Free agency can represent one of the most exciting and satisfying times of a player’s career, a checkpoint to take stock of — and often to appreciate — the body of work of six-plus seasons in the big leagues. For Red Sox outfielder/designated hitter J.D. Martinez, this offseason represented something a bit different.

Yes, his outstanding four-year run as an elite middle-of-the-order hitter gained greater attention, particularly when agent Scott Boras attached to it a meme-worthy title like the “King Kong of Slug.” That said, Martinez’s trip to the open market also came with an unexpected degree of scrutiny.

“I got to hear how terrible I am,” Martinez said. “I don’t get it. It blows my mind.”

The criticism focused on Martinez’s defensive résumé. The outfielder grimaced at the thought of MLB Network segments that were particularly unflattering, including a repeated viewing of a ball that clanged off his glove (Martinez recalled getting a good jump on the ball but losing it in the lights). As a player who always has put in time working with his coaches to improve his defense and who takes pride in that aspect of his game, Martinez was baffled.

Those media conversations about his defense were dominated by widely used, publicly available defensive metrics — Ultimate Zone Rating (UZR) on Fangraphs and Defensive Runs Saved (DRS), developed by Baseball Information Solutions.

Both defensive systems characterized him as having been a clear defensive liability in 2016-17, his performance more than 20 runs below a league-average right fielder over those two years. Those who used such numbers in search of sweeping conclusions about his defense arrived at a definitive one: Martinez was a butcher, a concern that seemed likely to grow as he aged into his 30s.

Martinez was both dismayed and puzzled by such characterizations.

“Every baseball guy is looking at me and saying, ‘I don’t understand why they say you’re a bad outfielder,’” said Martinez. “My mind gets blown. That’s where I’m coming at it from: What’s going on?”

To explore that question, Martinez agreed to meet earlier this season with Jeff Stern of TruMedia Networks, a sports analytics company based in Kenmore Square that consults with more than half of the 30 big league teams.

The 40-minute conversation between Martinez and Stern was illuminating in trying to assess Martinez’s defense on an individual level and in understanding the evolution of modern defensive statistics — and whether those numbers seen by the public are the same as those used by teams or analysts such as the TruMedia team.

AN EVOLVING FIELD

Thanks to the introduction of Statcast, a radar-based collection of cameras around the park introduced across Major League Baseball in 2015, there are now new statistics, new ways of measuring what happens on the field, that get to even more precise assessments of defense.

The location of a ball with Statcast is precise rather than approximate, and positioning information allows teams and analytics groups such as TruMedia with access to the Statcast data to get a better understanding of the likelihood that a player will or won’t track down a ball in play.

Defensive metrics also account for a number of additional factors, including the impact of a player’s throwing arm both in terms of how often he throws out runners and how often his arm acts as a deterrent to runners trying to advance. DRS also assesses credit and penalties for outfielders for good plays — such as fielding a ball well off the Green Monster and holding a batter to a single — and misplays (throwing to the wrong base to allow a runner to advance and missing a cutoff man, for instance). But the biggest component of a defensive evaluation is range, an area where the systems for measurement have changed drastically in recent years.

“Statcast data has changed the way that internally teams are doing defensive evaluations,” Stern told Martinez. “But to the best of my knowledge, I don’t think very much of that is public, so it hasn’t really changed any of the public-facing numbers that people have access to.”

Martinez had heard similar feedback last year after he was traded from the Tigers to the Diamondbacks. With Detroit, Martinez had graded as well below-average. After his trade, UZR and DRS offered favorable numbers for his work. Martinez recalled a conversation with Arizona head of analytics Mike Fitzgerald in which he discussed the disparity.

“My [UZR] has always been a negative in the outfield,” recounted Martinez. “Then I go to Arizona and my [UZR] is positive. I go, ‘What’s the difference?’ He said, ‘Now we’ve got you positioned right.’ ”

According to a major league source, Detroit ranked among the bottom few teams in the majors in outfield defensive positioning last year. Arizona was among the best. The difference was reflected in the defensive numbers Martinez delivered with the D-backs.

