Aaron Cook has agreed to a minor league deal with the Red Sox. (AP)

A compelling case can be made that newly added Red Sox pitcher Aaron Cook – who has an agreed to terms, pending a physical, on a minor league deal that includes an invitation to big league camp, with a $1.5 million salary should Cook make the big league roster — is the best pure sinkerballer in the majors over the last decade.

The right-hander, who turns 33 next month, has always had below-average swing-and-miss rates. His strikeout rates, too, are typically well below average. That suggests a pitcher who had little or no business succeeding with the Rockies while hitting in Coors Field, a park whose vast expanses give any ball hit in play — especially in the air — an excellent chance of finding a hole.

There are 79 big league pitchers who threw at least 1,000 innings in the last 10 years. Of those, Cook’s 3.8 strikeouts per nine innings represents the lowest mark in the majors.

Yet while Cook did not get swings and misses in his career with the Rockies, he still was a very good pitcher through most of his career in Colorado. In particular, from 2002-09, Cook was 63-50 with a 4.33 ERA (good for an ERA+ of 111, or roughly 11 percent better than league average when adjusted for ballpark and opponent) thanks to a turbo sinker (a pitch he’s thrown roughly 80 percent of the time in his career) and the fearlessness to pitch to contact in an environment that did not necessarily reward such a strategy. The former second-round selection was a career 36-32 with a 4.65 ERA in Coors Field, and 36-36 with a 4.39 ERA on the road.

Cook’s stuff makes him something of an outlier. Since 2000, just 34 pitchers in the majors have thrown at least 120 innings in a season, struck out fewer than 4.5 batters per nine innings yet produced an ERA+ of 100 or better (meaning league average or better). Only seven pitchers have done it multiple times. Cook has done it four times, more than any other pitcher in the majors since 2000. So, while he doesn’t represent the typical profile for a successful pitcher either in the AL East (which last saw such a season in 2006, when Chien-Ming Wang had such a year) or, for that matter, the majors, Cook has shown an ability to succeed in a fashion where others can’t.

However, he is now a couple years removed from the peak that made him one of the more effective pitchers the Rockies have ever had (and that led Colorado to sign the right-hander to a three-year, $29.5 million deal on which the Rockies declined a team option for 2012). Cook suffered a broken right index finger in spring training in 2011, didn’t pitch in a game until June and suffered from diminished command all year. The result was easily the worst season of Cook’s career: a 3-10 record and 6.03 ERA, along with a 1.691 WHIP, in 18 games (17 starts) and 97 innings.

That represented the continuation of a trend of decline. Since an All-Star 2008 in which he went 16-9 with a 3.96 ERA in 211 innings, Cook saw his ERA grow every year (from 3.96 to 4.16 to 5.08 to 6.03). His walks and WHIP also got worse on an annual basis, with his ERA+ and innings totals declining every year. Durability has also been an ongoing issue, as he has just two career seasons of 200+ innings, and three seasons of 160 or more innings. Some of that involved freak health issues — for instance, nearly fatal blood clots in his lungs in 2004 — but whatever the reason, he has not been a perennial innings eater.

That said, despite the physical woes, Cook is now believed to be healthy, and he has a close relationship with new Red Sox pitching coach Bob McClure, with whom he worked when McClure was a minor league coach in the Rockies’ system. He also will encounter another familiar face in Sox third baseman Kevin Youkilis, with whom he played on a national championship AAU travel team when both were 15.

Cook will compete for a rotation spot in spring training, joining a lengthening line of candidates for the last two spots in the rotation. Currently, the Sox will feature pitchers such as Daniel Bard, Alfredo Aceves, Felix Doubront, Andrew Miller, Carlos Silva and Cook in their rotation competition. Intriguingly, Silva, like Cook, is a pitcher whose best years occurred despite low strikeout rates (while Cook leads the majors in seasons of 120-plus innings with an ERA+ of 100 or better and a strikeout rate of 4.5 or worse, Silva is second in the majors since 2000 with three such years; his 4.0 strikeouts per nine innings are second lowest in the majors — to Cook — among starters with at least 1,000 innings over the last decade) — something that one source suggested was a coincidence rather than some kind of blueprint the Sox were seeking for buy-low starters.

If Cook is healthy and able to return to his peak, then the Sox will benefit from a pitcher who, at his best, isn’t terribly far removed in effectiveness from someone like Mark Buehrle, the left-hander whom the Marlins signed to a four-year, $58 million deal (in no small part because Buehrle has been one of the most consistent and durable pitchers in the game over the last decade) who is also a pitcher who succeeds despite low strikeout rates. And if Cook is either unhealthy or unable to pitch effectively, then the risk for the Sox will be minimal given the nature of a minor league contract.