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Statistically Significant: FIP

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Update from Susan Slusser:

Brett Anderson to go on dl with forearm strain. Landon Powell called up and in the lineup.

First, an introduction. This is the first in a series of statistics-related posts that will attempt to accomplish two things: be an introduction to a statistic for the completely lost, and give a more advanced in-depth mathematical look for those that are already comfortable with it. I've seen a lot of misconceptions about FIP, so why not start there?

The Basics

FIP, Fielding Independent Pitching, is a statistic falls into a class of baseball statistics called "ERA estimators". These statistics attempt to refine ERA and give a number that that shows how a pitcher actually pitched, rather than an ERA figure that is subject to all sorts of luck and variation in terms of bloop singles, defensive flubs, and screaming liners directly into gloves. Essentially every study that has been done has shown that ERA estimators like FIP, tRA, and SIERA are able to predict next year's ERA for any pitcher far better than ERA can.

So what does FIP do? I'll reference myself and quote the FIP definition in our ANcillary Terms:

FIP (Fielding Independent Pitching): A statistic that studies a pitcher's performance by only using the events that are directly under his control. Only home runs, walks, strikeouts, and hit by pitches are used in the calculation. The statistic is scaled to resemble ERA.

A little more than ten years ago, Voros McCracken shocked the baseball world and showed that pitchers have very little control over balls hit into play. (He showed this by demonstrating that while pitchers with high strikeouts tended to have lots of strikeouts the following year, pitchers that had low batting averages on balls in play (BABIP) did not experience very much carryover the next season.) In this spirit, Tom Tango created FIP, which is calculated using only those events that the pitcher directly controls. The equation is as follows.


What do you get with FIP? An ERA-like number that more closely resembles a pitcher's actual performance. As an example, last year, Florida Marlins pitcher Ricky Nolasco had a terrible first half. Before the All-Star Game, he only had two starts where he didn't give up a run. His ERA through May? 9.07. Rumors flew about Nolasco needing adjustment and fixing in AAA New Orleans. His FIP during the same time was a far more friendly 4.80, indicating that his early ERA was mostly a fluke. Nolasco went on after May and turned in a 3.82 ERA with 158 strikeouts in 141.1 innings.

FIP is a great tool for seeing through luck-based ERA variation. It's not an "ultimate stat" for pitching, but it's a whole lot better than what was around before it.

The Math

I apologize for the revision that I'm about to do, but saying that FIP only considers home runs, walks, and strikeouts isn't exactly true. It's more accurate to say that FIP considers HRs, BBs, Ks, and balls put into play. Every ball put into play is considered the same, as far as FIP is concerned. FIP doesn't consider them non-entities, it just lumps them all together. Why? To explain, I'll have to derive the formula (don't worry, it's not too difficult).

It's been used in a million different applications (like the Fangraphs WPA game graphs), but assigning average run values to events opened up hundreds of new avenues for sabermetrics analysis. The run vales pertinent here are in the table below. Click for a bigger version.


These values give the average amount of runs scored from the point of the event occurring to the end of the inning (Tango calculated these averages from every game played from 1974 to 1990). If we take every event resulting from a ball hit in play and average them out with respect to how often they occur, the average ball in play results in a net loss of -0.04 runs. To simplify the formula, Tom Tango added +0.04 to each run value, which algebraically excised balls in play. Simply multiply each modified run value by 9 innings, and you have the coefficients used in FIP (13 for HR, 3 for BB, and 2 for K). FIP doesn't actually ignore balls hit into play. Even though they don't appear in the final formula, run values for balls hit in play live on in the coefficients.

The A's are in St. Petersburg today as Ben Sheets opposes Wade Davis and the Tampa Bay Rays. First pitch is at 4:10 PM, Pacific Time.


Odds and Ends

  • Since the creation of FIP, several other ERA estimators have popped up, including xFIP (FIP with a normalized HR/FB rate), tRA (like FIP, but rather than lumping all balls in play together, tRA separates them into GB, LD, and FB), and SIERA (way too long and complicated to explain here, but you can click here or here for more).
  • For more information on FIP, this is a great, great article.
  • The 3.20 in the formula, by the way, is just a constant that adjusts FIP to bring it to ERA scaling. This is done so that the average FIP is the same as the average ERA. The constant changes from year to year, but 3.20 is a good enough approximation.
  • In some versions of FIP, intentional walks are subtracted and hit by pitches are added to the BB term in the formula. The end result tends to be around the same in most cases.