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This would be one of Detroit sports history’s all-time cross-ups.

A team is so flimsy of a playoff contender that even the front-office decides at midseason it’s time to unload attractive parts and look to the future.

And then that team, the Tigers, somehow catches fire.

It finds its starting rotation has calmed down. Its batting order, always muscular, scores a steady stream of runs and doesn’t seem to notice J.D. Martinez was one of the names jettisoned in a Tigers July liquidation sale. The bullpen cooperates even as one of its invaluable assets, Justin Wilson, is dealt ahead of the July 31 trade expiration date.

This is one screwy script. It also happens to be mathematically possible, at least if you’re into baseball improbabilities.

And this clearly is improbable.

The Tigers whipped the Twins again Sunday, 9-6, and are still closer to last place in the American League Central Division than they are to first-place Cleveland.

So, envision playoff scenarios at your own risk.

Here are the raw facts, which should discourage any postseason fantasies yet harbored within Tigers Nation.

The Tigers remain a team estranged from even the .500 mark as they bring a 45-52 record into Monday night’s game against the Royals at Comerica Park.

They are in fourth place in a division the confounding Indians rule with no better than a 51-45 record. That leaves the Tigers 61/2 games in arrears.

But what about that faithful friend of baseball’s ever-hopeful congregation, the wild-card race?

Ah, the Tigers’ version of the Optimists Club has its work cut out there, as well. The Tigers are ninth among a dozen American League wild-card contenders, which joins with other realities in suggesting Comerica Park’s playoff-ticket printer can for now remain in storage.

But here’s the catch. Numbers are irrefutable. And any team, in any race, which finds itself 51/2 games from the top spot, even in a stack-up of wild-card playoff contenders, can wonder what might happen if, well, weird stuff were to occur in a sports world that sometimes gives birth to mutant monsters.

The Tigers happen to have this going for them.

They’re very good in their division, at least compared with the rest of the gang.

Detroit is now 24-19 against its Central Division neighbors, best of any team in its grouping.

The Tigers are 6-3 against the Twins, 6-4 against the Twins. They’re even (6-6) with the Indians and White Sox.

And given their fortunes to date, they might — might — be happy that they’ve got another 10 games with the Twins, nine with the Royals, and seven each with the Indians and White Sox.

They also are staring at a bare minimum against baseball’s best bunch, the Astros, who arrive next weekend for a three-game series.

They have a mixed bag of interleague games remaining: four in a home-and-home series with the Pirates, followed by three late in August at Colorado. Their record to date in interleague tussles is 4-6, so nothing to date implies there will be any edge there, especially when Tigers general manager Al Avila hasn’t backed away from the trade throttle.

Ponder also a trip to New York next week for a three-game set against the Yankees.

By that time, the trade deadline will have passed and the Tigers will have a better sense for who remains part of a baseball family likely headed for further fragmentation.

Avila is in charge there, of course. And he already has expressed thoughts on this team’s playoff legitimacy. The boss’ verdict arrived last Tuesday with news J.D. Martinez was headed to the Diamondbacks.

Arizona, it should be noted, wanted Martinez for the sole reason it views itself as a postseason contender.

The team that sent him there showed either noble honesty or premature pessimism in coming to a different conclusion about itself.

We’ll go with the former. With respect to a so-so team’s playoff chances, sometimes the numbers do lie.

Division darlings

The Tigers have the best record in the AL Central in intra-division games this season.

Detroit .558 (24-19)

Cleveland .545 (24-20)

Minnesota .511 (23-22)

Chicago .452 (19-23)

Kansas City .439 (18-23)

Twitter @Lynn_Henning