Value is the name of the free agency game for Patriots

Matthews is set to make $1 million in 2018, with another $700,000 reportedly available in incentives.

Matthews comes to New England with plenty to prove. His 2017 season required surgeries on his thumb, ankle, and knee, and he finished with just 25 catches for 282 yards and one touchdown in 10 games with the Bills. So it’s understandable that he wouldn’t get much in free agency.

Matthews isn’t guaranteed a roster spot in New England, either. He received only $170,000 guaranteed (plus a $130,000 offseason workout bonus), and the Patriots won’t automatically give Matthews a roster spot just for paying him $300,000 before the season starts.

But if he’s healthy, he could be quite a steal. A 6-foot-3-inch receiver who plays mostly in the slot, Matthews scored 19 touchdowns in his first three NFL seasons, all with Philadelphia. Compare his salary with what the Patriots were going to pay Brandin Cooks — $8.459 million, fully guaranteed.

And it continues the theme of the Patriots’ offseason. They let all of their high-priced free agents walk and found value at every position. They added 18 players and subtracted 11 over the last month, yet have more salary-cap space now ($13.9 million) than they did entering free agency (about $12.3 million). This even accounts for the $2.4 million pay raise given to Patrick Chung, which didn’t increase his cap number.

Time will tell whether the Patriots’ value approach to free agency was the right one. Sometimes it works out, and sometimes you get what you pay for. But let’s take a look at their cost-saving moves at each position (dollar amounts are for 2018 season only):

IN

Rex Burkhead: $4.5m cash, $2.312m cap, $1.25m incentives

Jeremy Hill: $1.5m cash, $1.33m cap

Total: $6m cash, $3.642m cap, $1.25m incentives

OUT

Dion Lewis: $6m cash, $4.312m cap

Analysis: Hill might not make the team, and Burkhead has had durability issues throughout his career. But more of Burkhead’s money is tied to health and performance than Lewis’s, and Burkhead’s cap number is nearly half of Lewis’s.

IN

Cordarrelle Patterson: $3.25m cash, $3.25m cap

Kenny Britt: $1.5m cash, $1.45m cap, $500k incentives

Jordan Matthews: $1m cash, $1m cap, $700k incentives

Total: $5.75m cash, $5.7m cap, $1.2m incentives

OUT

Brandin Cooks: $8.459m cash, $8.459m cap

Danny Amendola: $6m cash, $6m cap

Total: $14.459m cash, $14.459m cap

Analysis: When you include Britt, signed at the very end of the 2017 season, the Patriots are getting three receivers for about the same salary as Amendola got from the Dolphins. Matthews and Britt have incentives, but that’s money well spent if either becomes a productive receiver.

If we want to just look at Cooks’s replacements, the Patriots are spending about half as much on Patterson and Phillip Dorsett as they would have on Cooks.

Cordarrelle Patterson: $3.25m cash, $3.25m cap

Phillip Dorsett: $1.54m cash, $1.54m cap

Total: $4.79m cash, $4.79m cap

And the Patriots clearly don’t put a high value on receivers. Amendola and Cooks will cost slightly less in cash and cap space than every receiver on the Patriots combined.

Chris Hogan: $3.5m cash, $3.28m cap

Cordarrelle Patterson: $3.25m cash, $3.25m cap

Julian Edelman: $3m cash, $4.17m cap, $500k incentives

Phillip Dorsett: $1.54m cash, $1.54m cap

Kenny Britt: $1.5m cash, $1.45m cap, $500k incentives

Jordan Matthews: $1m cash, $1m cap, $700k incentives

Malcolm Mitchell: $630k cash, $774,498 cap

Cody Hollister: $480k cash, $480k cap

Riley McCarron: $480k cash, $480k cap

Total: $15.38m cash, $16.42m cap, $1.7m incentives

IN

Troy Niklas: $940k cash, $940k cap

OUT

Martellus Bennett: $6.45m cash, $6.19m cap

Analysis: Niklas has to make the team first, but clearly, the Patriots had no interest in spending big money on another tight end. Interestingly, Dwayne Allen and his $5 million salary remain on the team. The Patriots liked Allen’s blocking abilities and locker room presence, but I’m very surprised that he has not been released or asked to take a pay cut, considering his contract has no dead money and he had just 10 catches for 86 yards and a touchdown last year.

