I always thought it was to me, the lowly redraft league manager.

Further reading: Surprisingly, considering how prominent the Injury Nexus has been in sabermetric writing since–I found more than 100 references in our archives–the piece that firmly established it is quite modest. Silver’s portion of the writing, in which he explains the methodology and findings, is about 300 words, with one simple chart:

And the entire article is barely 1,300 words. Very little discussion is given to speculating where further study could go, or the obvious limitations of the study–most notably the sample bias and the extremely imprecise injury scale that was available. History, it is said, tends to compress things, so reading an article on such a broad topic 10 years later we might expect everything that has even been said about a topic to be included. But of course this was just one important, incremental step forward. Its simplicity was probably an advantage, making it more accessible to a broad audience.

There are plenty of place to read more, if you’re into that. For instance, a few months later, Carroll and Lee Sinins looked at real-world results, with some 135 case studies. David Gassko expanded the inquiry to pitch types four years later. Shoot, for that matter, Silver himself wrote a follow-up before the piece even ran, when he gamed PECOTA to demonstrate the injury nexus’ effect on pitcher projections:

I tested the injury nexus theory by prematurely aging Peavy by exactly three years and re-running his PECOTA projection; all of his other statistics and attributes were left intact (as a college sophomore, I tried a similar trick with a scanner and an early build of Photoshop, but without so much success). The 25-year-old Peavy had a Breakout rate that jumped from 8% to 25%, and a Collapse rate that fell from 22% to 14%.

Naturally, Russell Carleton has summed up the appropriate response to this. Russell has, at some point or another, always summed up the appropriate response to everything that involves doubt and inquiry and where to go next:

I do agree that injury analysis isn’t really something that fits nicely into any of the Sabermetric models that we have now, but that’s more of an engineering problem. To really pursue this line of study, one would have to be familiar with bio-mechanics and statistics, plus have a fairly extensive injury database handy. (So basically, you, Will.) Even at that point, there’s going to be a lot of statistical noise. Suppose that Larry has an elbow problem and goes on the 15 day DL. Even if we assume that we know exactly when he was hurt (and when it started hurting his performance), we’ll never really know how hurt he was. How can we tell if it’s not just him having a bad string of luck? Maybe with a big enough sample, we can detect a signal, but it’s going to be hard to find. Calculating the complete absence of a player is fairly easy. Calculating what it means to have a player at 80% is a lot harder.

The other side of the Sabermetric-injury nexus is predicting who’s an injury risk. My guess is that some team (or several) out there hired an actuary to study just that and they’re keeping it close to the vest. (Can’t blame them.) Plus, with many teams already insuring contracts, someone out there in the insurance industry must be running some sort of tables.

Tables: 0
Graphs: 1
Equations: 0

On the Nate Silver Must-Read Scale: 2

Thank you for reading

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I was in a Strat-O-Matic league in the mid-1980s where members would occasionally submit articles to the league newsletter (all was snailmail back then!). A team owner named Tom Fish wrote an article about this subject, positing way back in 1984 that being 22 and younger in a MLB starting rotation was death on arms, citing guys like Wayne Simpson (age 21, 176 IP), Gary Nolan (19, 226.2) and Don Gullett (20, 217.2), I believe.

It's been a long time since I read that article, but it stuck with me because it seemed so prescient and has proved accurate to my eye over the years. Anyway, these ideas have been around a while, just not necessarily always among the baseball cognoscenti.

I have no idea whether it was Tom's idea originally, but it was the first I'd heard of this kind of health analysis, almost 30 years ago now. I can try and dredge it up if you're interested in seeing it, especially since it was written by an amateur analyst.
I'm interested!