August 6, 2014
Troy Tulowitzki and the Brittle Bones Hypotheses
In a twist of stunning unpredictability, Troy Tulowitzki is injured. Like the year before, and the year before that, Tulo is spending some time on the 15-day disabled list, after missing a handful of games for sprains and strains earlier in the season. Troy’s annual trip breaks up what was easily (on a rate basis) the best season of his career.
A glance at Tulowitzki’s injury history reveals a voluminous catalog of the many ways baseball players can be hurt. This year, Tulowitzki suffered a hip flexor strain. Last year, Tulowitzki had broken ribs. The year before, a torn muscle which necessitated surgery. Other injuries on his record include maladies in his foot, ankle, and hand.
Tulo’s pattern of recurrent injury stands as an example of the idea that some players are just injury prone, that is to say more vulnerable or likely to be injured on account of some inherent characteristic. Tulowitzki is not alone in being accused of this weakness: others who have borne the label include Jose Reyes, Carlos Quentin, and all pitchers ever (except Mark Buehrle). We don’t just have anecdotal evidence for the existence of a “health” skill, however. Using some regressions, I showed before that a strong predictor of a player’s number of days lost due to injury was how much time he had missed due to injury in the previous three years. This result gives credence to the idea that there is variance in a player’s intrinsic probability of being injured.
Tulowitzki’s case attracted my attention because of the way his injuries are all distinct from each other. In successive years he’s managed to strain a muscle in his abdomen, break a bone in his torso, and tear a muscle in his groin. While there are perhaps commonalities to these injuries, it’s clear that it isn’t a single, lingering problem that’s dogged Tulowitzki. He’s earned his injury prone tag by being hurt in different ways.
An even better example may be Tulowitzki’s Rockies teammate, and fellow injury prone hitter, Carlos Gonzalez. If Tulowitzki’s injury history is a catalog, CarGo’s could be an encyclopedia. Still a spry 28-year-old, Gonzalez’s rich and extensive report includes strains, contusions, lacerations, and flus. Like Tulowitzki, Gonzalez has suffered at many different body parts: his legs, his fingers, his back, his knee, his thigh, his trunk. Just as various are the causes of his injuries: running into walls, being hit by pitches, foul balls, viruses, bacteria, and cutting himself with a steak knife. Most recently, Gonzalez had to be operated on to remove a be-tentacled “fatty mass” from his fingers (which may or may not have been a Cheeto).
Even though we suspect, based on good statistical evidence, that there is something to the idea of injury proneness, it’s not clear what the cause of the injury prone property might be. In some cases, it’s obvious that old wounds have failed to heal properly. Carlos Quentin exemplifies this pattern. He’s suffered from some kind of knee ailment every year dating back to 2010. It’s clear that the issue has lingered and become exaggerated over time, causing longer and longer stretches of lost games. We could call this the “recurring injury” hypothesis.
But medical reports like that of Carlos Gonzalez argue for a different kind of injury proneness. As I noted before, Gonzo has no single disorder which could have caused all of the various injuries. Instead, it seems likely that there’s something inherent to Gonzalez himself that makes him more likely to be hurt in a wide variety of different situations. We might call this idea the “brittle bones” hypothesis, not because it need refer specifically to bones, but rather in reference to the actual syndrome (osteogenesis imperfecta). This disease, caused by a specific set of genetic mutations, causes sufferers to have structurally weaker bones that are more likely to fracture under stress. Similarly, we are positing here that Gonzalez and other injury prone players have some lowered capacity to resist injuries than other players.
There is scientific evidence for some aspects of the brittle bones hypothesis. For example, it is known that bone mineral density, which is associated with fracture risk, is quite heritable, i.e. genetically determined. It’s not only bone strength that is genetic: increased risk of ligament injury has been associated with particular genes as well. If you consider that baseball players are doing a lot of running around at ~15-20 mph, with some jumping, falling, and sliding thrown in, it seems entirely possible that the stresses of those actions affect some ballplayers less than others on account of stronger bones or ligaments.
