Matt Andriese, signed by the Red Sox last week, was 2-4 with a 4.50 ERA in 16 games with the Los Angeles Angels in 2020, 15 of those games in relief. AP Photo/David Zalubowski

Last week, the Boston Red Sox signed free agent swingman Matt Andriese, and invited five non-roster pitchers to spring training.

Andriese has a career 4.57 ERA. Of the five pitchers not on the 40-man roster, three have never pitched in the majors, and only one has pitched more than 25 innings.

Here is where we enter the snarky remark that Boston can start printing playoff tickets. But give the Red Sox and Chief Baseball Officer Chaim Bloom a break.

Bloom needs to accomplish two tasks before the 2021 season, and one is to build pitching depth – thus the signing of Andriese, as well as the minor league contract offered to Kevin McCarthy (the one veteran of the non-roster invitees, with 169 relief appearances with Kansas City, and a career 3.80 ERA).

Bloom’s other task is to improve the starting rotation – an imposing job that will likely determine Boston’s fate in 2021. Bloom knows the importance of the decisions that must be made this offseason.

“We need to be active,” Bloom said in a recent conference call with reporters. “We need to be fully informed. We need to make sure we have as much information as possible, and then try to make the best decision from there – looking at every decision in the context of the larger market.”

Safe to say that Bloom’s spreadsheet is crammed with possibilities or, as NESN announcer (and Press Herald columnist) Tom Caron wrote last week: “The Boston Red Sox are in on everybody.”

The “everybody” includes the role players, like Andriese, and possibly McCarthy. But, truly, the Red Sox need bigger help, as in a bigger name (or two) on the free agent market.

As we have mentioned before, it is a buyers’ market, although one possible target (Charlie Morton) has signed with the Atlanta Braves. The No. 1 free agent pitcher, Trevor Bauer, may be too expensive (beside also costing a second-round draft pick).

Boston’s top choice looks to be Jake Odorizzi, the Twins starter who also pitched five years for Tampa Bay (when Bloom was there). Odorizzi, 30, was 15-7 (3.51 ERA) in 2019. A variety of injuries limited him to four starts in 2020, but he appears healthy. And, maybe, his 2020 clunker might lower his asking price.

Other possible pitchers for Boston include Corey Kluber, Rich Hill and Japan’s Tomoyuki Sugano. Kluber, a two-time Cy Young winner, is a health risk (eight starts over the past two seasons). Hill is a possibility, although he turns 41 in March. And while Sugano is intriguing, his effectiveness in the major leagues is an unknown.

Whoever Boston signs, he (or they) need to slot near the top of the rotation. Boston has Eduardo Rodriguez and Nathan Eovaldi and then there is a drop-off, at least until Chris Sale returns from Tommy John surgery rehab. Odorizzi would fit in nicely. Adding another arm (Sugano, Kluber or Hill) provides veteran insurance.

With added arms, Boston would not need to rely heavily on pitchers like Nick Pivetta, Chris Mazza or Tanner Houck.

Pivetta was obtained last summer from Philadelphia in the Brandon Workman deal. Pivetta made 71 starts for the Phillies. In his two Boston starts, he struck out 13 and allowed two earned runs over 10 innings.

Mazza, claimed off waivers from the Mets, was inconsistent last year (1-2, 4.80 ERA), but still gives depth.

Houck shined when called up for three starts in September (3-0, 0.53 ERA). Houck could be eased into the rotation, at No. 5 – or begin 2021 in Triple-A.

Boston has pitching potential (and I did not even mention Bryan Mata as a possible call-up later in 2021).

But Bloom cannot rely on potential next season.

Proven arms will make Boston a proven contender.