Angels beat Reds, 9-2, in a game with more potential impact than you might think

A half-game separated the basement-dwelling Angels and Cincinnati Reds as they began a potentially pivotal series Monday night in Angel Stadium, where the Angels got home runs from five players in a 9-2 demolition of the Reds.

Five other teams — Oakland, Milwaukee, Tampa Bay, San Diego and Arizona — are within 1 1/2 games of the Angels, who are tied for last place in the American League West, and the Reds, who are last in the National League Central.

As August turns to September and pennant races heat up, the seven aforementioned clubs are jockeying for a prize that has nothing to do with division titles, wild-card berths or home-field advantage in October:

The third pick in next year’s draft.

With the 2017 draft going in reverse order of the 2016 standings, Atlanta (48-83) and Minnesota (49-82) are the favorites for the top two picks. Barring a September surge, the Braves and Twins, who are six games “ahead” of Arizona for the second pick, will be difficult to catch.

But with the Angels among seven teams bunched up near the bottom of the heap, they could go from picking third next year to ninth depending on their finish, a huge swing.

For example, Baltimore used the third pick in 2010 on third baseman Manny Machado, who blossomed into a three-time All-Star and most-valuable-player candidate.

San Diego used the ninth pick of that draft on a high school pitcher named Karsten Whitson, who did not sign with the Padres. Whitson eventually signed with Boston as an 11th-round pick in 2014, but his professional career has consisted of seven innings for the Class-A Lowell Spinners.

Tampa Bay used the third pick in 2006 on third baseman Evan Longoria, a four-time All-Star. Baltimore used the ninth pick that year on third baseman Billy Rowell, who never played above double A and was released after serving a 50-game suspension, having tested positive for marijuana in 2012.

Baseball has a strong aversion to the concept of “tanking,” even though the Chicago Cubs and Houston Astros did a good job of it while hoarding top picks to build into the contenders they are today.

But there is no denying the fact that the Angels could actually win by losing over the final month of the season.

To that end, the Angels took a 2-0 deficit in the first inning Monday night when Billy Hamilton singled ahead of Joey Votto’s two-run homer for the Reds.

They couldn’t hold it. Kole Calhoun doubled in the bottom of the first, Mike Trout blasted a two-run homer to center, his 25th of the season, and Albert Pujols crushed a solo shot to left, his 26th, for a 3-2 Angels lead.

Trout joined Frank Robinson and Eddie Mathews as the only players with five 25-homer seasons prior to their age-25 season. Pujols’ homer was the 586th of his career, tying him with Robinson for ninth place on baseball’s all-time list. It was also his 1,800th career run batted in and 1,200th extra-base hit.

Trout doubled in the third and scored on Pujols’ single, making Trout one of two players with five 100-run seasons before age 25. The other: Alex Rodriguez. C.J. Cron followed with a two-run homer to left, and Jefry Marte, swinging at a 3-0 pitch, lined a solo shot to left for a 7-2 lead.

Calhoun added a solo homer in the fourth, and Marte had an RBI double in the seventh to back Matt Shoemaker, who allowed two runs and seven hits, struck out seven and walked none to improve to 9-13 with a 3.91 earned-run average. The Angels have won five of six games.

“We’re playing to win,” Trout said, laughing at the notion that the Angels should lose more to improve their 2017 draft lot. “We’re not gonna just tank the rest of the season. We’re gonna try to end on a positive note and go from there.”

mike.digiovanna@latimes.com

Twitter: @MikeDiGiovanna