THE BOOK--Playing The Percentages In Baseball

I really enjoyed this. I was wondering the other day how the run values of things have changed with the lower run environment the other day. So, a more ‘flexible’ FIP equation would be something I’d like to see.

I wonder if Colin would implement a ‘flexible’ version at B-Pro.

Floating the 3.2 always struck me as “wrong” in that what’s actually changing must be the run values of k/bb/hr.  I assume you did it this way because re-calculating the coefficients is a lot of work and wouldn’t really make much difference.  Otherwise, yearly FIP equations would seem like the way to go.  I doubt anyone would freak out becuase they have to change 4 variables instead of 1 on their spreadsheet.  Although there’s probably an issue around the sample size required to calculate the linear weights that would require you to use some sort of rolling average, now that I think about it.

Same with PA (i.e. why not?).  It depends where you come down on simplicity v accuracy, I guess.

It wouldn’t be that difficult. Matt Klaassen has published year-by-year wOBA weights going back to 1871 based on a script that I think Tom published. The same could be done with FIP, no?

The year-by-year wOBA are on the right-side here:

http://www.tangotiger.net/bdb/lwts_woba_for_bdb.txt

I suppose that year-by-year FIP can be handled like year-by-year wOBA.  When I just want something quick, I rely on this for wOBA:
0.0: SO, other outs
0.7: BB, HB
0.9: 1B, ROE
1.3: 2B, 3B
2.0: HR

Keeps me happy and sane.  When it becomes important to calibrate and get more precision, then I have more work to do (hence, the above link).

So, yeah, I suppose I could sell FIP the same way.  There’s “Classic FIP” for those who just want something quick.  And after all, FIP itself was presented as a quick alternative to DIPS anyway.

A more robust FIP that would be more useful analytically might make sense too.

Bill James did “Tech Runs Created”, the more technical versions of Runs Created.  I suppose that’s the model here.

Now, what would a FIP equation look like for Mariano Rivera, or others in a very low run environment?

First we start here:
Runs above average =
-.17 SO
-.02 BIP
+.21 BB
+1.40 HR

That’s right around what Mo would give you.  Now we need runs per PA.  Figure about 36 batters per 9IP, and 2.5 runs per game, so .07 runs per PA.  So, continuing, we get:
Total Runs =
-.10 SO
+.05 BIP
+.28 BB
+1.47 HR

So we move .05 runs out, which gives us:
Total Runs =
-.15 * SO
+.00 * BIP
+.23 * BB
+1.42 * HR

+.05 * PA

We already said there are 36 PA, so:
Total Runs =
-.15 * SO
+.00 * BIP
+.23 * BB
+1.42 * HR
+1.80

With 9 IP per game, we get
Total Runs =
-.15*9 * SO/IP
+.00*9 * BIP/IP
+.23*9 * BB/IP
+1.42*9 * HR/IP
+1.80

Which is:
(
-1.35 * SO
+2.07 * BB
+12.9 * HR
) / IP
+ 1.80

And putting it on an ERA scale:
(
-1.2 * SO
+1.9 * BB
+11.9 * HR
) / IP
+ 1.66

Ok, so now we see an interesting pattern.  The coefficient for HR stays constant, while the other three floats, and is dependent on the run environment.

It should be easy enough, if a bit long in time, to come up with a run-environment based FIP after all is said and done.

By the way, the above two examples (average pitcher and Rivera) is the perfect example of where regression fails.

I laid out above a logical process as to how you can determine the coefficients for FIP.  And, as you can see, they are not only much different, but the changes are not even across the board (the HR is static).

Regression would never have picked this up.  Hence, the reason that regression is a first step, not a last step.

the logic is circular, isn’t it?  Mariano’s great, therefore he gets his own FIP equation that’s pretty certain to confirm his greatness.  Maybe I’m confused or not following…

You start with BaseRuns or a Markov chain.  That confirms Mariano’s greatness (his runs allowed).  Then, you find the marginal impact of adding or removing a single, walk, HR, K, out.  That gives you the run value of each event.

Then you try to turn that into a FIP equation.

Now, if you do all that, you don’t need to figure out his FIP because you did all the work already.

Ah.  It’s FIP’.  Getting at the non-linearity of the coefficients. 

Analogous to the squared terms in a regression, isn’t it?  For example, you’d find out that HR^2 had no explanatory power, and you’d throw that term out.

Basically, the coefficients are going to be a multiple of runs per game.

As a for instance, instead of “3.2”, maybe it’s “runs per game * 0.67”.

Maybe instead of “3” for the walk, it’s:
(runs per game + 1) * 0.5

And the HR would stick at 12.

The problem of course is that you need runs per game.  You can’t use the league number, because each pitcher is his own universe.  And since we don’t know what a pitcher’s runs per game actually is, then you’ve got circular reasoning. 

Hence, the need to establish his runs per game another way (simulator, BaseRuns, or Markov). 

But, if you go to the trouble of doing all that, then you don’t need FIP to begin with!

Sooooo… the idea is to try to infer the runs per game looking only at the three components.  And for that, we need to figure out some sort of shortcut method.

Tango, have you ever checked to see if 13/3/-2.5 or even 13/3/-3 correlates better with RA than does 13/3/-2 ?

I’ve done several of those tests.  It all depends on the sample of my pitchers.  As noted, since the coefficients depend on the run environment, then how I select my pitchers will determine the coefficients.  I ran one a few weeks ago where the coefficient of the HR was 11.

I guess I meant all pitchers since the offensive era in 1993

Right, but even so.  Don’t forget that a pitcher provides his own run environment as well.  If I were to separate the 1993-2010 pitchers between those with high BaseRuns and low BaseRuns, I’m going to get two different FIP equations (for reasons elaborated at the top of this thread).

That’s why I say that it all depends on which pitchers are in my sample.  It’s not helpful to say “average”, and then we end up talking about Clemens+RJ+Maddux+Pedro.

Bumping for fun.