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6/30/2014 10:26 P.M. ET

Like temperatures in Chicago, Abreu just getting warm

White Sox slugger on pace to set rookie, team marks for homers in season

CHICAGO -- Look out, Mark McGwire. You, too, Big Al Belle.

Jose Abreu is coming after you.

In fact, with the Major League Baseball season essentially at its halfway point, the big first baseman from Cuba is (just a little) more than halfway to the records you hold.

McGwire's 49 home runs with the 1987 Oakland A's are the most in a season hit by a rookie. Belle's 49 in 1998 are the most in a season for a White Sox player. Abreu, who entered Monday tied for the Major League lead with Edwin Encarnacion and Nelson Cruz, has already hit 25, which projects to -- guess what? -- 49.

And here's the reality.

If Abreu is healthy, and if the White Sox give him enough protection where he doesn't get the Barry Bonds treatment in terms of intentional walks, it should be no surprise if he flies past Big Mac and Belle. Abreu has made it past the tough part of the Midwestern baseball season and is entering the time when balls race into the seats at U.S. Cellular Field like bottle rockets.

Abreu doesn't hit cheap home runs. He blasts the ball into the distant seats in right field, as well as left. But when Abreu had his most impressive season to date, hitting .453 with 33 home runs in only 66 games for the Cienfuegos Elephants, he hit some soft flies that carried into the seats. That's going to happen this summer at U.S. Cellular Field, where the cheap homers will mix with the blasts halfway up the bleachers.

It's bound to happen, as Angels manager Mike Scioscia confirmed before Monday night's game against the White Sox was rained out, prompting a Tuesday doubleheader.

Even though Abreu was 1-for-12 in a series at Anaheim, Scioscia acknowledged that he's a special talent.

"We pitched him really tough and [he] still was dangerous at the plate when we played him in Southern California," Scioscia said. "You could see the bat speed. He just missed some pitches. We contained him, but I can see why he's putting up the numbers he is."

Abreu did blast a homer off the Angels' Tyler Skaggs in Spring Training, when he went 4-for-8 the two times he faced the Halos.

"He looks just like he has a special skill set at the plate, with the power and the bat speed, being able to drive the ball to all fields," Scioscia said. "If you miss your spots, he's going to let you know."

Abreu was the American League's Rookie of the Month and the AL Player of the Month in April, when he hit 10 home runs and drove in 32 runs for a White Sox team that was scoring runs at an unexpectedly high rate. He repeated the 10-homer output in June. Abreu didn't drive in as many runs, as nothing is coming easily for the White Sox now, but he started hitting for average.

That was the part that was missing early, and anyone who had seen Abreu in Cuba knew that it was only a matter of time until his average climbed toward .300. He was batting .260 at the end of May, but he hit .313 in June -- a sign of things to come.

"I think he's starting to understand when people are going to pitch to him and when they're going to pitch around him," White Sox manager Robin Ventura said. "Early on, he was being very aggressive in situations where guys were going to pitch around him, no matter who was batting behind him."

Abreu was known for his patience in Cuba, where he had more walks than strikeouts in each of his last four seasons in Serie Nacional. But excitement has gotten the best of him at times since signing his $68 million contract with the White Sox. Abreu told me early in the season that he doesn't swing at first pitches, but he wasn't able to stop himself from doing that.

Teams were able to exploit Abreu's overaggressiveness, but not so much lately. He had five home runs on the just-completed 11-game trip, including two over the weekend against Toronto. Ventura believes that Abreu has adjusted.

"There are just some teams that aren't going to give him anything to hit," Ventura said. "I think smarter pitchers are going to do that. They throw something out there and hope he'll swing. He's getting a lot better at understanding that -- when to be aggressive and when not to. That's been the learning curve for him, understanding that."

For his part, Abreu seems much more concerned about helping the White Sox get back into the playoff chase than dueling it out with Encarnacion and Cruz for the home run lead.

"First I want to thank God for getting those three [wins] in Toronto," Abreu said through translator Lino Diaz. "If you think about it, all those games, even in Baltimore, we were close. Everything was right there. They just played well. They played good baseball. They played good baseball, but we were happy to get those games. We played well in Toronto."

Abreu was asked if he believes that he can follow up his terrific first half with a strong second half.

"I can't predict what's going to happen, but the only thing I can tell you is my preparation is going to be there and I want to stay healthy," Abreu said. "If that happens, that's all we really have control over. We just continue to do the same things we've been doing and we'll see if we continue to have the same success."

If Abreu is healthy, if he gets pitched to, he'll have a better second half than his first half.

Some people argue that veterans coming from other countries, like Abreu and Masahiro Tanaka, should not qualify as rookies, but few players of any age are going through bigger transitions than the slugger from Cuba and the ace from Japan. It's remarkable what both of them have done to this point.

And from all indications, they're just getting started.

Phil Rogers is a columnist for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.