According to a Diamondbacks source, over two and a half months, Martinez made all but a couple of plays that an above-average defensive outfielder would have made — and on one of the plays he didn’t make (a D.J. LeMahieu triple into the right-field corner), Arizona was pleased that Martinez pulled up rather than potentially smashing into a metal wall and risking injury.

The difference in the evaluations of Martinez’s defense with Detroit and Arizona hinted at some of the distinctions that come into play with Statcast-based data involved in analyzing defense.

The added measurements Statcast uses creates a database in which apples-to-apples plays made (or not made) by different players can be compared. For instance, on April 26 in the third inning of a game against the Blue Jays, Martinez (playing right field) tracked down a long fly ball off the bat of Lourdes Gurriel Jr.

From where he was positioned to where he caught it, Martinez had to run 99 feet. The ball had a hang time of 5.1 seconds from the moment of contact. The ball was hit 364 feet with an exit velocity of 97.5 m.p.h. and a launch angle of 29.8 degrees, with the fence about 5 feet from Martinez by the time he tracked down the ball.

Based on the history of similar plays, MLB.com’s Statcast analysts pegged the play as having a catch probability of 52 percent (meaning it’s a ball caught 52 percent of the time). That play represents, according to the same analysts, the lowest Catch Probability (the most difficult play) on which Martinez made a catch all year.

Martinez got a roughly average jump time on the play, took an efficient route with little wasted motion, but perhaps most importantly, he got up to a top-end running speed of 28.1 feet per second — faster than an average play on the ball.

Based on the proximity of the ball to the wall in Toronto, TruMedia actually measured the play as having a considerably higher degree of difficulty than even the Statcast system, with the catch representing one more frequently made by elite outfielders and rarely made by below-average ones. The disparate interpretations of the same play demonstrates that multiple groups (or different teams) using the same defensive measurements can reach very different conclusions about defense.

The impact of Martinez’s speed on the play became clearer when Stern called up another play with similar variables involving another right fielder, Nick Markakis. The ball landed in the gap, a good distance from the outfielder, for a two-run extra-base hit.

“To me, that’s a double,” Martinez said.

Ordinarily, that assessment would be accurate. According to TruMedia, it was a play that generally would not have been made by an average outfielder. (Statcast, by contrast, had it as a ball that would be caught with an almost-routine probability of 88 percent).

But Markakis was running at a below average speed on the play — 24.9 feet per second, according to Statcast — so once he got up to top speed, and with three seconds at top speed, he would have run roughly 10 fewer feet than Martinez did on the play against the Blue Jays, likely explaining why Martinez caught the ball against the Blue Jays and why Markakis did not.

“A 3 m.p.h. difference between you and Markakis on comparable plays is a huge difference,” said Stern. “You can’t really see it. There are things, when you watch the video, you can see that you can’t know from the data, but there are things the data tells you that you can’t see from the video. I couldn’t tell you that you were running that much faster than Markakis, nor could I have told you your jump was a 10th of a second faster than his. I couldn’t have seen that through the video. But the data gives us some context. The video gives us some context. What a smart team should do is try to combine the two.”

Smart teams are, in fact, doing that. So, for that matter, are smart analytics groups such as TruMedia and Baseball Info Solutions. While the publicly available version of DRS doesn’t incorporate Statcast data, BIS does use such information as part of its consulting work with teams — and that data separates positioning from range in order to provide more precise views of an outfielder’s skill set than the publicly available information.

All of that is a way of saying that the defensive stats that frame public dialogue about a player — UZR and DRS — aren’t as sophisticated as what is being done with Statcast data. So, while dialogue around Martinez was chiefly unflattering, what do the more sophisticated, proprietary numbers say?

IS J.D. MARTINEZ A GOOD OUTFIELDER?

