# Stats Sunday – True Average

This is an archived article and the information in the article may be outdated. Please look at the time stamp on the story to see when it was last updated.

The following post appeared in 2012 as part of WGN’s Stats Sunday series. Thanks to Jay Jaffe for this article.

One of the hardest aspects of introducing a new sabermetric measure to a wider audience is providing a frame of reference. Even OPS — on-base percentage plus slugging percentage, what official Major League Baseball historian John Thorn referred to as “the Masonic Handshake,” the key to entering the world beyond the basic box score — lacks a familiar scale. What on earth does an .800 OPS mean to somebody who’s never encountered it?

True Average, a total offensive measure from Baseball Prospectus, attempts to provide an extremely familiar frame of reference to those who would use it, because it’s mapped to the scale of batting average: .300 is very good, .260 is league average, .230 is replacement level. What True Average is actually expressing is a player’s rate of runs created per plate appearance, incorporating not only familiar ingredients such as hits, walks, and total bases, but also strikeouts, sacrifices, reaching on error, and even situational hitting — double plays grounded into, as well as the so-called productive outs that move runners over, the kinds of things that announcers like to point out “don’t show up in the box scores.” Well, they’re in here.

True Average is computed using a set of linear weights which is applied to each player’s batting line, with each event assigned a value based upon the average number of runs it produces. An infield single is (http://www.baseballprospectus.com/article.php?articleid=11686) worth 0.41 runs, an outfield single — which tends to advance runners further — is worth 0.467 runs, a double 0.744 runs, a triple 1.004 runs, a homer 1.393 runs, an unintentional walk 0.310 runs, a strikeout −0.281 runs, an out on a ball in play −0.277 runs, and so on. The results of (http://www.baseballprospectus.com/article.php?articleid=11717) certain situational outs in various base-out states are included as well. The sum of all of those events is divided by the total number of plate appearances, and added to the league-wide average number of runs per plate appearance that year — 0.115 this year — with some (http://www.baseballprospectus.com/article.php?articleid=12047) park adjustment incorporated into the mix as well.

Though it’s not something that can be easily calculated the way OPS can, the virtue of this approach is that it correlates better with actual scoring rates than other stats such as batting average, on-base percentage, slugging percentage, simple OPS, or OPS+ do. Where the OPS-based formulas equally weigh the on-base and slugging components of a hitter’s performance, True Average properly places more emphasis on the on-base end of things, which is roughly twice as important as the slugging end of things. Where True Average has its advantage on (http://en.wikipedia.org/wiki/WOBA) Weighted On-Base Average (wOBA), which is mapped to the less familiar scale of on-base percentage (.400 is very good, .300 is subpar) is that it’s adjusted to park and league scoring levels in addition to using a scale that has about a century’s worth of a head start carving out headspace.

The result of this is that a .300 True Average in a year where scoring is high — say 2000, when teams scored 5.14 runs per game, their highest level since 1936 — is every bit as valuable as a .300 True Average in a year where scoring is low, such as 1968, when teams scored just 3.42 runs per game. A .300 True Average produced by a hitter playing half his games at Coors Field is as valuable as a .300 produced at Petco Park. Here are a handful of hitters who finished a season with a True Average of exactly .300 with enough plate appearances to qualify for a batting title, sorted from lowest OPS to highest:

 Player Team Year AVG OBP SLG OPS TAv Ron Fairly Dodgers 1964 .256 .349 .385 .734 .300 Dick McAuliffe Tigers 1968 .249 .344 .411 .755 .300 Greg Gross Astros 1974 .314 .393 .377 .770 .300 Mark McGwire A’s 1989 .231 .339 .467 .806 .300 Cesar Cedeno Astros 1975 .288 .371 .440 .811 .300 Don Mattingly Yankees 1988 .311 .353 .462 .816 .300 Pete Rose Phillies 1979 .331 .418 .430 .848 .300 Stan Musial Cardinals 1956 .310 .386 .522 .908 .300 Sammy Sosa Cubs 2003 .279 .358 .553 .911 .300 Carlton Fisk Red Sox 1977 .315 .402 .521 .922 .300 Ken Griffey Jr. Reds 2000 .271 .387 .556 .942 .300 Garrett Atkins Rockies 2006 .329 .409 .556 .965 .300

Note the wide ranges encompassed by these players with regards to the more familiar rate stats as well as OPS and even home parks. McGwire and Rose are 100 points apart in batting average, yet their overall offensive contributions are the same on a per plate appearance basis. McAuliffe’s production in 1968, the “Year of the Pitcher,” is equivalent to Griffey’s production in 2000. Fairly has a slugging percentage 181 points lower than Atkins, and an OPS 231 points lower, yet their contributions are equivalent because at Dodger Stadium in 1964, teams scored 3.20 runs per game, whereas at Coors Field in 2006, teams averaged 5.36 runs per game.

Here are the top tens for each league in True Average, accompanied by their more traditional rate stats, through the games of September 7

 Rank Player Team PA AVG OBP SLG TAv 1 Mike Trout Angels 532 .329 .393 .563 .354 2 Edwin Encarnacion Blue Jays 569 .283 .381 .568 .333 3 Miguel Cabrera Tigers 593 .330 .395 .593 .330 4 Prince Fielder Tigers 588 .315 .412 .529 .324 5 Adrian Beltre Rangers 566 .319 .355 .556 .316 Josh Willingham Twins 554 .263 .368 .538 .316 7 Ben Zobrist Rays 565 .266 .373 .468 .313 8 Albert Pujols Angels 571 .285 .343 .531 .312 9 Josh Hamilton Rangers 560 .289 .355 .582 .310 10 David Murphy Rangers 433 .316 .394 .500 .309
 Ranks Player Team PA AVG OBP SLG TAv 1 Buster Posey Giants 519 .323 .399 .521 .342 2 Andrew Mccutchen Pirates 564 .343 .406 .558 .334 3 Ryan Braun Brewers 576 .312 .387 .606 .333 4 Melky Cabrera Giants 501 .346 .390 .516 .332 5 Giancarlo Stanton Marlins 439 .285 .353 .593 .323 6 David Wright Mets 575 .312 .402 .499 .319 7 Chase Headley Padres 597 .287 .370 .488 .317 8 Matt Holliday Cardinals 584 .304 .378 .521 .316 9 Andre Ethier Dodgers 527 .290 .357 .469 .311 10 Yadier Molina Cardinals 473 .323 .374 .508 .310 Paul Goldschmidt Diamondbacks 500 .289 .360 .505 .310

Note the presence of some players with batting averages in the .260s, OBPs in the .340s and .350s, and SLGs well below .500. All of which goes to show that from an offensive standpoint, there’s more than one way to be an elite hitter. You can see updated leaderboards (http://www.baseballprospectus.com/sortable/index.php?cid=1091251) here.

Jay Jaffe writes the daily Hit and Run blog at http://mlb.si.com. He is a Clubhouse Consultant for MLB Network’s Clubhouse Confidential television show, a contributor to Baseball Prospectus since 2004, and the founder of the FutilityInfielder.com website. Follow him on Twitter at @jay_jaffe.

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• ##### James Collison

There are a lot of big names on that list. I think there should be an asterisk beside Mark McGwire's stats though due to his steroid use.

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