It would be easy to have overlooked Matt Magill coming into this season.

He’s 28 — he’ll be 29 in November — and he came into this year with a couple of shots of espresso in the big leagues. Not necessarily good ones, either.

The short answer is that he had a 6.47 ERA, more walks (33) than strikeouts (27), more walks than innings pitched (32) and hadn’t seen a big-league mound since a 4.1-inning stint with the Reds in 2016.

His numbers in Triple-A El Paso (Padres) last year were nothing to get too excited about, either. He worked just under 100 innings — almost exclusively as a starter — with a 3.95 ERA, 6.9 strikeouts per nine innings, 3.9 BB/9 and a WHIP of 1.53.

The common thread here, however, is that affiliation with the Padres. Last year, Garvin Alston started the year as a minor-league pitching coordinator in San Diego’s system before finishing the year with the Oakland A’s as the big-league bullpen coach.

What did Alston know about Magill coming into this year? “A little,” Alston said with a smile after Monday night’s game, perhaps suggesting there was more than he was willing to let on in the moment.

Sometimes it’s the small connections that lead to big-league ties.

Sometimes it’s also a small switch that can make a major change in what a player brings to the table.

In this case, the move to full-time reliever agreed with Magill in a big way. It was clear from the outset, as the big righty was absolutely dominant at Triple-A Rochester. Through 8.2 innings before the Twins purchased his contract in late April, Magill was unscored upon with 13 strikeouts and just two walks.

The stretch was so dominant, Magill didn’t even give up an extra-base hit as opposing batters hit just .161/.212/.161.

And what’s kind of funny is that Magill only came up because the Twins needed some length out of the bullpen. Sure, it helped that Gabriel Moya and Alan Busenitz were not yet eligible to return from Rochester due to the 10-day rule — a player sent back must wait 10 days to return, unless a player is placed on the disabled list — but it also helped that Magill was primarily a starter previously and had thrown 20-plus pitches in each of his last three outings with the Red Wings.

In fact, it’s one of the shortest tenures in Twins history which led to Magill coming up in the first place. The Twins went through a tough series against the Yankees in late April, and brought reliever David Hale back with them as he was designated for assignment during the series (by the Yankees) and claimed (by the Twins) as it ended.

Hale’s claim was processed on April 26, and he was activated on April 27. That night, he threw four innings of relief in a loss to the Cincinnati Reds, and was promptly designated for assignment after the game.

Magill was in the clubhouse next day, curiously enough sporting Cincinnati Reds luggage — the last MLB team he played for, but also the team in the opposing clubhouse. Magill even sheepishly joked with reporters that he’d just turn that side of the luggage to the wall to avoid any conflict.

The initial role for Magill was to provide some depth to a beleaguered bullpen, and he did just that. But with Phil Hughes being moved into a long relief role, that — along with Magill’s quick adjustment to the level — has allowed manager Paul Molitor to shuffle the deck chairs a bit.

Magill worked two-plus innings in three of his first four outings in the big leagues, but has not worked more than an inning in any of his last five. That doesn’t mean he’s necessarily throwing huge spots — just two of those outings have come with an above-average leverage index, according to Baseball Reference — but it has been a usage pattern more consistent with a pitcher working his way up the power structure, one might say.

Regardless of usage, the numbers are impressive.

“Magill’s done a nice job,” Molitor said at Target Field on the last homestand. “We all know the story behind his getting back to the big leagues. He’s a strike-thrower — two-pitch mix — and he’s got enough velocity for some of those parts of the lineup where he can elevate a little bit and get them to chase, you’ve got a good chance. Plus he’s been a little bit more resilient than I expected. I’ve been able to use him quite a bit.”

The strikeouts haven’t entirely followed Magill from the International League, but he’s fanned 10 batters with just one walk through 11.2 innings and has an ERA of 1.54 with just one homer allowed.

One thing that jumps off the screen is that according to Fangraphs, Magill is averaging 94.6 mph with his fastball. He throws that and his slider pretty much exclusively, and that represents a nearly 3.0 mph jump from his average fastball to this point of his career (92 mph).

