This dash for Kimbrel appears to have a starting gun. At 12:01 a.m. Monday, the 31-year-old truly will be free — of compensation penalties that drop from him when the amateur draft arrives this week; those are Major League Baseball’s rules. By the Fourth of July, he will be in game shape and, almost surely, atop someone’s pitching mound.

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Baseball has wondered since November why no one has signed the free agent pitcher with the lowest ERA (1.91) in the past 100 years. Meanwhile, Kimbrel, who now will miss at least half this season, sat and waited. How did this happen?

Questions soon should start getting answers. Was Kimbrel’s wildness in his last 45 innings of 2018, with 32 walks and a 4.00 ERA, a sign that he is getting old fast?

Are MLB’s current penalties for signing a player who turned down a qualifying offer from his old team ($17.8 million in 2018) so onerous that they can slash the value of a near-legendary closer? Or were Kimbrel and his agent delusional about his value in a relief market that has cratered with the top deal for a free agent closer dropping from $86 million to $52 million to $39 million over three years?

No team is in a tougher spot than the Nats, who have a heinous bullpen with an ERA (7.23) far worse than any team in this century. Should the Lerners go all-in on this season, and 2020 and 2021 as well, when their three rotation stars are all in D.C.? Would Kimbrel, coupled with Sean Doolittle, fix their bullpen instantly and transform the Nats into contenders in what has felt like a lost season? Or by the time Kimbrel is set to pitch, will the Nats’ hopes for this season be dead? By the July 31 trade deadline, will they be sellers? By next season, will Anthony Rendon, now in his walk year, think the Nats, with or without Kimbrel, are going nowhere and leave D.C.?

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Then we might see Kimbrel as just another dumb Nationals decision this season.

The stakes are high. The teams who miss Kimbrel, especially if he signs soon for a sensible $60 million or so, will be reminded constantly for years — especially if the team that lands him is in the same division. In the National League East, the injured Phillies and closer-needy Braves are certainly eyeing Kimbrel.

Seldom have teams, especially the 25-33 Nats, faced such a double-edged sword that might slash through their problems — or leave them bleeding worse.

Here’s the big temptation: On Monday, all it will cost to acquire Kimbrel is just dirty ol’ money. Those who signed Bryce Harper, Manny Machado and Patrick Corbin suffered compensation penalties in amateur draft picks forfeited, as well as international bonus pool money lost.

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But how much money is Kimbrel worth?

Seldom has there been such a crazy divergence in rumors and reasoning. This week, deals of more than $100 million and as low as $40 million have been reported as possible prices. Some say that, now free of compensation, he has wisely maximized his value and will ignite a bidding war. Others note that, by sitting out, he has presumably already sacrificed half-a-year’s value in his next contract.

The main point to grasp in Kimbrel’s weird situation is the impact of the now-seen-as-disappointing signings of Aroldis Chapman, Kenley Jansen and Mark Melancon for a total of $226 million after 2016. Doesn’t Kimbrel grasp that the relief market is now defined by the deals of Wade Davis ($52 million before the 2018 season) and Zack Britton ($39 million) last offseason? Why should Kimbrel dream he’s in a different universe?

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This is where the mystery gets fascinating. Will a contrarian team, perhaps the Nats, spot a bargain in a market segment that’s irrationally oversold? Will they pay a sane price to take a sensible risk on a pitcher who has been insanely superb?

Modern major league baseball prides itself on following the methods of Wall Street, always searching for “market inefficiencies” through stats and math. That’s fine. But great inefficiencies also can be driven by psychology. Herds often run in the same direction — even off cliffs. Every crash ends in a panic that, in hindsight, was overdone by mass fear.

Another fog-of-war factor is that no team knows exactly how other teams value those dastardly compensation penalties in picks and international money.

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MLB executives have pitched the angle for two years that they are staying away from players such as Kimbrel because they can’t face losing precious draft picks. What? When the chances are maybe 100-to-1 on finding a Kimbrel?

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All of this makes me think Kimbrel soon may discover that the “compensation problem” was not the issue that held down his market price. Maybe it’s more a case of happy owners and executives finding reasons to depress salaries. Nothing is easier than convincing yourself of something you deeply want to believe.

My gut is that, just as with Bryce Harper and others, Kimbrel is never going to get the deal he thought he would, either in choice of new home or salary. Someone may get Kimbrel for $60 million. But they may have to break from the pack, as the Nats did in offering $140 million to Patrick Corbin because he was a perfect fit for their starting rotation.

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If Corbin changed the Nats’ rotation for years and makes D.C. an appealing spot for Rendon to stay, then how much would Kimbrel uplift the Nats’ bullpen and show good faith to Rendon, too, for half the cost or less?

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The Nats know they have more than $30 million dropping off their books after this season. They can afford Rendon and Kimbrel and stay under the luxury tax ceiling next season and beyond, with plenty to spare.

Their bullpen is burning down. Kimbrel is the best fireman of his generation.