April 8, 2014

Moonshot

Miguel Cabrera and the Bearable Heaviness of Being

by Robert Arthur

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A little over a week ago, Miguel Cabrera agreed to an historic contract extension amounting to no less than $248 million dollars. While the response to the deal from many corners was one of concern, it was well understood why the Tigers made the commitment. Nevertheless, in the midst of an MLB-wide trend toward locking up young talent, the Tigers bucked that trend in taking a bet on an aging slugger ripe for regression.

The contract has been dissected from almost every angle, and so I won’t attempt to rehash the various projections or what they mean for overall value in a $/win framework. Instead, I intend to consider an ancillary factor in the Great Contract Debate, one which was brought up in a handful of discussions: Miguel Cabrera’s considerable weight (240 pounds, listed).

Cabrera’s paunch is not expected to significantly impair his superhuman skill at swinging a bat, and what little effect there is has already been integrated into projection engines like PECOTA. However, there are also indirect ways in which weight might affect other aspects of Cabrera’s career. I will examine how weight affects injury probability and career length, with the expectation that general conclusions from this analysis can be applied to the specific case of Cabrera.

Injury Probability
Weight enters the calculus of injury probability in a rather straightforward way: Folks with larger body mass put more stress on their bones, especially in the act of performing physically-demanding athletic maneuvers like running the bases. At the outset, we expect more weight to correlate with a greater incidence of injury, especially lower body strains and fractures (or so the medical literature suggests).

I’ll scrutinize injury probability in position players with a logistic regression model, similar to the approach used by Jeff Zimmerman for pitching injuries. In previous studies, I found age and prior injury history to be dominant determinants of injury probability. I calculated a Body Mass Index (BMI) based on Lahman’s player database. BMI relates height and weight to produce a number that is generally indicative of girth: High values of BMI indicate obesity, low values slimness. I integrated the BMI data and asked whether BMI was at all associated with injury.

The above graph charts Body Mass Index as a function of injury status, based on the 2012 disabled list data. There’s a very small difference between the players who were injured (red) and those who weren’t (blue); typically, the injured players had a BMI which was about .2 higher than the uninjured players. More formally, I used the logistic regression to figure out whether BMI was predictive of injury status.

While the model estimates BMI as being associated with higher injury probability, the difference is slight and not significant. For comparison, the effect of BMI is dwarfed by the much more significant increase in injury probability due to age and injury history. Therefore, this analysis suggests that any increased injury probability due to Cabrera’s weight is likely small.

For reference, I decided to calculate the model’s best guess at Cabrera’s injury probability in the coming year. Overall, about 30 percent of all position players spent some time on the DL in 2012, so we can regard this as a sort of baseline injury probability. Given Cabrera’s age and a clean injury history, his predicted probability of injury is 35 percent, or five percent higher than the average position player. However, Cabrera was injured last year; even though he spent no time on the disabled list, he suffered a groin tear. If we treat Cabrera’s prior year status as injured, his predicted risk shoots up to 44 percent.

This year will be an important test for Cabrera: if he remains healthy, his predicted injury probability may actually decline next year, despite his increasing age. If he suffers yet another strain or pull or break, it may be the first indication of a long-term injury spiral, which will cut away playing time and effectiveness. From here on out, injury probability begins to get dramatically worse.

Career Length
Another place to look for the signal is in career length data (which I’ve used before). One might reasonably believe that BMI exercises only a small effect in any individual year, but that the effect is magnified over the course of several years, such that larger players tend to show shorter careers. I test that using a survival model, as described before.

In an overall sample, BMI shows a small, positive relationship with increased hazard ratio (hazard ratios above 1 [the black dotted line] indicate more risk of a career ending than the baseline, and hazard ratios less than 1 indicate less risk than baseline). Yet, again, the effect of BMI is dramatically overshadowed by effects I’ve reported before, such as the trend over time and by position.

Maybe BMI is bad, but only for older players. To test this, I cut off the sample and looked only at players who had already played at least nine years in the league.

The influence of BMI on decreasing career length is stronger, but BMI remains, at worst, only slightly associated with increased injury risk.

Perhaps BMI is only bad for players at specific positions. Long ago, Cabrera started off as an outfielder, but he’s played most of his career at 3B.

For third basemen, the hazard ratio is the same as it was in the pooled analysis. Cabrera is now moving over to first base, so let’s examine the effect of BMI there.

Again, the effect of BMI is somewhere between mild and nothing. Summarizing this section, BMI appears weakly (but inconsistently) associated with increased hazard ratio, such that bigger guys tend to have slightly shorter careers.

Conclusions
To a first approximation, BMI seems to have little or no effect on increasing injury probability or decreasing career length. In the language of science, what we have discovered is a set of negative results. Negative results make for an awkward interpretation, because they can arise for two distinct reasons: 1) there really is no effect of BMI on injury probability and career length, so fans of Cabrera and rotund players everywhere need not worry, OR 2) there is an effect, but the data or methods we’ve chosen to study it are inadequate to detect that effect.

I leave it to the reader to determine which of these two possibilities is most likely, but I’d also like to mention a few factors that bear on this distinction. One issue is that of the weight data being used. The estimates of player weight I obtained are self-reported and, for that reason, likely inaccurate. They are point estimates, and so whereas player weights change quite dramatically over the course of careers, the calculated BMI from the database does not vary. For example, Prince Fielder certainly weighed 270 at some time in his life, as the database reports, but I suspect that time is in the distant past.

Furthermore, because the heights and weights are self-reported, they are likely to be biased in a particular way, that is, toward lower weights than the players actually carry (especially for the larger players). This kind of bias wreaks havoc on statistical approaches of all kinds and works specifically against finding an effect of weight on injury probability or career length. For that reason, I suspect any signal of the effects of BMI is going to be severely damped.

A second factor that comes to mind is that there is abundant evidence that supports the notion of more weight placing more stress on the bones and ligaments. That evidence comes from the medical literature and so pertains to the general population, not elite, world-class athletes. Nevertheless, the core principle is simple and likely applicable: More weight is more mass, more mass being accelerated is more force, and more force is more likely to cause injury than less force.

This prior evidence suggests that BMI is likely to drive increased injury probability. Even though the medical literature wasn’t accounted for in the model specifically, we can integrate this prior knowledge into our interpretation of the results. My best guess is that there is an effect of BMI toward driving increased injury probability and shorter careers, but that the effect is small. One thing that negative results can tell you is that the effect of BMI, if it exists, is likely to be subtle, which surprises me (but note the data quality issues discussed above). If anything, this study suggests that weight isn’t likely to be a major concern for Cabrera or other large players, although perhaps in the aggregate, larger players are a slightly greater risk than smaller players. The Tigers ought to be able to bear this risk, given Miguel Cabrera’s lofty stature as a franchise icon and surefire Hall of Famer.

Robert Arthur is an author of Baseball Prospectus. Follow @No_Little_Plans
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