In his first game back from a serious Fourth of July fireworks accident that cost Giants defensive end Jason Pierre-Paul his right index finger and parts of two others, his presence was felt.

As the Giants tried to protect a late lead, Pierre-Paul pressured Tampa Bay quarterback Jameis Winston on consecutive plays. He registered a quarterback hit on the first.



The Giants held on to win that game (a rarity in 2015) and Pierre-Paul flashed signs of what he used to be -- a difference-making defensive end. It happened often during the final nine weeks of the season, when he finished fifth in the NFL with 41 total pressures, according to Pro Football Focus.



Even though Pierre-Paul managed one sack in eight games but struggled against the run, the Giants were "pleasantly surprised" by his contributions, according to multiple sources. Even they weren't sure what they were getting when Pierre-Paul returned in late-October following a serious accident. That's why he was given an incentive-laden deal upon his return.



Not much has changed since. Four months later, Pierre-Paul remains a relative unknown. The Giants remain unconvinced about his long-term prospects after playing eight games with a club on his right hand. They're not sold on investing in him long-term, according to a person with knowledge of the situation.



The expectation is that Pierre-Paul will hit the open market. The Giants will monitor the situation, but it's likely they'll only seriously enter the mix if the price dips.



It may. Nobody can realistically know what to expect with Pierre-Paul. There are no comps for defensive ends without a full set of fingers.

Free agent file



Jason Pierre-Paul



Position: Defensive end

Age: 27

Experience: 6 years

Will Giants pursue WR Mohamed Sanu?



Projected contract: 2 years, $21.2 million with $6 million guaranteed

One individual surveyed also suggested the transition tag, which would give the Giants the right to match an outside offer. They would not, however, receive compensation if Pierre-Paul went elsewhere.



(Note: The projected contract was derived from the average of five league sources surveyed. The panel consists of a front office executive, salary cap experts and agents.)



Comparable contract: Greg Hardy (Cowboys)

Hardy was signed by Dallas last offseason to a one-year, potential $11.3 million deal despite an impending suspension for a domestic violence incident. Of course, a lot of that was based on incentives that he was unable to collect. It was similarly structured to the deal Pierre-Paul signed when he returned from the accident. Much of Pierre-Paul's deal was based on performance-based incentives he never collected.

Market:

Everybody needs pass rushers, the Giants among them. They desperately need players to provide pressure off the edge. The Falcons, Bucs, Jets, Texans and Dolphins are some others with needs at the position. Pierre-Paul will draw plenty of interest. He experienced some success off a serious injury and should only get better. It's just how much and how long a team is willing to invest. Pierre-Paul surely comes with some risk.

What he brings:

Pierre-Paul has size (6-5, 270) and athleticism. He proved capable of still being able to provide pressure off the edge after returning. Only four players had more pressures over the final nine weeks of the season. Pierre-Paul also led the Giants with five batted passes.

Synopsis:

Predicting Pierre-Paul's long-term value and effectiveness is the ultimate crapshoot. Clearly he'll be able to provide something in terms of pressuring the quarterback. But what he can do against the run and whether he'll ever be able to consistently take down quarterbacks remain unknowns. Pierre-Paul played with a club on his right hand last year. He had surgery this offseason and the hope is to eventually shed the club. Whether that will ultimately be possible long-term remains unknown. It makes him a difficult free-agent evaluation.

Chance he returns to Giants:

25%

The Giants aren't ready to dump a lot of money into such an unknown. Pierre-Paul comes with tremendous risk and uncertainty. It makes him difficult to sign to anything other than a one-year, incentive-based deal. But this could be Pierre-Paul's last payday. It would befit him to entertain all options and take whatever he can get on the open market. He'll see if there is anybody out there willing to offer more than one year. There might be. If not, than the Giants again become a possibility.

TALK IS CHEAP, Ep. 42: Which free agents should Giants keep?

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Jordan Raanan may be reached at jraanan@njadvancemedia.com. Follow him on Twitter @JordanRaanan. Find NJ.com Giants on Facebook.