Prospectus Toolbox

Value Over Replacement Player

by Derek Jacques

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Welcome to Prospectus Toolbox, your weekly tour through the shadowy world of performance analysis, where we try to answer questions like "what the heck is that supposed to mean?" and "how on earth do I make this work?" This space is dedicated to the reader who might not know his VORP from his WARP, who thinks WXRL is a country music station and PECOTA a utility infielder-turned-competitive bass fisher.

So, as a famous man recently asked, what's VORP? VORP is a statistic developed by Keith Woolner, who just on Monday joined the Cleveland Indians' front office. The acronym stands for Value Over Replacement Player. VORP is a way of wrapping a position player's offensive performance--or a pitcher's performance on the mound--into a single number.

The "value" part of VORP is measured in runs, so VORP is considered a counting stat--like runs scored, hits, or RBI, things that are accumulated over the course of a season--rather than a rate stat like batting average or ERA. As with any counting stat, a player's VORP total is going to depend heavily on how much playing time he gets. If you prefer to think in terms of wins, we usually consider every 10 runs a player produces to be worth one win, so sometimes you might hear a player with a VORP of 30 be referred to as a "three-win player."

Now that we understand the "value" part, what about the "over replacement player" part? A replacement player is a theoretical construct, representing roughly the lowest level of performance that a major-league team should get from a player on their active roster. The idea is to measure a player's contributions by how much he adds over the kind of fringe talent any ballclub could pick up by signing minor-league free agents or claiming guys off the waiver wire. So if the Giants had to replace Barry Bonds' performance with that of a replacement player coming out of spring training--not a far-fetched scenario given Bonds' knees and the depth of the Giants' roster--you'd expect the San Francisco offense to have lost 22 (Bonds' VORP as we go to press is 22.4) runs from the total they've produced so far.

Since 1959, the range of VORP has run from 145.1, Bonds' VORP in 2001, to the -48.3 accumulated by Pittsburgh pitcher Steve Blass in 1973, the year the term "Steve Blass Disease" entered the sports lexicon. Here's a quick look at the best and worst performances of the past five decades, hitting and pitching, by VORP:

         Best             VORP   YEAR      Worst            VORP    YEAR

2000s    Barry Bonds      145.1 (2001)     Neifi Perez      -27.4  (2002)
         Pedro Martinez   112.0 (2000)     Roy Halladay     -38.0  (2000)

1990s    Mark McGwire     107.0 (1996)     Brian L. Hunter  -27.8  (1999)
         Roger Clemens    109.3 (1997)     Todd Van Poppel  -38.0  (1996)

1980s    Robin Yount      101.0 (1982)     George Wright    -32.3  (1985)
         Dwight Gooden    111.3 (1985)     Mike Parrott     -28.0  (1980)

1970s    Joe Morgan        94.4 (1976)     Coco Laboy       -25.4  (1970)
         Jim Palmer        94.3 (1975)     Steve Blass      -48.3  (1973)

1960s    Mickey Mantle     98.3 (1961)     Bill Virdon      -27.0  (1962)
         Sandy Koufax      94.9 (1966)     Jim O'Toole      -27.1  (1965)

Listening to sabermetricians talk about the replacement player is sometimes like reading arguments between theologians over how many angels can dance on the head of a pin. How bad would a team composed entirely of replacement players be? As bad as the 2003 Tigers? The 1962 Mets? The 1899 Cleveland Spiders? Worse than that, even? Is a replacement player as bad with the glove as he is with the bat? How many replacement players does it take to screw in a light bulb?

For our purposes here, none of these questions are relevant. It helps to think of statistics like automobiles. Some people want to get under the hood, make modifications to the engine, figure out new ways to squeeze out a few extra horsepower. Most of us, however, just want to drive. So long as the vehicle will get us from point A to point B, we're not as concerned about the engineers' arguments over what the most elegant or efficient way to build the car is as we might be in whether it's available in a our favorite shade of red.

So from that perspective, what do you need to know about this stat to use it properly? Here are a few of VORP's qualities:

Factors in all components of run scoring - every hit, walk, stolen base, and out is incorporated into VORP when calculating a player or pitcher's contribution, which allows for comparisons between players whose performance is completely different from each other. Did the high-average contact hitter with a lot of stolen bases have a better season than the "three true outcomes" guy who strikes out a lot, walks a lot and hits a bunch of home runs? VORP puts both players on the same scale, so that you can compare them directly.