Rob Gronkowski is a good bet to land a restructured contract this offseason, and the Patriots can actually lower his $10.9 million cap number while paying him more than his $9 million salary.

IN

LaAdrian Waddle $1.5m cash, $1.5m cap, $1m incentives

Luke Bowanko: $835k cash, $675k cap

Matt Tobin: $815k cash, $655k cap

Total: $3.15m cash, $2.83m cap, $1m incentives

OUT

Nate Solder: $22m cash, $10m cap

Cameron Fleming: $2.5m cash, $2.5m cap, $1m incentives

Total: $24.5m cash, $12.5m cap, $1m incentives

Analysis: Let’s take Solder out of the equation, because the Patriots probably still have to find a starting left tackle in the draft (who of course will cost a fraction of what Solder is making). The interesting comparison is Fleming, who signed with the Cowboys, and Waddle. The Patriots went with the cheaper option; Waddle gets $1.5 million in cash with $1 million in incentives, while Fleming got $2.5 million in cash, with $1 million in incentives.

The Patriots’ other two signings are for the veteran minimum, and both Tobin and Bowanko will have to make the team.

IN

Adrian Clayborn: $6m cash, $4m cap ($1.5m incentives in 2019)

Danny Shelton: $2.03m cash, $2.03m cap

Total: $8.03m cash, $6.03m cap

OUT

Alan Branch: $3.7m cash, $4.55m cap, $1.25m incentives

Analysis: Defensive line is the one area where the Patriots spent a little money, but even then, they got great value. Shelton will cost about half of what Branch was set to make before the Patriots declined his option. And Clayborn’s $6 million cash payout ranks 21st among 4-3 defensive ends, while his $4 million cap number ranks 29th, per OverTheCap.com.

IN

Marquis Flowers: $1.75m cash, $1.75m cap, $800k incentives

OUT

Shea McClellin: $2.75m cash, $3.18m cap, $1m incentives

David Harris: $2.25m cash, $2.75m cap, $1m incentives

Total: $5m cash, $5.93m cap, $2m incentives

Analysis: Flowers is a decent backup linebacker and solid special teams contributor, while McClellin’s career is likely over because of the concussions he suffered, and Harris was a waste of a signing who didn’t contribute on defense or special teams.

The Patriots likely need to find another linebacker in the draft, but rookies are the best value in the NFL, particularly players drafted in the second round and later.

IN

Jason McCourty: $3m cash, $2.97m cap

OUT

Malcolm Butler: $14m cash, $6m cap

Analysis: This was a simple one-for-one swap. Butler’s cap number is manageable because the Titans gave him a five-year deal and a $10 million signing bonus, but they’re realistically on the hook for $25 million over two years. The Patriots, meanwhile, believe they have a starting-caliber cornerback for just one year and $3 million.

IN

Cordarrelle Patterson: $3.25m cash, $3.25m cap

Nate Ebner: $2.8m cash, $2.025m cap

Matthew Slater: $2.6m cash, $2.1m cap, $100k incentive

Brandon King: $1.425m cash, $1.18m cap

Brandon Bolden: $880k cash, $720k cap

Total: $10.955m cash, $9.275m cap

OUT

Johnson Bademosi: $3.5m cash, $3m cap

Analysis: This was the other area where the Patriots spent a little money, because we all know how much Bill Belichick loves his special teams. The interesting comparison is Patterson to Bademosi. Both play gunner on the punt coverage team, and Bademosi will make $3.5 million in 2018, while Patterson will make $3.25 million. None of the other four Patriots special teamers got as much as Bademosi did, either.

Ben Volin can be reached at ben.volin@globe.com. Follow him on Twitter @BenVolin.