September 7, 2012; New York, NY, USA; Atlanta Braves right fielder Jason Heyward (22) hits a solo home run during the fourth inning of a game against the New York Mets at Citi Field. Mandatory Credit: Brad Penner-USA TODAY Sports

Determining the Value of Hitting


This is the first of hopefully many sabermetric pieces, outlining the pros and cons of many of the concepts widely debated in recent years.  This first piece outlines the hitting component of WAR, the most complex and important part of the calculation.

Hitting value is also one of the most agreed-upon concepts in sabermetric realms.  Both FanGraphs and Baseball-Reference use a linear-weights method called wOBA, compiled from actual results, to determine run values for events.  Walks are less valuable than singles, which makes sense considering the other baserunners can’t move up more than one base on a walk.  When compared to OPS, wOBA also values extra base hits a bit less.  A home run (5.000 OPS)is 2.5 times more valuable than a single (2.000) when using OPS, but only 2.3 times more with wOBA (2.08 vs. 0.89).  The actual weights change year-to-year, usually by very little, to adjust to the style of play in the league.  The exact ratios aren’t what’s important; it’s the concept of the additional baserunners affecting the outcome.

B-R includes more factors than FanGraphs, which will never hurt the model.  Outs have zero value on FG, but B-R separates K’s from batted outs, with the K’s rating around -0.007 and non-K’s around +0.01.  It’s doesn’t seem like much, but even the best hitters make outs 60% of their PAs, which adds up throughout a full season.  The rates were much more significant in the early days of baseball when errors were so prevalent.  They also differentiate singles as infield or outfield, since runners have much more opportunity to take extra bases on hits into the outfield, creating a difference of about .1 run.  They also include ROEs, which are slightly more valuable than OF singles.

When determining the run values, context is not included.  A hit in a clutch situation will not have a higher run value than the same hit in a blowout.  This creates less of a “true” value, but clutch ability has been generally categorized as a product of noise, not individual talent, so it’s better for predictive purposes.  Intentional walks do not have any value in the formula, but those plate appearances are removed from the wOBA calculation, then added back in for the upcoming figure.

(There is a formula in this paragraph.  I’m only putting it in here to show what factors are used in determining run totals.)  The next step is to turn wOBA into a run value, relative to league average, called wRAA (weighted Runs Above Average).  The formula is: ((wOBA – lg avg wOBA)/wOBA “scale”) * PA.  The league-average wOBA excludes pitchers and is park-adjusted, so players aren’t over/underrated due to their home park.  This season, .320 was the MLB average, but “average” in Colorado was .340 and “average” in San Diego was around .310.  The scale just makes the league wOBA match the league OBP for that season.

The park factors used are multi-year run-scoring adjustments.  Right/left factors are not used, since we are looking at value to the team, not true talent.  For example, if a righty and lefty each have a .350 wOBA in Boston, the lefty is likely the better hitter, but each is of the same value.  There can be some discrepancies with the park factors, but they are usually within a couple points of each other.  wRC+ is the metric used to compare hitters across the league, similar to OPS, but this does not have an effect on the run value.

For the Braves last season, park factors did cause some difference in the run totals.  B-R had Turner Field has a slight hitter’s park, while FanGraphs had the park at neutral.  This is part of the reason that the team totals differ by 50 runs, -28 at FanGraphs and -78 at B-R.  The strikeouts also explain some of the B-R deficit, as a team K rate of 22% was one of the five highest in the league.  B-R also has a separate figure for double plays, with Michael Bourn and Jason Heyward at +3 runs and the other regulars at -1.  As you can see, it’s not a big factor, but a few runs here and there can add up.

FG RAA B-R RAA
Michael Bourn 6.6 0
Martin Prado 17 14
Jason Heyward 18.9 14
Dan Uggla 5.6 0
Freddie Freeman 13.9 8
Brian McCann -5.5 -11
Chipper Jones 16.3 15

Chipper’s difference is the smallest, since he was a low-K guy who had one infield hit and had one of the higher ROE rates.  Bourn, on the other hand, was the exact opposite, hence the bigger margin.  B-R seems to have the better methodology, but the park factor seems off.  Turner Field has always been more of a pitcher’s park, so one freak season may be throwing off the factors.

There are a lot of parts that go into this single number, but it is the most important number.  There are limitations to wRAA, even with the B-R version.  However, it does a lot better job than batting average and RBI.  If anyone has any questions about how the numbers are derived or want some mathematical explanations, leave a comment and I’ll do my best to answer them.

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  • fireboss

    Just an observation that the formula is probably too down in the weeds for folks who just want to understand an outline of where it comes from. A link to a definition or at least a warning like the “Warning boring mathematical formula ahead” before you start. The formula begs questions not so easy to answer for folks who have trouble with a checkbook,

    Well, off to the hospital. Have to get the rotator cuff fixed if I’m going to pitch this season. . .that’s pitch trash into the recycle bin of course :)

    • Lee Trocinski

      Thanks. As my update says, I just wanted to show what is used to determine RAA.