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April 23, 2013

BP Unfiltered

Should Players Get Preventative Appendectomies?

by Russell A. Carleton

On Today's episode of Effectively Wild, Ben Lindbergh reported on the unfortunate case of Jason Heyward, who underwent an appendectomy on Monday night in Denver.  Certainly, all of us here at Baseball Prospectus wish the J-Hey Kid a quick recovery, but maybe more could have been done to prevent Heyward from his DL trip.  Ben noted that appendix is a non-essential organ and people get along just fine without their appendix.  Why wouldn't a player just have it out during the off-season before anything happened?  Perhaps in November, teams should send each of their players to have an outpatient appendectomy?  Let's do a little cost-benefit analysis.

Warning! Gory Mathematical (and Anatomical) Details Ahead!
The average annual incidence of appendicitis in the United States is roughly 1 in 1,000.  That means, each year, roughly one in a thousand people will need to have their appendix out.  Men have higher rates, and rates are higher in the summer.  So, assuming 1,000 MLB players (including the active roster and the fringe/floater guys), we would expect one of them to need an appendectomy each year (again, on average).  We're also making the assumption that all cases of appendicitis happen during the baseball season, when it will impact a player's productivity.

One estimate pinned the cost of an intact laproscopic appendectomy (the appendix had not burst) at $7,800.  For $7,800, the team gets an insurance policy against a 1 in 1>,000 chance that they will have to foot the bill for a "real" appendectomy, both in terms of the surgical costs (although that would likely be covered by insurance) and the loss in productivity, which will probably be consistent with a 15-day DL trip (call that 1/10th of the season?), and during which he will be replaced by a replacement level player.  The team could instead divert that $7,800 to buying a slightly better player in free agency.  If a win above replacement costs $5 million, then to justify the cost of the operation, a team would need to believe that it will get an expected savings of more than .00156 of a win for the purchase to make sense.  Because the chances are 1 in 1000 that the player will need an appendectomy this year, the team would have to believe that the cost in lost productivity of those two weeks would be 1.56 wins.  That translates into a 15 win (seasonal) player.  I don't think such a player exists.
However, the team would get multiple years worth of benefits from the surgery (it's not like you have to renew the surgery each year).  If a team asked a rookie to get a preventative appendectomy, and the team retains control over the player for 6 years, then the team could amortize that expectation over those 6 years.  The break-even point for that player would be that an absence of 2 weeks would cost the team 0.26 wins.  So, the team would have to believe that this rookie would return an average of 2.5 WARP per year during his years of team control.  That's not every player in the system, but those guys are out there.  So, yes.  A preventative appendectomy for a prospect who is expected to be a regular first-division starter makes sense from a financial standpoint.
Or would it?  Let's revisit our assumption that all cases of appendicitis would happen during the season, since the baseball season only takes up 6 months of the year (7, if you're lucky), teams would only realize half the benefit.  A player could have appendicitis in January, and it wouldn't matter to the team.  Suddenly, the calculations change.  Since, teams would only reap the benefit of "scheduling" the appendectomy half the time, the risk of loss must be twice as big.  Even accounting for the fact that rates of appendicitis are higher in the summer, this means that a team has to account for the fact that it's a 1 in 1000 chance that it would be their player who needed emergency surgery and a slightly more than half (call it 2 in 3 once we adjust for seasonal rates?) chance that it would be at a time when it affected productivity.
Now, suddenly, that rookie would need to be expected to put up 3.7 WARP per year from his rookie to his 6th season. Now, we're looking at guys who are in the "pretty good/sometimes All-Star" and up range.
Then there's the issue of complications.  Laproscopic appendectomy has a complication rate of about 18% (1 in about 6).  That will drive up costs.  A player who gets a "natural" case of appendicitis, such as Heyward did, and has an appendectomy may also have complications, but those would be covered under medical insurance.  I wonder if complications from the elective procedure would also be.  There's also the possibility that the player might miss extra time that could have been put toward training and/or even actual games due to these complications.  The net result is that the expected return from the player in terms of WARP that would be needed to justify the procedure continues to go up.  We're already looking at a level of player who projects to be a really good to All-Star level player, on average, for the first six years of his career.  There just aren't a lot of those guys around.
Then, there's the matter of the blame game.  Even if you had a prospect for whom -- after you ran all the numbers -- it made sense to denude him of his appendix, why did the team ask him to undergo a surgery that he did not need when they knew that there might be complications (and at a 1 in 6 rate!) when the chances that it would save a bout with appendicitis was only 1 in 1000 (and when it happens, you can throw up your hands and proclaim "How were we supposed to know that would happen?")  What kind of idiots do you have working here?  (The finest in New York.)
Oh yeah, and would the player in question actually... want this done?

Yes, now that we know that Heyward was the 1 in 1000 unlucky enough to have to undergo an appendectomy, it's easy to look back and wonder whether we should have done something, but you can't prevent every risk, and even for the ones that you can prevent, it doesn't always make sense to do so.

Russell A. Carleton is an author of Baseball Prospectus. 
Click here to see Russell's other articles. You can contact Russell by clicking here

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