# Wins Relative to Average Player (WRAP)

Alan Schwarz of the New York Times had an article November 7th, 2004 titled “Game Theory Posits Measure of Baseball Player’s Value” in which a new statistic is introducted – Wins Relative to Average Player (WRAP) which can be said to be similar to VORP – Value Over Replacement Player. This statistic, while flawed (“The damage done by fielding errors must be assessed to the culprit. And while WRAP does a great job in determining value in a finished season, its reliance on clutch performance — which has been proved to be quite ephemeral — saps some of its predictive possibilities.”) has promise. Before explaining what WRAP is, let me show you the best five hitters and pitchers in the AL and NL via WRAP.

 NL HITTERS WRAP AL HITTERS WRAP Barry Bonds, Giants Albert Pujols, Cardinals Lance Berkman, Astros Jim Edmonds, Cardinals Adrian Beltre, Dodgers 12.16 6.85 6.49 5.85 5.33 Gary Sheffield, Yankees Vladimir Guerrero, Angels Mark Teixeria, Rangers Alex Rodriguez, Yankees Melvin Mora, Orioles 5.60 4.45 3.88 3.87 3.84 NL PITCHERS WRAP AL PITCHERS WRAP Eric Gagne, Dodgers Brad Lidge, Astros Jason Schmidt, Giants John Smoltz, Braves Armando Benitez, Marlins 5.69 5.55 5.39 4.91 4.40 Joe Nathan, Twins Curt Schilling, Red Sox Johan Santana, Twins Mariano Rivera, Yankees Tom Gordon, Yankees 5.47 5.15 5.01 4.70 4.32

So what is WRAP, exactly?

The method’s logic is actually very simple: every confrontation between pitcher and batter affects, however marginally, each team’s chances of winning. With various numbers of outs and men on base, a double or a strikeout or even a runner-advancing grounder either adds or subtracts a specific amount from the inning’s run-scoring potential. Depending on the game’s inning and score, each of those amounts takes on varying significance to the final outcome.

An example: when Beltre stepped to the plate on Aug. 23 with the Dodgers down, 7-4, in the top of the seventh in Montreal, Los Angeles had a 12.17 percent chance of coming back to win. (This percentage, derived from extensive data from the entire season, would have been 1.29 percent if there were two out in the ninth.) Beltre delivered an R.B.I. single, making the score 7-5 and the Dodgers’ chances of winning 19.11 percent.
So Beltre was awarded with the difference in percentages, or 0.0694, of what Lonergan and Polak call Wins Relative to Average Player (WRAP); and on the other side of baseball’s double-entry bookkeeping, the pitcher who surrendered the hit, Luis Ayala, was credited with a minus 0.0694.

This just goes to prove how damaging those intentional walks to Barry Bonds are. If they pitched him like a regular batter, his WRAP would probably be around 7.00 – which is less than 12.16. Walking Barry leads to wins by the Giants, period.
Where is Manny Ramirez on that list? Well –

Ramirez ranks sixth because more of his hits came in game situations that did not have a big effect on the outcome of Boston games.

This statistic seems to be more geared to offensive production by the batters than the pitchers. While Eric Gagne is definitely an awesome closer, he has a WRAP of 5.69 compared to Santana’s 5.01. Based on WRAP alone, you would pick Gagne over Santana if you were building a team … but in actuality, you wouldn’t, and I’m not factoring age, salary, or anything else of the like. Face it – an ace starter is better than an ace closer.