Training camps opened across Florida and Arizona last week, and baseball also took center stage briefly in Boston at the annual meeting of the American Association for the Advancement of Science. How to quantify fielding ability was a topic for the largest general interest scientific organization in the world.

Shane T. Jensen, an assistant professor of statistics at the University of Pennsylvania’s Wharton School, presented a new statistical measure for defensive performance, which he devised with two colleagues.

Jensen developed a method to calculate the probability that the average fielder would have caught a flyball or line drive, or gloved a grounder, hit to any spot on the field. Using defensive data from the 2002 to 2005 seasons, the group broke the field down into small squares, tracked where every ball landed and each player’s performance.

The analysis generates an overall rating for each player. Positive values indicate runs saved, whereas negative values indicated runs cost, averaged over the 2002-05 seasons. Among players who were on the field for at least 600 balls in play during the four-year span, here are Jensen’s leaders by position.

Jensen’s Top Defenders by Position, 2002-05
(min 600 balls in play)

1B. . .Ken Harvey (2.85). . . . . . Doug Mientkiewicz (1.92). . . . . Eric Karros (1.75)
2B. . .Craig Counsell (10.97). . . .Brandon Phillips (8.72). . . . . . .Chase Utley (8.34)
3B. . .Damian Rolls (7.75). . . . . .Craig Counsell (6.79). . . . . . . . Placido Polanco (5.26)
SS. . Clint Barmes (11.63). . . . . Alex Rodriguez (10.40). . . . . . . Jason Bartlett (9.37)

LF. . .Coco Crisp (9.22). . . . . . . Reed Johnson (7.59). . . . . . . .Carl Crawford (6.95)
CF. . Jason Michaels (12.41). . . .Andruw Jones (8.84). . . . . . . . Darin Erstad (7.59)
RF. . Gary Matthews Jr. (6.78). . Trot Nixon (5.56). . . . . . . . . . Dustan Mohr (4.19)

Yes, that’s Alex Rodriguez listed among the best shortstops -- he placed second among his peers according to Jensen’s formula -- and the interesting twist is that Jensen ranked teammate Derek Jeter the worst shortstop in those four years. A-Rod moved from the Rangers to the Yankees midway through this span, and switched to third base instead of replacing Jeter at short.

That’s not to say that Jeter doesn’t contribute in many ways and help the Yankees score more runs than his defensive game allows, but would the Yanks be better overall if A-Rod was in the middle infield? That could be debated a long time.

STATS also breaks the field down into zones and tracks every ball hit. One measure generated from the data is infielder’s zone rating. An infielder’s zone rating is the number of outs recorded on groundballs to the player, divided by the number of balls hit into his defensive zone, as recorded by STATS reporters.

Infielder’s Zone Rating, 2002-05
(min 200 games at position)

1B. . . Julio Franco (.894). . . . . Scott Spiezio (.892). . . . . . Doug Mientkiewicz (.889)
2B. . . Mark Ellis (.881). . . . . . . Chase Utley (.868). . . . . . . Rey Sanchez (.867)
3B. . . Pedro Feliz (.837). . . . . .Scott Rolen (.806). . . . . . . Adrian Beltre (.804)
SS. . . Alex Rodriguez (.888). . . .Jose Valentin (.879). . . . . . Adam Everett (.872)

Jensen’s formula and STATS’ infielder’s zone rating are two different animals, yet there is some overlap in players ranked among the best by both. Doug Mientkiewicz, Chase Utley and Rodriguez make both lists, with A-Rod generating the highest infielder’s zone rating among shortstops between 2002 and 2005.

Here the 2002-05 leaders in outfielder’s zone rating by position, defined as the number of outs recorded on flyballs and line drives hit to a player, divided by the number of flyballs and line drives hit into his zone:

Outfielder’s Zone Rating, 2002-05
(min 200 games at position)

LF. . Reed Johnson (.918). . . . . . . Brian Jordan (.910). . . . . . . .Craig Monroe (.905)
CF. .Aaron Rowand (.922). . . . . . . .Darin Erstad (.915). . . . . . . . Mike Cameron (.898)
RF. .Austin Kearns (.921). . . . . . . .Alex Rios (.910). . . . . . . . . . .Brian Giles (.901)

Jensen ranked Toronto left fielder Reed Johnson second and long-time Angel Darin Erstad third at their respective positions. Johnson finished behind Coco Crisp but ahead of Carl Crawford. Jason Michaels and Andruw Jones ranked ahead of Erstad, according to Jensen’s research.

Putouts, assists and errors have been recorded since the earliest days of the major leagues, but for decades, fielding percentage was the only means to compare players defensively.

It’s a statistic that offers little more than what small percentage of balls a player drops or throws poorly among the dozens and dozens of chances he handles in a season. It doesn’t consider how much territory he covers or how quickly he starts on batted balls. In fact, getting to more balls means more chances to commit errors.

In the last quarter century, statistics such as range factor and zone rating have emerged. Now Jensen makes his contribution to quantifying defensive performance. All of the new measures have their weaknesses or limitations, but statisticians and baseball researchers continue to give us new ways to look at an aspect of the game that lags behind all others in statistical analysis.