THE BOOK--Playing The Percentages In Baseball

Monday, February 14, 2011

Reader mail of the day: Chain of Fools

Here is what I don’t get about WAR. Suppose I have two catchers. My starter is +5 wins/600 PA and my backup is +1 win/600pa. I plan on my starter getting 600 PAs and my backup 100. My expected value from the catcher position is thus 5.17.

Now, if my starting catcher was to be hurt before the year, I would now have (to make it consistent) 600 PAs of my backup catcher, and 100 of my replacement level catcher (we’ll call him +0wins/600pa. So what do I have, I have a catcher position worth 1 win.

So, by losing my starting catcher (valued at +5 wins), I actually lose 4.17 wins.

Do you follow, if his true value over replacement was 5 wins, I would lose 5 wins by replacing him, but in fact, I don’t, because the back up (by way of being on the 25 man roster instead of being a freely available player) is actually better than replacement level. So, I guess the question is, should WAR be adjusted to accommodate that most players aren’t replaced by a minor leaguer, but rather a guy off of the bench?

Suppose your first catcher is +3 wins above average per 600 PA, and the second catcher is -1 wins relative to average per 600 PA.  You give the first guy 600 PA and the second one 100 PA and so this team is +3 -1/6 = +2.83 wins above average.

Now, your main guy goes down, and the backup at -2 wins relative to average per 600 PA comes up.  Now you’ve got -1 -2/6 = -1.33 wins relative to average.

Instead, your backup goes down, and his backup takes his place.  We have +3 -2/6 = +2.67 wins above average.

What do we have?  If the main guy goes down, the team goes from +2.83 to -1.33, or a change of 4.17 wins.
If the backup goes down, the team goes from +2.83 to 2.67 or a change of 0.17 wins.

How do we want to represent that first catcher?  +3 wins per 600 PA above average?  +4.17 wins above the chained replacement?  +5 wins per 600 PA above the “minor league callup”?  How do we want to represent his backup (-1 relative to average, +0.17 relative to chained replacement, +1 wins above minor league callup) ?  And what of the callup?

Don’t use replacement level unless you know what you are doing with regards to handling the playing time issue and roster management.

What you need is performance relative to average.  Use that.  But at some point, you are going to need playing time.  The moment you need playing time, you need to stop and figure out how things work.  You’re going to end up with some sort of replacement-level model.

What replacement level gives us is a very useful shortcut.  It gets us to where we want to go.  It sets the lower boundaries to match the salary of the players (league minimum).  It lets us do comparisons simply and quickly.

But we can “break” replacement-level by creating various scenarios.  That just means you haven’t appreciated replacement level well-enough.

In the above example, we can call our player +4.17 wins per 600 PA above the chained replacement.  But the chained replacement is not going to cost you the league minimum!  We want to set it so that the zero point is the league minimum.