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THE BOOK--Playing The Percentages In Baseball

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Wednesday, May 26, 2010

The fallacy of “paying too much for out years”

Year    $perWAR    WAR    Salary$    DiscRate    Disc$    Flat$    DiscFlat$    Diff$
2010     $5.0      4.5      $22.5     100%     $22.5      $16.6      $16.6      $
2011     
$5.5      4.0      $22.0     95%     $20.9      $16.6      $15.8      $
2012     
$6.0      3.5      $21.0     90%     $19.0      $16.6      $15.0      $
2013     
$6.5      3.0      $19.5     86%     $16.7      $16.6      $14.2      $
2014     
$7.0      2.5      $17.5     81%     $14.3      $16.6      $13.5      $
2015     
$7.5      2.0      $15.0     77%     $11.6      $16.6      $12.8      $(2)
2016     $8.0      1.5      $12.0     74%     $8.8      $16.6      $12.2      $(5)
2017     $8.5      1.0      $8.5     70%     $5.9      $16.6      $11.6      $(8)
2018     $9.0      0.5      $4.5     66%     $3.0      $16.6      $11.0      $(12)
                                
Total     $6.3      22.5      $143     86%     $123      $149      $123      $(7)

Here what that means:


Year: year paid and performed
$perWAR: cost per win
WAR: number of wins
Salary$: salary if paid for performance
DiscRate: standard 5% discount rate (use whatever you want)
Disc$: Salary$ x DiscRate
Flat$: flat salary
DiscFlat$: Flat$ x DiscRate
Diff: difference between performance-based salary and flat salary

The flat salary was set so that the discounted flat salary equals the discounted performance-based salary.  That chart says this:

“It’s the same thing to pay someone 16.6MM$ per year for 9 years totalling 149MM$, as it is to pay someone a total of 143MM$, starting at 22.5MM$ the first year and ending at 4.5MM$ the last year”

So, there’s no such thing as “it’s really going to cost them down the road”.  They are SAVING 6MM$ the first year by paying him a lower flat salary than he deserves, and end up LOSING 12MM$ the last year by paying him too much.  But overall, the difference in the (discounted) salary is zero.  Therefore, you canNOT just look at the out-years in isolation.  You need to look at the salaries paid in context to the whole contract.

If that wasn’t clear, perhaps someone else can write that better.  I just don’t want to see any more articles about the out-years issue.

(6) Comments • 2010/05/27 • SabermetricsFinances
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