The Red Sox have agreed to a three-year deal with free agent Mike Napoli. (AP)

NASHVILLE, Tenn. — The Red Sox finished 2012 ranked ninth in the American League with 165 homers, 10th in OBP (.315), 12th in OPS (.730) and second to last in walks (428). They needed to find ways to infuse both power and plate discipline into their lineup.

Now, though they are leaning heavily right-handed, they have moved aggressively to improve upon those deficiencies.

According to multiple major  league sources, the Sox have reached a three-year, $39 million deal with free agent Mike Napoli.Napoli thus becomes the third signing by the Red Sox this winter who fits the profile of a power hitter who exhausts pitchers with tenacious at-bats.

Though Napoli hit just .227 in 2012, he still had a strong .343 OBP, .469 slugging mark and .812 OPS on the strength of 24 homers and 56 walks in 417 plate appearances. He walked in 13.4 percent of his plate appearances, up slightly from his 11.9 percent career rate, and went deep once every 14.7 plate appearances, also slightly better than his career average of a homer per every 15.5 plate appearances.

There are a couple of red flags from his 2012 season, including the fact that he missed about a month in August and September due to a leg injury (believed to be a considerable part of the Rangers’ reluctance to make him a qualifying offer, thus meaning that he didn’t cost the Sox a free-agent pick), that he had very few doubles, leading to a career-low rate extra-base hit rate of 8.4 percent and that he struck out in a career-high 30 percent of plate appearances.

Still, even in what represented a down year, Napoli represented a player capable of sliding into the middle of the Sox lineup and helping to address a couple of the team’s foremost weaknesses. And he’s not alone.

David Ross has 24 homers in 663 plate appearances over the last four seasons as a part-timer in Atlanta. He’s walked in 11.3 percent of plate appearances in that time, with a .353 OBP.

Jonny Gomes is coming off a season when he slammed 18 homers in just 333 plate appearances with a career-high .377 OBP thanks to a 13.2 percent walk rate.

All three also produce steady at-bats along the lines of what the Sox relied on during their run as a perennial elite offense from 2003-11. Gomes averaged 4.03 pitches per plate appearance last year; Ross averaged 4.26 pitches per plate appearance; Napoli averaged a whopping 4.41 pitches per plate appearance. In other words, the Sox — who are still short an outfielder — have now constructed a team that will feature hellacious at-bats, particularly against left-handers.

A look at how the Sox lineup might look, pending the acquisition of another outfielder, against left-handers:

Jacoby Ellsbury

Dustin Pedroia

David Ortiz

Mike Napoli

Will Middlebrooks

Jonny Gomes

David Ross

??? (OF)

Jose Iglesias (assuming that the Sox do not acquire another shortstop)

That’s a top seven that has an impressive capacity to knock opposing starters out of games early and then to do damage against other teams’ most vulnerable element, middle relief. It also seems like a group with the potential to assault the left field at Fenway Park.

Against lefties, the team could replace Gomes with Ryan Kalish or Daniel Nava, with Jarrod Saltalamacchia (unless he is traded) taking over for Ross behind the plate.

Either way, it’s a deeper and more threatening lineup than the one that the Sox featured last year; if the group remains healthy, then the quick outs that characterized the later stages of last year may prove a distant memory in 2013.