Ballpark adjusted - One aspect of incorporating all those components is taking the context of a player's performance into account. One of the ways VORP does this is by applying park factors, recognizing that two players with identical performances shouldn't have the same VORP if one played all his home games in Colorado, and the other played his in San Diego.

Position adjusted - Because a shortstop who hits .300/.350/.450 (using the traditional statistical trifecta of batting average/on base percentage/slugging percentage) is worth a whole lot more to his team than a first baseman who puts up the same rate stats in the same playing time, VORP adjusts for positional difficulty. Take two players who had very similar conventional statistics: Joe Mauer and Nick Johnson. Here's how their performances last season stacked up head-to-head:
```
            BA    OBP   SLG   PA    H    2B  3B  HR   BB

Johnson    .290  .428  .520   628   145  46   0  23  110
Mauer      .347  .429  .507   608   181  36   4  13   79
```
Don't let the 50-point gap in batting average fool you: these are very similar performances. Mauer's advantage in hits is almost completely offset by Johnson's advantage in walks drawn. However, if we look at VORP, we see that Mauer is well ahead of Johnson, 66.9 to 51.0. What accounts for this difference? The average NL first baseman batted .290/.372/.507, so while Johnson's performance was good, it wasn't that far above the average first base performance, just 69 points of OPS ahead. In contrast, the average AL catcher hit .271/.332/.417, 193 points of OPS away from the AL batting champion's performance.

Pitchers as well as hitters are included - The primary measures for looking at batting performances and pitching performances leave you comparing apples to oranges. Which is more valuable, a .300 batting average or a 3.00 ERA? VORP places both batting and pitching performances in the same context, making for an apples-to-apples comparison. Take the 1986 AL MVP race. At the time, there was a lot of hand-wringing as to whether Don Mattingly's .352 batting average, 31 homers and 53 doubles were more valuable than Roger Clemens' 24 wins and 2.48 ERA. VORP would provide a better starting place for that debate, giving Mattingly a slim 1.2-run advantage over eventual victor Clemens, 85.8 VORP to 84.6 VORP.

Sortable reports - This isn't so much a quality of the stat as a feature of the Baseball Prospectus website. VORP for both pitchers and hitters is available as a sortable report for our premium subscribers, which gives you the tools to perform searches in our standard VORP report, or to include VORP in your own custom-made statistical reports. For example:
Worst shortstop seasons in New York Mets history.
Best seasons by an AL first baseman, 1959-2007.
Top National League rookie pitchers, 1986.

For all its good points, VORP has a number of limitations to keep in mind when you're thinking of using it:

Only goes back to 1959: If you're thinking of using VORP for a historical study, it had best be limited to the last 48 years. One of the issues that we see is that as better records are kept of ballgames, the quality of information we have about games in the recent past becomes far greater than it was in the distant past. VORP is based on a strong data set that runs only from the 1959 season to the present. If better data becomes available, it is likely that we'll see more of baseball's history covered by VORP.

No adjustment for quality of defense: While VORP adjusts for the position that a given batter plays, all players at that position are considered equal. For example, Albert Pujols and Ryan Howard are both first basemen, but they're not quite in the same class defensively. Pujols is a bonafide Gold Glover at first, while Howard, um�does the best he can. The relatively small gap between the two players' VORP (85.4 for Pujols to 81.5 for Howard in 2006) doesn't reflect the substantial difference in their defensive skills.

No adjustment for pitcher leverage: Because of the huge differences in playing time between starting pitchers and relievers, VORP values even the most elite relievers at a far lower rate than a comparable starter. The best reliever in baseball last season, Boston's Jonathan Papelbon, ranked only 37th in VORP, roughly on a par with Scott Kazmir. While many feel that this is an appropriate valuation, some metrics give relievers extra credit for pitching in higher-leverage situations than their starting pitcher colleagues. We'll have more about those systems in future editions.

FURTHER READING

Keith Woolner, "Why is Mario Mendoza so Important?" in Baseball Between the Numbers (Keri, ed., Basic Books, 2006)

Keith Woolner, "Introduction to VORP: Value Over Replacement Player"

Derek Jacques is an author of Baseball Prospectus. You can reach Derek by clicking here or click here to see Derek's other articles.

Derek Jacques is an author of Baseball Prospectus.
Click here to see Derek's other articles. You can contact Derek by clicking here