February 25, 2010
Prospectus Hit and Run
Call it True Average
by Jay Jaffe
If you've followed us at Baseball Prospectus for any length of time, you're probably familiar with Equivalent Average, or EqA, one of our signature hitting stats. If you're not, here's the skinny: it's the expression of how many runs a player created per plate appearance, translated to the familiar and easy-to-understand scale of batting average.
A .350 mark is outstanding; last year Albert Pujols (.368) and Joe Mauer (.346) led their respective leagues. A .300 mark is very good; last year Justin Upton and Jorge Posada both put up .301 EqAs. A .260 EqA is the definition of league-average figure; Rafael Furcal (.262) and Stephen Drew (.259) were both right around that mark. A .230 mark is replacement-level, the caliber of what a waiver-wire pickup or a Class AAA player could provide; a team has almost nothing to lose by trying something different than a player at this level. Note that the Rockies' Garrett Atkins (.230) and the Marlins' Emilio Bonifacio (.228) both lost their starting jobs last year.
There's a lot of sausage grinding involved in turning hits, walks, total bases, stolen bases, caught stealing and other data into this batting average-like form. We even build park and league adjustments into the formula, so that a .300 EqA in hitter-friendly Coors Field has the same impact on scoring as it does in pitcher-friendly Petco Park, and a .300 today has the same impact as it did in the low-scoring 1960s or the high-scoring 1930s. It's all worthwhile, because EqA does a much better job of predicting scoring levels than batting average, on-base percentage, slugging percentage, OPS (on-base plus slugging), OPS+, and more complicated run estimators.
This spring, we at BP have chosen to rebrand EqA as True Average (abbreviated TAv). Why? Because we feel strongly that the new name underscores our ability to get a "True-r" grasp on the quality of a hitter than the aforementioned traditional or more modern stats do. Quite frankly, we're hopeful that this simple, easy-to-remember name can reach a wider audience.
The best way for those unacquainted to understand True Average is to look at several examples using our 2010 PECOTA hitter projections. Below are five players whose True Averages are higher than you might expect given their batting averages, OBPs, SLGs and other stats, and five whose True Averages are lower.
TAv higher than you might think
Prince Fielder, 1B, Brewers
Forecast: .287 AVG/.409 OBP/.586 SLG, 41 HR
True Average: .326
Say what you will about the impact of Fielder's unique physique on his long-term prospects but the man can hit, and PECOTA loves him for it, forecasting Fielder to bop more homers than any other major-leaguer, and to post the highest True Average of any hitter this side of Albert Pujols. What boosts his TAv so far above his batting average is that it's accompanied by 101 walks. Not only does he draw about 20 intentional passes per year, but his unintentional walk rate has risen from 8.3 percent in his 2006 rookie season to 12.4 percent last year.
Adrian Gonzalez, 1B, Padres
Forecast:.287/.393/.533, 34 HR
True Average: .325
At first glance, Gonzalez's rate stats and homer total don't look like they belong in the same ballpark as those of Fielder-and they don't. While the Brewers' Miller Park is somewhat pitcher-friendly, reducing scoring by about three percent, the Pads' Petco Park curbs scoring by an MLB-high 11 percent, visibly depressing hitting stats. What True Average tells us is that relative to their environments, Prince and Gonzo are essentially equal in their productivity with the lumber.
Alex Rodriguez, 3B, Yankees
Forecast: .288/.403/.578, 39 HR
True Average: .320
According to PECOTA, A-Rod gets a 38-point boost in slugging percentage from the new Yankee Stadium, but even when his numbers are adjusted for context (and really, how often is the ever-controversial Rodriguez left in proper context?), he's still among the game's top sluggers. Only Fielder projects to hit more homers. Boosting Rodriguez beyond those already-impressive stats is his projection for 17 steals in 20 attempts, good for a few extra runs. True Average properly credits him for that small but measurable gain.
Grady Sizemore, CF, Indians
Forecast: .271/.387/.491, 26 HR
True Average: .306
Elbow woes and a sports hernia turned Sizemore's 2009 into a painful proposition, but prior to that, he was a top-notch hitter, and PECOTA expects a rebound. Like Rodriguez, Sizemore gets a boost beyond his strong OBP and SLG rates via a projection of 26 steals at a 79 percent clip.
