FOXBOROUGH, Mass. — The New England Patriots head into the NFL draft with their usual needs at wide receiver and in the secondary.

Maybe Bill Belichick will make better choices than he did in his other 13 years as their coach.

He’ll have only five chances, the fewest picks in team history, barring trades, so there could be increased emphasis on signing players who don’t get chosen in the three-day draft that ends Saturday.

“They’re always part of the equation,” Patriots director of player personnel director Nick Caserio said. “We’re going to be adding 20 more players to the team before we go to training camp. That could come from draft picks. It could come from undrafted free agents. Whether or not they play a larger role this year, possibly. There are still street free agents that are available. You’re always looking at a multitude of ways to put your team together.”

Two free agents, defensive lineman Justin Francis and running back Brandon Bolden, made contributions as rookies last year. BenJarvus Green-Ellis led the Patriots in rushing for two seasons after not being drafted and before signing with the Cincinnati Bengals a year ago.

But drafted players have a better shot at productive pro careers, even if that often hasn’t been the case with the Patriots. Five of the eight defensive backs they picked in the first four rounds during the past six years are no longer with the team.

At receiver, the Patriots have chosen four in the last seven years. Jeremy Ebert, a seventh-round pick in 2012, is the only one who remains. And with the departure of their top two receivers from last season, Wes Welker and Brandon Lloyd, the Patriots need help at that position.

So how can they avoid the same mistakes?

“As a team, we look at everything that we do: on the field, off the field, strength and conditioning, draft, etc.,” Caserio said. “We’re always trying to find ways to improve our systems and make them better, whatever it may be.”

The Patriots added veteran receivers Danny Amendola, Donald Jones and Michael Jenkins in the offseason as new targets for Tom Brady. But of the eight players they drafted at that position over the last 10 years, only Julian Edelman has made an impact, only as a backup.

Wide receivers who could be a good fit include DeAndre Hopkins of Clemson, Keenan Allen of California and Markus Wheaton of Oregon State. In the secondary, they might choose among cornerbacks Xavier Rhodes of Florida State and Jamar Taylor of Boise State, and safeties Matt Elam of Florida and Eric Reid of LSU.

The Patriots also could use a speedy defensive end and might consider Damontre Moore of Texas A&M.

The secondary is considered a strong position in this draft.

“One of the things that’s probably unique about that position is you’ve seen a few more players have actually played multiple positions. Some of them have played safety, have played corner, some have played the nickel position, like the Matt Elam kid,” Caserio said. “You’re looking for guys that are versatile, can play multiple spots. Some of those players have played in more passing-oriented divisions and conferences.”

The receiving and offensive line groups also have good depth, Caserio said.

But the Patriots have just one pick in each of the first, second and third rounds and two in the seventh, the 29th choice in each.

They traded their fourth-rounder to Tampa Bay last Nov. 1 for cornerback Aqib Talib, who improved the secondary, and an extra seventh-rounder. The fifth-round choice went to Washington on July 29, 2011 for defensive tackle Albert Haynesworth, who played just six games with the Patriots.

And the sixth-rounder, plus a fifth-rounder last year, went to Cincinnati for wide receiver Chad Johnson the same day the Patriots obtained Haynesworth. Johnson, then called Chad Ochocinco, had only 15 catches in 15 games in his one season in New England.

The Patriots have had three strong drafts after a weak stretch. In 2010, they added defensive back Devin McCourty, tight ends Rob Gronkowski and Aaron Hernandez, and linebacker Brandon Spikes. In 2011, they chose offensive tackle Nate Solder and running backs Stevan Ridley and Shane Vereen. And last year they drafted defensive end Chandler Jones and linebacker Dont’a Hightower.

The fewest picks the Patriots have had were six in 2002.

“You know going in, ‘OK, you have X amount of selections that you’re going to make.’ You have to be prepared every time your name comes up,” Caserio said. “That doesn’t change from one year to the next. However many picks you have, you make the pick and if there’s an opportunity that’s out there that makes sense for you to (trade), then you consider if it’s the best thing for ourselves at the time, then we’ll do it.”

But the draft is just one step in the process as the Patriots try to build a team that can do better than a 12-4 record but an AFC championship game loss to the Baltimore Ravens 28-13 at Foxborough.

“It’s ongoing,” Caserio said. “It really never stops.”