Unquestionably, the failure to account for positioning was punitive and potentially unfair to Martinez. Moreover, there were other circumstances that may have played into Martinez’s poor defensive grades as calculated by UZR and DRS over the last two years. In particular, the start of Martinez’s 2017 season was delayed by a sprained foot ligament that diminished his speed.

“I couldn’t run, but they needed my bat,” Martinez said. “When I was in Detroit, they were like, ‘We need your bat. We don’t care if you get to those balls.’”

Thus, Martinez played, and his numbers may have taken a hit. But by late last year in Arizona and again this year, he’s running faster, with a more favorable view of his defense following. Stern noted that Martinez has shaved a fraction of a second off his jump time, something that has him covering several more feet of ground on many balls he chases.

There aren’t that many plays by which to make such an assessment. Most plays for an outfielder are either completely routine — made something close to 100 percent of the time — or completely impossible. Over the course of a full year, there are only about 50-100 plays that are neither routine nor impossible. As of the All-Star break, TruMedia had Martinez involved in just 14 outfield plays that didn’t involve those two extremes, with such a small sample creating a risk of distortion.

That said, among those 14 plays, TruMedia — which graded his defense as below-average in 2016 and 2017 — had his overall body of work as being average to slightly above-average this season. While Martinez has failed to make a couple of relatively high-probability plays, he’s offset those with a couple of very good plays (the one in Toronto, another in Texas) in which he ranged back into the gap. Interestingly, TruMedia graded him as above-average in right — where he’s played for most of his career — while characterizing his work in left as slightly below average.

Some major league sources who analyze defense disagreed with TruMedia’s characterization of Martinez’s outfield performance to date as average.

“Speed drives outfield defense more than anything else,” said one executive. “It’s just a hard sell to think this guy is even average based on the history of the numbers. I don’t think he has bad instincts. His issue is that he’s just lumbering. We have him below average — not the worst, but significantly below average.”

That said, Arizona — which doesn’t have the ability to use Martinez as a designated hitter — was comfortable enough with his outfield defense to consider re-signing him with the expectation that he would be defensively adequate for at least a few more years. And BIS (the company that produces the widely used DRS statistic) views him as adequate in the outfield.

“My general thought on J.D. Martinez is that he’s, honestly, except for the one year in 2016 when things didn’t go well, he looks to me to be about an average corner outfielder,” said Baseball Info Solutions research analyst Joe Rosales. “He’s certainly not someone you’d ever want to trust in center field, but in terms of his ability as a corner outfielder, he’s fine.”

Obviously, the Sox prefer to feature Andrew Benintendi over Martinez in left field on most days — no surprise, given that Benintendi is one of the faster left fielders in the game. Through 98 games the Red Sox had put Martinez in the outfield to start in 39 percent of its games, and in nine of his 38 starts in the first half, the team opted for a defensive replacement at the end of the game.

Yet those decisions appear to be based chiefly on the team’s belief that the outfield alignment of Benintendi in left, Jackie Bradley Jr. in center, and Mookie Betts in right is elite, rather than based on a view of Martinez as defensively inadequate.

At the least, the range of opinions surrounding Martinez’s defense suggests that some caution is in order when trying to evaluate a player’s defense using the most common, publicly available defensive metrics. While Martinez ended up landing a five-year, $110 million contract from the Sox that ranked as one of the largest by any free agent this winter, he believes his market was severely limited by misperceptions about his defense.

“Think about it — think about what it cost me, what it hurt me in free agency to hear people saying that. All of a sudden, I’m considered a DH because of it. I’m like, ‘What the [expletive]?’ ” said Martinez. “Fortunately for me, my offense makes up for a lot of [the perception of] my defense, so for my life and career, I was able to get the money I was able to get, but there’s guys out there that [defensive statistics] would tell a team, ‘This guy is no good,’ and then that guy is done.”

Alex Speier can be reached at [email protected]. Follow him on Twitter @alexspeier.

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