Adam Dunn, 1B, Nationals
Forecast: .250/.387/.493, 31 HR
True Average: .302
A classic low-average hitter who strikes out a ton (he set a single-season record with 195 in 2004) Dunn also provides plenty of power (41 homers per year since 2004). Additionally, he draws a huge number of walks (over 100 per year since 2004) because of his ability to work the count, not to mention the fear factor; pitchers would rather try to get the next guy out, than risk him hitting a homer.
TAv lower than you might think
Yuniesky Betancourt, SS, Royals
Forecast: .289/.313/.428, 10 HR
True Average: .239
Betancourt's .289 average with 10 homers may pass first muster considering that he's a shortstop, but his unwillingness to take a walk (one projected for every 30.5 plate appearances) and his ineptitude on the base paths (five projected steals in nine attempts) erode his value to the point where he's well below average with the stick, and a significant drag on the Royals' already-wheezing offense.
Delmon Young, LF, Twins
Forecast: .296/.335/.439, 16 HR
True Average: .258
Superficially, the batting average and home run totals look like solid progress for the 24-year-old Young, who has yet to live up to his one-time top prospect status. Alas, his hacktastic ways (a projected 101/28 K/BB ratio, still better than last year's 92/12) undercut his contributions considerably, leaving him a tick below league average at an offense-first position.
Placido Polanco, 3B, Phillies
Forecast: .305/.355/.425, 9 HR
True Average: .264
The contact-oriented Polanco is very difficult to strike out, but his lack of power or patience mean he needs to hit above .330, not .300, to be a real offensive asset. He did that as recently as 2007, but he's now 34. In a hitter's park such as Citizen's Bank, the above numbers won't go very far.
Robinson Cano, 2B, Yankees
Forecast: .297/.338/.493, 26 HR
True Average: .270
That batting average and homer total make Cano look like the second coming of Jeff Kent, but the combination of playing in a power-friendly park, a low walk rate (projected 5.2 percent) and atrocious base running (two steals in eight attempts) all chip away at his the true value of his offensive contributions considerably.
Ichiro Suzuki, Mariners
Forecast: .317/.364/.414, 7
HR
True Average: .272
There's no getting around the fact that Ichiro annually bedevils
PECOTA, because the system simply doesn't expect a man of his profile to keep putting up batting averages on balls in play north of .380, as he's done twice in the past three years. Ignoring the actual projections for a moment, the take-home is that even with last year's .352 batting average and 26 steals, Ichiro's low walk and homer totals (32 and 11) kept his True Average at just .298. He's risen above .300 just once, in 2004. An excellent hitter, if not an elite one.
A version of this story originally appeared on ESPN Insider 
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Why is TAv better than wOBA?
1. The fact that the stat is scaled to batting average makes it easier for the average fan to understand than wOBA being scaled to OBP. ".300 is good" is a notion with t over 100 years of baseball history behind it.
2. EqA is park adjusted, wOBA isn't, at least as I understand it.
3. The two have virtually identical correlations to runs scored, but TAv produces a smaller RMSE. I'll leave the defense of that statement and the grisly math to Clay Davenport, who's got data showing that. He'll have an article on the topic soon once he gets the PECOTA cards up, but perhaps I can get him to chime in here as well.
Though EqA is derived from results, not batted ball types, so there's more noise in the signal on a player-by-player basis.
And, as Tango points out in his rebuttal, the wOBA published at StatCorner is park-adjusted - both are available so users can choose which they prefer.
Is BP actively trying to alienate the knowledgable audiece, here?
There's plenty of noise when it comes to relying on batted ball types for ANYTHING. See Colin Wyers' work on line drive rates, press box heights, and scorer bias (http://www.hardballtimes.com/main/article/when-is-a-fly-ball-a-line-drive/) or our lengthy roundtable on BABIP and line drives (http://www.baseballprospectus.com/article.php?articleid=9928), or the Seidman/Swartz SIERA series on SIERA.