There isn’t much in the way of reputable velocity metrics for minor leaguers, but Magill estimates he was right around his career velocity last year with El Paso.

“It was probably low-90s last year starting,” he said. “But this year it has been nice to just go out and throw everything I’ve got at the guys, going two or even three innings. It just feels more comfortable.”

The slider — some places call it a cutter — averages 85.9 mph and gets a healthy swinging-strike rate of 14.6 percent. He won’t throw the changeup much, but when he does, hitters haven’t made too much contact on it (18.2 percent whiff rate).

“The slider has always been my bread-and-butter pitch to put people away,” Magill said. “This year my changeup has really stepped up. It gets a little drop and a little fade. It’s not so crazy, but I’ve been more comfortable throwing it in any count. I think that helps me really offset the fastball. It makes hitters have to think about a third pitch from me, which helps me consistently throw fastballs. I throw it mainly up in the zone to help me get hitters staying off my fastball.”

While Magill has only thrown 11 changeups, it’s something he’s tinkered with — and oddly enough, found in a catch session with his pops.

“It was a different grip I changed it to,” Magill said. “I just did it myself. I was playing around with grips one day in the offseason. I was throwing with my dad, and I said ‘Let’s try a different grip.’ I put my middle finger to the side of the ball and my ring finger on the other side. My changeup has always been too hard, and I want separation. It’s still pretty hard, but my fastball is coming out better now than in the past. So I’ve added to the fastball and subtracted from the changeup.”

The velocity jump-started in Rochester, and like most pitchers it certainly helped a lot that he was working in shorter bursts out of the pen, as opposed to being asked to face the same lineup two or three times.

“I think I’m finally growing into my body a little bit,” Magill said. “I think my body is getting stronger and I’ve been having better success in my offseason works in elongating. My workouts have gotten better as I’ve gotten older and gotten to know my body better.”

Strangely enough, time away from the game helped as well, Magill said.

“Honestly too, the Tommy John surgery in 2015 allowed me to take a year off,” he said. “That allowed my body to rejuvenate. I’ve been playing since I was 10 years old. Having that year off from baseball, I think, was great for my body.”

But while the year away was good for Magill physically, it was difficult mentally.

“It was tough,” Magill said. “But it also helped me appreciate the game better, so that’s what I really loved about it. It helped me appreciate every moment and game I got to play. Obviously in the bullpen, throwing shorter spurts allows you to throw everything you’ve got at them.”

Changing his workouts has been key for Magill as well, as he’s changed his mindset from lifting and bulk to a more yoga-based approach. Glen Perkins noted his velocity jump after scoring traditional weightlifting in favor of a less-obvious strength regimen.

“I’m trying to elongate my muscles instead of build up bulk,” Magill said. “I’m doing more explosive stuff with medicine balls and yoga. Slow, stretching workouts instead of grabbing huge plates and putting them on the squat bar and squatting and benching as much as you can. I’m doing plyometrics, and that type of thing. Resistance bands. Getting away from the traditional football-type workouts.”

How much velocity a pitcher can gain after making the change from starter to reliever is not always consistent. Perkins is sort of the gold standard in this respect, as his fastball went from as low as 89.7 mph on average in 2009 to 94.9 in 2012 and again the next year.

Brian Duensing, meanwhile, bumped up briefly in 2013 — his first year as a full-time reliever — from a consistent 91 mph to 92.2, but found himself right back where he was beforehand in the subsequent years. Tyler Duffey saw a jump in velocity — 90.4 mph to 92.1 — but was unable to turn it into sustained success.

It’s a guessing game, and frankly even the players themselves can’t be too sure how it’ll play out.

“I think it’s just ‘Let’s see what happens,’” he said. “I’m throwing everything I have behind every pitch, because you just never know which guy is the last one you’ll face. I just want to give everything I have. I felt like if I gave up a hit because I didn’t put everything behind that pitch, I’d be upset with myself. So I’m just going to throw everything I have.”