Using Corey Dawkins’ excellent curated injury database, I tried to look for evidence of the recurring injury and brittle bones hypotheses. I limited analyses to position players, because wholly different dynamics might hold for pitchers, and other, smarter people are already working on those questions. For the sake of simplicity, I looked at injury records from 2013, but results were consistent in other years as well.
I first looked at whether players tended to miss the most time for the same or different injuries between years. For each player, I looked up the injury which was associated with the most lost days; I term this the most costly injury. Of the 453 position players with more than 100 PAs in 2013, 265 had injuries in both 2013 and 2012. From the 265, 239 (90 percent) had their most costly injuries in different body parts (meaning 10 percent had most costly injuries in the same body parts). Broadening the definition slightly to consider all injuries (instead of the single most troublesome one), 44 percent had injuries to the same body part. In other words, the majority of the time, injuries in consecutive years are to different parts of the body.
I can also perform the same sort of analysis I did before, but limiting myself now to cases in which players suffered injuries to distinct body parts. In this subgroup, we can ask whether the previous year’s amount of time spent on the DL was at all predictive for the next year’s number of DL days. Just like before, we find that, if a player’s injury causes days to be missed in a given year, they are likely to miss more days in the next year (p = .002), even when the injury occurs in a different body part in the consecutive years. This result is evidence for the brittle bones theory and against the idea of recurrent injuries—the injury proneness isn’t rooted in a trauma to a particular body part.
There’s an interesting detail about injuries in the same body parts, though. In general, when a player suffers significant injuries to the same area (for example Carlos Quentin’s creaky knees), the number of days missed is substantially higher. For these injuries, the average number of overall days missed is 48, which is about 50 percent higher than for players with most costly injuries in different body parts (~32 days missed). Despite the small sample size, that’s a statistically significant difference. These kinds of lingering problems may, therefore, be more severe, even if they are also less common. Players with injuries to the same body part weren’t significantly older on average, and didn’t miss significantly more time in the prior year.
It would appear then that injuries in successive years are most often to different body parts. This fact argues that injury prone players suffer predominantly from an underlying increased risk factor, rather than from re-aggravations of the same lingering problem. The recurring injuries might constitute a distinct and possibly more dangerous subset of maladies, however.
I should note that even though I’ve called it the brittle bones hypothesis, the underlying cause might have nothing to do with any physiological factors. It might be related, for instance, to an athlete’s style of play. This idea has come up before with Bryce Harper, a player who is rapidly acquiring the dreaded injury prone reputation. Harper plays with a sort of violence which both suits his personality and probably inspires fear in the hearts of all Nationals fans. Whether sprinting into walls or taking savage swings at unsuspecting baseballs, everything Harper does is full-bore, and it’s not impossible that it’s his attitude that is bad for his health, rather than something to do with his joints or his ligaments.
Alternatively, the appearance of evidence for the brittle bones hypothesis could be because players are having to adjust for old injuries in ways which predispose them toward new and different injuries. Swing and pitch mechanics experts alike can tell you that often a player will modify his swing or his throw to compensate for damage in some part of the normal action. Sometimes that benefits the hitter, but in other cases it can result in elevated stress on a different part of the anatomy, which then breaks, resulting in an injury in a different location than the one which prompted the change. So many baseball motions use the whole body that I can’t rule this possibility out without some extensive further analysis.
Regardless of the mechanism, health is a skill with some very significant implications. As the Rockies ponder whether to trade Tulo and Tulo coyly attends Yankees games, all parties involved would do well to consider Tulo’s value in the context of the amount of playing time he can realistically provide. On the bright side, Tulowitzki is an incredible player who’s presently building an enviable Hall of Fame-class resume. It’s a comment on both Tulowitzki’s skill and his health that he’s doing so in a fraction of the plate appearances and innings a healthy player would accrue.
More broadly, as the Yankees and other teams have discovered in the recent past, injuries can make a big difference in terms of a player’s value. Not all players are so outstanding that they can make an above-average full-season WARP in a half a season’s worth of playing time. It seems likely that at least some of those injury-prone-labelled players are risky bets, and ought to be treated as such.
Thanks to Corey Dawkins for building the amazing injury database.