Consider also that information on batted ball types occupies just a tiny sliver of baseball history, and that the power of TAv (which by its original name has been in existence since BP's gestation days in the rec.sport.baseball newsgroup) is that it's built to enable cross-era and cross-environment comparisons, including the century-plus swath for which we have no batted ball data.
For those interested, you can read Tango's response here: http://www.insidethebook.com/ee/index.php/site/article/eqa_renamed_tav_true_average/
One classic analysis of EqA/EqR is found here:
http://walksaber.blogspot.com/2008/05/analysis-of-clay-davenports-eqr-and-eqa.html
I would read that before asserting that it's better or worse than anything. It's an accurate analysis (as far as I can tell) of the basic construction of the stat, and gets at some technical issues.
From the past, also see:
http://www.insidethebook.com/ee/index.php/site/comments/why_is_eqa_so_complicated/
From the more recent past, see the excellent wOBA/EqA analysis done by current BP writer Colin Wyers (sorry if this has already been linked here, seems like a natural place for it):
http://www.hardballtimes.com/main/blog_article/is-eqa-better-than-woba/
And,
I'm familiar with that work, and I'm also familiar with data that's been circulated internally within BP which will rebut that. As I said before, I'm leaving the math-level details regarding the formula and its construction to Clay Davenport.
I was just putting it out there for people to read, not to make any particular claim. I eagerly await the publication of the internal studies you mentioned, since transparency benefits everyone. I assume that you wouldn't refer to those studies if they weren't going to be made available to everyone, given your comment above. It would be really interesting for all to see. Was Colin convinced?
I won't presume to know what Colin thinks, but I can tell you that he's been crunching numbers on this, too.
I imagine the data and discussion will be presented along the lines of Clay's "About EqA" piece from 2004 which was linked above: http://www.baseballprospectus.com/article.php?articleid=2596
One of the key take-home points from both that and Colin's linked THT piece above is the time range of comparison, because these formulas have been "tuned" to a given period. I'm not sure if this has changed, but at the time, Fangraphs only had wOBA going back to 1974. In Clay's piece, which was written in 2004, before wOBA was unveiled, he noted that there were ranges of time where EqA was essentialy on par with other systems, and ranges where it was significantly superior, and that he could improve its performance over recent eras with a greater number of category inputs (remember, stats like sacrifices, intentional walks and caught stealing have relatively limited histories). I imagine all of that will find its way into the discussion.
If you're saying that people are going to publish on this, I look forward to it. It will be good to know what data sets there are, so that the results can be independently checked by disinterested parties.
I assume Colin will be publishing his results however they turn out?
I'm curious to see if he finds his earlier article to have been wrong. Of course wOBA is of the nature that, since it's just straight linear weights converted to a rate stat, that it could be adapted to any set of weights
Currently the "Leaders" on FanGraphs will only show wOBA back to 1974, but you can go back more than that for individual players. For instance, Babe Ruth had a wOBA of .600 in 1920 (and keep in mind that wOBA is purposefully set to be in the OBP scale).
Perhaps it's true of TAv, but I don't know that it's accurate to say wOBA is "tuned" to a given time period. Instead I believe it is tuned to the run environment of the league for that season. In other words, we don't (or at least shouldn't) apply the correct linear weights from 2009 to figure out Babe Ruth's wOBA in 1920...we apply the correct linear weights from the AL in 1920 to figure Babe's wOBA in 1920. There are also different machinations you can go through to adjust for team-specific run-environments if you like (and I believe Rally at Baseball Projection does this for his linear weights if I'm not mistaken).
I look forward to reading the internal studies that have been floating around BP, but I think it would take quite a substantial result to trump wOBA. In my opinion the tie should go to the system that has better logical foundations, and I think wOBA fits that bill. It finds the "correct" value for each type of batting event and adds them together. If TAv has a tiny edge in RMSE that wouldn't make it better than wOBA because wOBA has a significant edge in principled foundations (also note that wOBA was not engineered for the purpose of minimizing RMSE of predicted team runs scored).
I believe you are correct about the FanGrapphs implementation of wOBA, which I think is based on
http://www.insidethebook.com/ee/index.php/site/article/woba_year_by_year_calculations/
Your other points are important as well.