THE BOOK--Playing The Percentages In Baseball

Monday, September 13, 2010

How much value is going deep to your team?

Suppose you have a great pitcher, someone like CC, who gives up 3.78 runs per game, and starts 35 games, and pitches 6.8 innings per start (that’s 100 runs allowed in 238 IP).

Suppose he goes away, and you can’t spend any more money.  So, you make due with what you have.  His 35 starts are cobbled together at the replacement level of 6.00 runs per game, with only 4.8 innings per start.  That’s 168 innings and 112 runs allowed.

You still need 70 innings to find somewhere in relief.  Because of roster limits, and you don’t want to bring up/down too many pitchers, you start to tax your current relief corps.

Your current relief corps, with the great starter in the rotation, threw 490 innings at 4.35 runs per game (237 runs allowed).  However, without the great starter, they pitch more and are less effective.  So, they need to pitch 70 more innings to make up for the loss of the starter, and instead of giving up 4.35 runs per game, they give up 4.55 runs per game.  So, in the 560 innings at 4.55 runs per game, they give up 283 runs, instead of 237.

So, let’s tally it.  The 168 starter innings by the ragtag team gives up 112 runs, and the 70 extra relief innings, including the extra runs allowed by the current relievers, yields 46 more runs in relief (283-237).  All in all, that’s 238 innings to makup, and a total runs of 158 runs allowed.

That becomes the replacement level.  And 158 runs in 238 innings is 5.97 runs per game.

Now, waitaminute.  The starter replacement level is 6.00 runs per game.  How did we end up at the same place?

Well, let’s break it down a bit.  As we noted, only 168 of the 238 innings were being replaced by pitchers in a role of starters.  That left 70 innings to be replaceed by pitchers in role of relievers.  But, it’s alot easier to pitch in relief than to start.  A pitcher, as a starter giving up 6 runs per game will only give up 5 runs per game as a reliever.

Well, sh!t, you may be saying, let’s replace ALL 238 innings by relievers.  Sure, you can try that, but you’d be taxing your bullpen like crazy.  As it stands, while we gave 70 innings to relievers giving up 5 runs per game, we also taxed the rest of the bullpen who gave up about 0.20 runs per game more than they would have otherwise give up.  Where did I get that 0.20?  Quite frankly, I made it up to make sure I got the result I wanted.

Is 0.20 reasonable?  I don’t know, I guess.  You can argue for more (or less) if you want.  But, I’ve shown a path using reasonable assumptions, to get at exactly at the same point that a simple standard replacement-level model would suggest: 6.00 runs per game as replacement level.  You want to come up with something different, then roll up your sleeves, and show us your model.