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March 14, 2014

Attrition By Position

How Long Do Players at Each Position Last?

by Robert Arthur


Like many baseball fans, I was taken aback by Derek Jeter’s declaration of his impending retirement. Together with Roy Halladay’s somewhat quieter conference and Mariano Rivera’s farewell tour, a trio of players I admired tremendously will soon be out of baseball. It’s a bittersweet fact of the big leagues that just as one generation of transcendent superstars is born (e.g. Mike Trout, Bryce Harper), another trails off gently into retirement.

The question of career length has more than emotional import within the business of baseball. Owing to the advanced age at which many players are hitting the market, for many free agent contracts there is substantial risk that a player’s useful career will end before his deal does. Even when a player does remain employed late into his 30s, between injuries and the tireless decline of aging, the terminal years of his career can be unproductive.

We usually view the question of when a given player’s career will end as largely unforeseeable. One twisted swing of the bat or one wrong pitch can cause catastrophic, career-destroying damage. After Halladay’s magnificent 2011 (arguably the best season of his illustrious career), and his relatively healthy history to that point, who could have foreseen that a string of seemingly innocuous strains would bring about the end of his career?

Because of the randomness of injuries and the overarching shadow of survivor bias, studying career length is a statistically thorny issue. To overcome these obstacles, I’ll employ a special type of regression model called a Cox Proportional Hazards Model. This kind of model was built specifically to estimate how survival varies as a function of different medical treatments; it’s the kind of tool medical researchers use to understand whether patients on a drug live longer than those given a placebo. The analysis is therefore somewhat macabre, if also (and more importantly) technically accurate.

Indicators and Myths
The first factor I wanted to investigate was how career lengths might differ depending on the dominant position a player fielded. I was inspired to look into this by the collection of heuristics on the subject I have seen repeated in baseball circles: that second basemen and catchers fall off in their early 30s, and that first basemen last longer.

Some methodology, should you be interested or wish to confirm my results: I used Sean Lahman’s player database to extract career lengths for more than 10,000 players, and I limited my sample to careers beginning post-1900. I linked these records to fielding data and extracted the position at which a player had logged the most innings as his dominant position. Then I fit the survival model.

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Related Content:  Aging,  Attrition,  Career Length

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