March 25, 2014

Moonshot

Attrition Over Time

by Robert Arthur

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Of the four major sports that permeate American culture (football, basketball, hockey, and the best, baseball), none has existed in its current form for as long. Yet despite its relative stasis, baseball has evolved. Although the basic rules of the game have remained the same, it is not isolated from the broader currents of time and technology. One of those currents has been medicine’s ceaseless march toward the curing of disease and the extension of healthy life.

We’ve seen this current manifest in baseball via the introduction of new treatments and surgeries. Only 30 years ago, the notion of Bartolo Colon going abroad to get stem cell injections to heal his arm would have been science fiction. One year ago, this treatment was likely behind the success of a 40-year-old pitcher with a 92 mph fastball and a 2.65 ERA.

More broadly, Colon’s medical miracle raises the question of whether medicine is prolonging careers and if so, how. Technically and statistically, studying career length is not trivial. But, as before, I’ll use a Cox Proportional Hazards model, borrowed from epidemiology, to understand how career length has varied over baseball’s long history.

The Marvel of Modern Medicine
I’ll draw once again on Lahman’s database, from which I use only the time period 1910-1989. I compute each player’s year as the first year in which he appeared in an MLB game (his debut), and his dominant position as the one at which he fielded the most innings.

As a point of departure, I ask the simplest question possible: Are careers getting longer or shorter over time?

The model’s answer is that careers are generally getting longer, to a significant degree (the hazard ratio represents the risk of a career ending, wherein numbers less than one represent less risk, and numbers greater than one, more risk). The hazard ratio suggests that, in this case, the risk is going down about .1 percent per year, or about 1 percent per decade. In both cases, although these gains are slight over any period of a few years, they increase rapidly when considering the differences as they accrue between, say, 1925 and 1965.

As an example of career length increasing over time, consider these survival curves, which chart the percentage of players remaining in the league at a given point in time for three different decades: the 1920s, 1950s, and 1980s.

Generally, the red curve (1920s) is below the purple (1950s), which is below the blue (1980s), although things get a bit squirrely toward the very long careers (where sample size is much smaller).

Without entreating you to learn too much #GoryMath, there’s another approach that could be of use, which is to estimate the hazard ratio on a decade-by-decade basis. Whereas the former approach summarized the overall trend (toward longer careers), this method allows individual decades to vary independently from each other. I graph it as follows.

While the dominant trend is visible—toward a decreasing hazard ratio through time—there are notable and interesting sub-narratives. For instance, consider the huge spike in the 1940s, some of which seems to echo into the ’50s. I would posit that this increased hazard ratio corresponds to World War II, which imposed a hazard of an altogether different sort upon many MLB players of that time. A similar spike may be at work in the decade 1910-1919.

Many of the longest career lengths are found in players who debuted in the 1960s. Curiously, after the 1960s, the hazard ratio begins a gradual upward acceleration. I can only speculate as to why that is, but speculate I shall: From the 1970s onward, the rise of free agency changed the economic calculus of the game, especially from the player’s perspective. Whereas before players were often forced to work jobs after baseball, with the increased compensation afforded to players in free agency, it became worthwhile to sacrifice long-term health for even a relatively short major-league career.

Strength training started in earnest. Steroids began their insidious creep into the game, with pernicious and still somewhat unknown long-term effects. Many MLB players began to push to their physiological limits, perhaps sometimes to the detriment of their long-term survival in the league. But, in the absence of definitive data on these potential factors, these thoughts will have to remain speculation.

Trends by Position
Another angle on the question of survival curves through time is to examine the effect on a per-position basis. It may be the case that while players at some positions are lasting longer in the major leagues, players at other positions are actually decaying more rapidly.

In the above table, I am displaying the effect of time on the aging pattern of each position, calculated separately. Overall, the hazard ratio is pretty consistent for all the different positions. Third basemen, for whatever reason (if indeed there is a reason), show the strongest decrease in risk over time. While technically third basemen are the only position to show a significant decrease in hazard ratio, all positions except catcher do show decreases. For this reason, when the positions are pooled, it makes sense that the overall trend would be one of decreasing risk over time.

I want to focus now on pitchers, whose shorter career lengths relative to position players I noted in the last piece on this subject. Pitchers have benefited from one of the most profound shifts in sports medicine in recent history: Tommy John surgery (rest in piece, Frank Jobe). The surgery can significantly prolong the careers of pitchers who suffer injuries to the ulnar collateral ligament, making what was a formerly career-ending injury only a major inconvenience (in most cases).

It stands to reason that Tommy John surgery itself may have altered the career lengths of pitchers. I examined this possibility by considering whether pitcher career length had increased post-1974, when the first Tommy John was performed. This method is inexact, but sufficient for a first look.

In fact, pitchers since 1974 have a five percent reduced risk of their career ending at any given point. Even though this difference is substantial, it is not significant because of how recent 1974 is (p=.248). With that said, I am inclined to attribute some of the observed decrease to the advent of the surgery. As time goes on, and the players from the ’90s end their careers, the impact of Tommy John ought to become more clear.

Conclusions
Examining the vast scope of baseball players from 1910-1990 shows that career lengths have increased overall. However, the increase has been uneven and subject to variation, especially in times of war. In the recent past, the hazard ratio may have been increasing (and career length decreasing), for reasons unknown.

Dividing the dataset by each player’s dominant position, I find that almost all positions are growing healthier over time, and third basemen especially so. For pitchers, the invention of Tommy John surgery by Dr. Frank Jobe coincides with a decrease in the hazard ratio, but causation is difficult to infer without a more thorough analysis using historical data on Tommy John surgeries.

There are still more factors at work in determining career length, many of which have yet to be examined. Conspicuously absent so far in my analysis is any variable corresponding to the quality of each player and the league as a whole, and such a variable is undoubtedly the dominant determinant of whether and how long a player sticks around. Beyond quality, there exist more subtle influences on career length, such as the physical shape of a player. I’ll hope to tackle these and other factors in future articles in this vein.

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