tRA and ROA, a new pitching metric.

ED 1/5/08: It's been brought to my attention that Ducksnorts has just linked to this diary. Since comments on it are now closed, if you're reading this and have any questions, drop me an email: gym21(at)


We like putting run values on performance. By converting what a player does on the field to one universal currency, we can measure batting against fielding against pitching, or convert an entire team's roster into projected wins. Fantastic.

However, we don't really have a widely available coherent metric for pitchers which tells us how good a pitcher is, independent of his home park and defence (and if anyone's tempted to say 'ERA' here, read Dave Cameron’s article on pitcher evaluation first). FIP and xFIP are really the most commonly used general pitching stats we have, and they're not really good enough, as they only look at 3 possible outcomes of an at-bat: K, BB, HR.

There is therefore a distinct motivation for construction of a metric which takes into account every action a pitcher is responsible for, and turns those numbers into runs, based around a highly logical and transparent mathematical framework.

Theory and Background

There are essentially only eight possibilities for the state of a baseball at the instant the contest between batter and pitcher has resolved itself. The batter may walk, strike out, or be hit by a pitch. He may also hit a line drive, a ground ball, an outfield fly, a popup, or a home run. Others, such as bunts and intentional walks, are essentially subsets of the more important outcomes.

The past few years have seen individual-play run values enter the statistical field. By making use of a combination of Dave Studenmund's 'Batted Balls Redux' in the 2007 Hardball Times Annual and Tom Tango's run values we can assemble a table of run values for each of the eight outcomes mentioned above:

If these are combined with the frequency with which a pitcher gives up each outcome (HR is modified according to park) and multiplied by total batters faced (TBF), we can determine how many runs that pitcher would have given up in a neutral park in front of an average defence. From there it is a simple exercise to convert these numbers into a R/9 analogue or runs saved/lost above average (called tRA and ROA respectively).

Another point worth considering is regression towards average. Certain pitching stats are known to fluctuate quite wildly from year to year, and in order to correct for this every outcome is regressed towards the mean based on their year-by-year r values and the total batters that a pitcher has faced on the season, with less regression applied the larger the sample size. The actual values which regression is applied to are as follows:

K%, BB%, HBP%, GB per ball in play%, IFF per ball in air%, LD per ball in air%, and HR per FB%

The order is extremely important, as influencing GB% will have an effect on LD% later, and so on, sometimes causing regression away from the mean in unusual situations.

Once a pitcher’s line has been regressed, the same algorithms used to generate tRA and ROA are applied again to give tRA* and ROA*. It is hoped, although not yet tested, that tRA* will prove superior in predicting future R/9 than xFIP is at ERA.


HR correction: HR/FB is subjected to a park effect correction. Park factors specifically for home runs were taken from THT (Thanks, Matthew!)

tRA: Pitcher runs per batter faced, multiplied by TBF, divided by innings pitched (IP), then multiplied by 9. Analogous to runs given up per 9 innings.

ROA: Pitcher runs per batter faced minus league average runs per batter faced, multiplied by TBF. Analogous to runs created above average.

xRuns: Pitcher runs per batter faced multiplied by TBF, then corrected for park (park run values taken from averaging 3 years of data from Baseball Prospectus 2007).

All data were gathered by hand from fangraphs. Averages from different leagues and different classes (i.e. starter and reliever) were kept separately for ROA and regression purposes. A starter was defined as pitcher who had started in 50% or more of their appearances; a reliever was anyone who had thrown a pitch in major league baseball who didn’t get classed as a starter


Run values will be appropriate for both starting pitchers and relievers in each league.

Errors caused by failure to include intentional walks and bunts are unimportant compared to the level of accuracy enjoyed over metrics such as xFIP and ERA.


The following links lead to spreadsheets with results from every pitcher in the 2007 season (ED: they're slightly out of date. Contact me if you want the newest versions):

    AL Starters
    AL Relievers
    NL Starters
    NL Relievers


I imagine this is what you all want to see at this point. Top ten and bottom five in ROA from all four categories…


Thanks to everyone who helped me with this, but especially plunkage and DCMariner, who gathered most of the NL data for me. Cheers, guys.

Other stuff

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