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The easy thing to do would be to let it go, to say there’s too much ground to make up and not enough time to get there.

After all, the numbers suggest that’s the case, right? The Tigers began this crucial 10-game homestand at Comerica Park with the second-worst record in the American League. According to Fangraphs, they have a 6 percent chance of making the playoffs.

Yet Mikie Mahtook was facing the same long odds late Tuesday night in the top of the fifth inning of the series opener against Kansas City. The Tigers had just stretched their lead to 5-3 in the fourth, and Justin Verlander appeared to have settled in after a shaky start. But then came the crack of the bat from Salvador Perez, the Royals’ catcher who always hits Verlander hard.

This one was hit really hard, though — 106 mph off the barrel, according to MLB’s Statcast — and by the numbers, the “hit probability” was 94 percent. To the naked eye, even that seemed a bit low, as Mahtook, the center fielder who’d been shading Perez toward left-center, took off running.

“I didn’t think he had a chance on that ball,” Tigers manager Brad Ausmus said. “I didn’t think there was any chance he would catch it.”

Mahtook wasn’t quite as convinced, however. In fact, he was still kicking himself over one that got away in the first inning, when Verlander allowed the Royals five consecutive hits before recording a single out.

The first of those was Whit Merrifield’s ground-rule double to center, a line shot that one-hopped over the fence into the shrubbery.

“I didn’t like pulling up at the end and the ball bouncing over,” said Mahtook, the 27-year-old acquired from Tampa in January. “I may not have been able to get it, but it’s one of those things where I just wish I would have maybe taken an extra step to lunge and get there. Those kind of stay with you, especially after they score a few runs.”

But after the Tigers scored some of their own, thanks to home runs by J.D. Martinez and Miguel Cabrera, and then tacked on another run in the fourth to make it 5-3, Mahtook figured he had a chance to make amends, even if no one else did.

“I knew I had a pretty good jump on it,” he said. “At that point, it was just a matter of whether I was gonna be able to get to the ball in time.

He did, just barely, leaping and extending his left arm — and snaring the ball in the heel of his glove — just as he crashed shoulder-first into the wall, the collision sending him into a backward somersault on the warning track. He managed to hold on to the ball, and from the pitcher’s mound, Verlander raised both arms in celebration while the crowd roared. Perez, who was nearing second base, doffed his batting helmet in salute. Mahtook, meanwhile, was still on the ground trying to figure out if he was OK,

“The wall doesn’t feel good, ever — I don’t care how much padding there is,” he said. “I think every bone in my back and my body cracked, so at that point I was just trying to get the air back in my lungs.”

By the time he reached the infield, he was breathing better. And so was Verlander, who was there waiting for a hug and a high-five.

“He came off the field and said, ‘I owed you that one,’ ” laughed Verlander, who insisted the feeling was mutual. “It’s always a great moment seeing your teammate lay out and sacrifice his body to make a play for you. It doesn’t get much better than that.”

Of course, it couldn’t get much worse than what we’d seen from the Tigers lately, coming off a 1-6 road trip, an eight-game losing streak and losers of 14 of their last 20 games.

“We were struggling, inventing ways to lose, it felt like,” catcher James McCann said.

And yet it hasn’t felt like the effort wasn’t there, whether it’s Justin Upton making a diving catch or taking an extra base or Jose Iglesias chasing a foul pop-up into the stands.

“Even though we’ve struggled, the clubhouse has always been good, the players have always gotten their work in, they play hard,” Ausmus said. “Even when we’re struggling, these guys are busting their butt down the line. I’ve been happy with the way the guys have gone about their business.”

Tuesday night, that was especially true, as the Tigers played some inspired defense behind Verlander. Mahtook’s catch might’ve been the highlight, but there was Cabrera diving to smother a hard shot off the bat of Alex Gordon and then scrambling on all fours to toss the ball to Verlander for the out. And there was Iglesias — again — ranging far to his left behind second base to make the final out in the eighth with a backhanded flip to Ian Kinsler. In the ninth, it was Andrew Romine coming in cold as a defensive replacement and immediately making a bare-handed grab to nab Gordon on another liner, this one a ricochet off closer Justin Wilson.

Whether that’s contagious or not, time will tell. But Ausmus admits Mahtook’s recent play might spark something. He’s batting .364 with a .955 OPS in June, and after Sunday’s game-winning hit in San Diego, Mahtook added two more hits out of the No. 2 hole Tuesday, including a single off a nine-pitch at-bat that helped set the table for Cabrera’s three-run homer.

“He’s been swinging the bat well,” Tigers manager Brad Ausmus said. “He had a big hit on Sunday and had some big hits today. … He has worked real hard on his swing through the spring — staying through the ball, staying on the ball longer. I think we’re starting to see the dividends pay off.”

And for Mahtook, that could mean more than a strict platoon in center field. He has been limited to facing left-handed starters, for the most part, but Ausmus kept him in the lineup Wednesday to face righty Ian Kennedy.

“Whatever we think helps us win ball games,” Ausmus said.

But whatever they think, Mahtook knows what matters is the effort — and it shows.

“You win games here because you wanna play for the guys in the clubhouse,” he said after Tuesday’s win. “To be able to come up with a play like that and have the guys meet me in the dugout, it was great. It’s something that obviously I hope I can do a lot more of. The guys in here give you the motivation to go dive into walls.”

john.niyo@detroitnews.com

twitter.com/JohnNiyo

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