On a strict cost-to-benefit, dollars-to-innings ratio, the rebuilding Twins signing their 33-year-old closer to a lucrative long-term contract this spring didn't make much sense to a lot of people.

Here's when it makes sense: When you've just clawed back from a 6-0 deficit to take a 7-6 lead into the bottom of the ninth, the fleet Curtis Granderson is on second, and the powerful Miguel Cabrera is standing at the plate, threatening to tack an ugly ending onto a wonderful homestand.

Sunday gave us one of those iconic baseball moments -- elite closer facing elite hitter, closer cuts loose, hitter takes a cut ...

And, this time, misses. Of course, when Nathan's on the mound, that result is all too predictable. Sunday, Nathan earned his 11th save of the season, giving the Twins a sweep of the Tigers and the homestand and giving Nathan 18 consecutive save conversions.

This is why Nathan's four-year, $47 million contract made sense even for a revamped Twins team: The front office was able to sign an elite player at a reasonable price without giving him a no-trade clause. And there is no debating just how elite he has become.

As a Twin, Nathan has converted 171 of his 185 save opportunities. That's 92.4 percent -- the highest in baseball since he became a Twin in 2004. His save total -- 171 -- is second in baseball during that time to San Diego's Trevor Hoffman.

With Nathan in place, the Twins are in first place in May -- better than any rational observer would have expected. Nathan has an 0.69 ERA this year, and the only run he allowed came in a nonsave, get-some-work-in outing in Texas. And he has yet to find his groove.

When Nathan is on his game, he can blow away hitters with his fastball and slider. Lacking dominant stuff at times this season, he's relied on a two-seam fastball.

"The second half of last year I wanted to throw something hitters had to think about, to get them off my slider," Nathan said. "It runs the opposite way of my slider. Last year I gave up a lot of hits and a lot of hard-hit balls, and a lot of them were off my slider. That let me know that guys were looking for it. Last year I got comfortable with the two-seamer.

"We say we try and learn in this game every day."

Nathan throws a four-seam (straight) fastball, a two-seam fastball that tails a bit, a big curve and a slider. "I know when I go to the plate, I'm trying to eliminate pitches that I have to worry about," said catcher Joe Mauer. "With Joe, you can't. He can beat you with four pitches."

And maybe someday five. Nathan works constantly on a changeup in the bullpen, although he said he has thrown only a few in games. "I feel like maybe sometime in my career I'm going to have to learn to change speeds a little better," he said. "The more I can learn to throw it, the better off I'll be."

His save on Sunday was accompanied by his usual idiosyncrasies. When Nathan takes the mound, he tends to shake his head, flutter his lips as he violently exhales, and flick his head, equine motions that have caused at least one Minnesotan to call him Joe "Neigh-than."

"I hear about it quite a bit," he said. "From the fans. From my family. Well, not my family so much any more.

"When you're out there in a tight situation there are things everybody does, whether you do it because you don't know that you're doing it or it's a comfort thing, or a routine.

"I do have some quirks. Some of them are out of my control, some are within my control. It just gets me to a relaxed state where I feel comfortable, where everything feels right. It's like a hitter adjusting his batting gloves before he's seen a pitch, or a golfer's routine before a shot.

"I might do a little more than they do, and it might be a little more quirky, but it's the same agenda."

It's a routine to which we've grown accustomed: Nathan enters, twitches, dominates, exults.

He's the best closer in Twins history, and the best closer in the game since 2004. And if he keeps this up, his new contract will soon be viewed more as a bargain than as a luxury.

Jim Souhan can be heard Sundays from 10 a.m.-noon on AM-1500 KSTP. jsouhan@startribune.com