On Sept. 29, 2002, at a venue then known as Pro Player Stadium, Tim Raines played the final baseball game of his 23-year career. He reached base once, for the 3,935th and last time, before a defensive substitute replaced him. Raines exited the sport as a potential candidate for the Hall of Fame, but by consensus he seemed a Cooperstown long shot.

Raines had fallen well short of traditional milestones such as 3,000 hits, 400 home runs or a .300 career batting average. He had never produced more than 71 RBI in a season and only once led the league in average. But he had an unforeseen edge on his side. On June 17, 2003 — 261 days after Raines’s final appearance — came the release of Michael Lewis’s “Moneyball: The Art of Winning An Unfair Game.”

Wednesday evening, in his 10th and final chance, Raines gained election in the Hall of Fame with 86 percent of the vote, up from his initial total of 24.3 in 2008, his first year on the ballot. Just five others in the past 40 years have made up such a large gap to reach the 75 percent required for induction. One of the fastest runners and most patient hitters of his era, Raines was likely the second-greatest leadoff hitter of the 1980s, behind only Rickey Henderson. He made the Hall on merit.

But Raines also came along at just the right moment. He benefited, like perhaps no player before him, from the advancement and widespread adoption of new methods for measuring a ballplayer’s value. And his case could be pressed through ever-expanding channels, which placed new pressures on the 442 members of the Baseball Writers’ Association of America who vote.

[Bagwell, Raines, Rodriguez voted into Baseball Hall of Fame]

Raines’s supporters pointed not to gaudy counting totals, but to Raines’s .385 on-base percentage, his 84.7 percent success rate when stealing bases — the best ever for a player with at least 400 attempts — and 68 career wins above replacement.

For six years, Raines did not fret about his Hall of Fame fate.

“I didn’t really have the votes to actually even consider the next year I would get it,” he said in an interview on MLB Network. He finished 23 votes shy last year. By this year he received overwhelming support.

Wednesday, then, signaled another victory for the sabermetric movement. It feels worn to use the phrase “the sabermetric movement” in 2017, with advanced metrics having taken hold at every level of the sport, from average fans to front offices. Still, the arc from Raines’s last day as a player to his entry into the Hall of Fame mimics the rise of the tenets that burst from Lewis’s seminal book: from outright skepticism to total acceptance. If on-base percentage, base stealing efficiency and wins above replacement can get a deserving player into the Hall of Fame, what battles are left for the advanced-stats crowd to fight?

Raines’s triumph also illustrates, depending on one’s perspective, either the power of modern communication to persuade or the dangers of its ability to promote groupthink. In recent years, voters have increasingly publicized their ballots. (The Post is one of several media organizations that prohibit its BBWAA members from voting.) The public ballots led to debate — but also outrage and shaming.

The BBWAA has moved officially in the direction of transparency. Three voters who omitted Ken Griffey Jr. last year, thereby preventing the center fielder from becoming the first unanimous Hall of Famer, remained anonymous. Partially in response, the BBWAA will force voters to reveal their ballots, starting in 2018.

One professor told the Wall Street Journal this week that an open ballot would “actually be in violation of principles of democratic elections.” Another told the newspaper it opened up the possibility of voting being affected by social desirability bias, in which respondents vote to satisfy others rather than hew to their own beliefs.

“Sadly, I think that’s a real issue because frankly I think some people just don’t want to endure [analytics-minded ESPN baseball writer] Keith Law or whomever hammering them on Twitter,” New York Post columnist Mike Vaccaro wrote in an email. “That said: There have always been guys whose pathway is interesting in retrospect. I’d like to think that’s what happened with Raines, and why the ability to stay on the ballot so long is a good thing, allowing for a thorough and continuing review of a guy’s career. I actually wish it was still 15 years. I hope Raines wasn’t guilt-tripped to this, because his career is far more worthy than that [and I voted for him].”

Contemporary award voters did not look upon Raines as an elite talent. He made seven all-star teams, but none after he turned 27, for the final 12 seasons of his career. He never finished higher than fifth in the MVP vote and earned just three top-10 finishes.

Bathed in the light of modern statistical analysis, though, Raines’s accomplishments began to look grander. He famously reached base more often than surefire Hall of Famer Tony Gwynn (although just four times, and in about 120 more chances). In his seven-year peak from 1981 to 1987, Raines reached base at a .396 clip and averaged 72 steals.

As a younger generation of BBWAA members more likely to embrace newer methods of evaluation gained voting status, and older voters cycled out, Raines’s percentage surged. Last year, nine of the 10 first-time voters who revealed their ballots voted for him. By Wednesday afternoon, Raines had been named on all 14 public first-time voters’ ballots, as tracked by Ryan Thibodaux, a tireless 35-year-old fan from Oakland, Calif.

For some voters who checked the box next to Raines’s name for the first time, a longer lens and sound arguments swayed them.

“Time gives all of us more perspective, and now that Raines and [Lee] Smith are in their final year of eligibility, I rethought their cases,” first-time Raines voter John Perrotto wrote at FanRag Sports. “An extremely informative email from [Raines advocate] Jonah Keri and a bombardment of pleas from fans helped change my mind on Raines.”

Longtime voter Marc Topkin of the Tampa Bay Times also switched from no to yes on Raines this year.

“No, that wasn’t because he had a good 2016 season,” Topkin wrote. “Yes, it was in part, at least subconsciously, because it was his final year of eligibility. . . . While not suddenly transforming into a Raines truther, after a fresh, detailed look aided but not misled by sabermetric tools, I felt good enough — or thought I felt good enough — to check his box.”

“The more I studied Tim’s résumé and statistics,” said MLB.com’s Hal Bodley, a Raines first-timer who has covered baseball since 1958, “the more I realized I’d made a mistake not voting for him in the past.”

Bodley, like so many other voters, had help shaping his view from outside forces. Raines earned his way to the Hall of Fame, but change, in the way the game is watched and the way votes are tracked, is what finally got him there.