"He is the best," says Eckersley, who is now an MLB analyst for TBS.
Eckersley's decline started around Rivera's current age. At 41, Eckersley's arm speed slowed, his precision waned and he bounced from Oakland to St. Louis to Boston to retirement, knowing the whole time it was over.
"I knew for three years," says Eckersley, who threw his last pitch at 43.
From age 35 to 39, Eckersley had nearly identical numbers to what Rivera has had the past five seasons. From 1990 to 1994, Eckersley earned 197 saves, while Rivera has picked up 190. Rivera's ERA was 1.89, Eckersley's 2.62. Their WHIPs were in the same range (0.97 for Eckersley, 0.90 for Rivera).
Eckersley thinks that closers last longer now because of how managers use them.
"You don't see any closers throwing more than 75 innings max, right?" Eckersley says. "If anything, that has to be why they are lasting longer."
Yankees GM Brian Cashman says closers aren't lasting longer. Rivera, 40, is a "freak of nature," according to Cashman, and when you look around the majors, closers are great one year, gone the next.
"They don't last," Cashman says. "They burn out. They do it three or four or five years, and then they burn out."
Since Rivera's first season as the Yankees' closer in 1997, saves leaders have come and gone. In 1997, the Orioles' Randy Myers, 34 at the time, notched 45 saves. A year later, he was out of baseball. The Reds' Jeff Shaw saved 42 to pick up the '97 National League title. He was out of the game by age 34.
In 1998, Red Sox closer Tom Gordon led the American League with 46 saves. Now 42, he's had just one season with 30 or more saves since. In 1999, Rivera won the AL saves title, while Montreal's Ugueth Urbina took the NL crown. Urbina was done by 31.
From Robb Nen (NL saves leader at 31, out of baseball a year later) to Eric Gagne (152 saves in three years from 2002 to 2004, 51 saves since), the evidence points to Rivera being a physical and statistical anomaly.
When the Red Sox finally broke The Curse to win the World Series in 2004, Boston's closer, Keith Foulke, threw 97 innings, including 14 in the postseason. Although he didn't know it at the time, The Curse wasn't the only thing to end that season -- Foulke's career essentially did, too.
"Foulke was so good for a number of years," says Diamondbacks GM Josh Byrnes, who was a Red Sox executive during the curse-breaking season. "He pitched great in 2004. We really leaned on him in the postseason. Maybe that took something out of him because he was hurt in '05."
Foulke saved a total of 16 games in his final three seasons -- and was out of baseball by 35.
Hall of Famer Rollie Fingers isn't as quick as Eckersley to anoint Rivera the greatest ever. Fingers says Rivera doesn't do as much as closers from his generation did.
"He's up there, but it is tough to compare him to the class we were in because it is different eras," Fingers says. "He is a one-inning pitcher. We threw three or four innings. It is apples and oranges."
Fingers pitched an average of 110 innings per season, including the postseason. Rivera has averaged 82.
But Rivera has thrown 133 1/3 postseason innings; Fingers threw 57 1/3. Those high-stress, high-leverage innings are the ones that evaporate a closer before your eyes.
"That is the other part of Rivera," Byrnes says. "Most of his career, he has pitched an extra month and he has pitched great in the postseason, and he keeps on going."
In terms of modern closers, Trevor Hoffman is comparable to Rivera, at least during the regular season. Hoffman, 42, has a major league-record 591 saves in 17 seasons. Rivera has 526 in 15 seasons.
Still, Hoffman, who missed 2003 thanks to shoulder surgeries, has pitched predominantly in a low-pressure environment on teams that aren't often in contention. And when he has been given the chance in October, he's melted.
Injury is the most common way that closers finish their careers, but it also can come down to how they are used, Fingers says.
In 1985, Fingers and Brewers manager George Bamberger didn't get along. Fingers, who felt he got stronger with more work, didn't like all the days off that Bamberger gave him.
"We didn't see eye to eye," Fingers says.
At age 40, Eckersley had nearly a 5.00 ERA but still had 29 saves in his final year with the A's in 1995. He followed Tony La Russa to St. Louis but felt he left his best stuff in Oakland. During his final three seasons, the last one in Boston, Eckersley posted 67 saves, a 3.89 ERA and a WHIP of 1.19.
From the outside, those are serviceable numbers. Inside, Eckersley knew better.
"The last three years, I didn't really throw the ball very well," Eckersley says. "It's really hard to find out because you have such a small piece of the game that you can get by without really throwing all that well for a long period of time. You can kind of hide a little bit. You have to blow three or four in a row before you open somebody's eyes and they say, 'Wait a minute.' It takes a while. It is not like one day all of a sudden you just drop off."
Rivera's velocity has dropped, but his production hasn't yet. Yankees manager Joe Girardi is handling him with care -- especially during the regular season.
Rivera says he will be the first to know when it's over, and he won't wait years to leave.
"One day that will happen," Rivera says. "That day, I will go."