THE BOOK--Playing The Percentages In Baseball

Thursday, October 25, 2007

Paying for performance

Studes is back at it again this year, with the Net Win Shares Value.

As much as I don’t like Win Shares, this is a good application of it.  It’s aggregated at the group level, so all the problems I have with it, cancel out.  Well, not all.  Let’s take a look at the data:

First up, in 2007, there were 2443 win shares above bench, which is 814.3 wins above bench.  What does this imply?  In 2007, every team played 162 games, plus the one-game “playoff”.  The total number of team games played was 4862.  Therefore, the number of wins above bench, per game, is +.1675, which sets the bench level at .3325.  That’s a very reasonable number.

A sanity check: let’s consider regular players to be .550, with 75% of the playing time.  The rest of the 25% of the playing time would be made up of .350 players. 

The total salaries paid, above minimum, was 2.175 billion$.  That sets the salary above minimum per wins above bench at 2.67 million$ per win.  This does imply that the bench player (the .3325 win% player) is worth the minimum.  I do have a small problem with that.  I would prefer setting the minimum salary at a .300 win% level, implying 972.4 wins above baseline, and 2.24 million$ per win.  Otherwise, the implication is that the average bench player gets paid the minimum. 

What if instead we said the average bench player makes 750,000$? That means that the total salaries paid above this level will be 2.175 billion minus 370,000 times 1000 or so players, or 1.805 billion$ above “reasonable bench price”.  And 1.805 billion$ above the bench price divided by the 814.3 wins above the bench level gives us 2.22 million$ per win.  And this is consistent with my 2.24.

Now, how did I pick out that the average bench player would make 750,000?  It was a reasonable guess.  I set the replacement level so average is 972.4 wins above that. Studes is at 814.3 wins above bench.  The implication is that the bench level is 158 wins above replacement. The minimum salary is 380,000$.  If we presume 1000 players earning “full time” pay, and with 2.24 million$ per win, then 158 wins above replacement times 2.24 million$ per win divided by 1000 players plus 380,000$ is $734,000.

This is why I think we should stick with replacement level of .300 being worth 0 marginal dollars.  It all works out real nice.

So, when looking at studes’ cost per win above bench, and you want to convert it to cost per win above replacement, subtract his number by 0.43MM (2.67 minus 2.24).

Anyway, let’s continue back to studes’ article.  Free agents earned 1.764 MM per win share above bench, which is $5.3MM per win above bench, which itself is 21% higher than last year.  Whoah.  Teams are spending like crazy.  That number translates to $4.86MM per win.  Similarly, the arbitration players are paid $2.09MM per win, and the slave players are paid basically nothing above replacement. As you can see, arbitration players (2.1MM) are paid close to the league average(2.2MM).  The free agents are earning their money on the backs of slaves. 

Next up is the position splits.  I use the following replacement levels: .380 for nonpitchers, and .410 for pitchers.  This implies that nonpitchers gets +.12 wins per game while pitchers get +.09 wins per game.  The pitchers get 42.9% of the wins.  Win Shares above Bench gives the pitchers 40.7% of the wins.  Pitchers are being slightly shortchanged according to me.  However, if you believe the 40.7% number as accurate, then this would imply replacement levels of .375 for nonpitchers and .415 for pitchers.  Certainly these numbers are close enough that you can argue either way, and I won’t make an issue of it.

The split between starters and relievers.  The replacement level is .380 for starters and .470 for relievers.  The average starter is around .485 and the average releiver is .530, making the average starter +.105 wins above bench per game, and the average reliever as +.060 wins above bench.  However, starters pitch 65% of the games, so the +.105 becomes +.068 and the +.060 becomes +.021.  So those values (.068, .021) implies that starters should generate 76% of the pitching value.  The WSAB gives only 67% of the pitching value to starters.  This can’t be right.  Why?  If starters and relievers were in fact equal, then simply their workloads would give a 2:1 split in favor of the starters.  But starters are in fact better than relievers.  The WSAB needs to be modified to turn the 67% into something closer to 75%.  I suspect that starters are not being fairly valued, and therefore, they need a lower bench line to bring them inline with the relievers.