The Bengals now have a third-round pick, a fourth-round pick, AND Michael Johnson.

PHOENIX, Ariz. - The Michael Johnson magic act is now complete. The gift that keeps on giving.

In a textbook walk-through of their philosophy on free agency, the Bengals on Monday received an extra third-round pick and a fourth-round pick in the mind-numbing formula that is compensation for losing players to other clubs. The announcement of the picks came here as the first day of the NFL owners' meeting ended.

Based on a perplexing formula calculating losses of unrestricted free agents, signing unrestricted free agents, value of contracts, and playing time, the Bengals got another third-rounder in the draft (pick No. 99) courtesy of losing Johnson to Tampa Bay last year on a five-year, $43 million deal. They get the pick eight days after they re-signed Johnson, their starting right end, in the wake of his release from the Bucs.

Then, to continue the sacking of Tampa, they got the extra fourth (No. 135) in exchange for losing backup tackle Anthony Collins on a five-year, $30 million deal a month after the Bucs also released him.

It is a NFL front office version of a coup.

"We are aware of it. Every team is anymore," said Bengals preside

nt Mike Brown of the strategy. "You can go out and acquire a player and it seems as though it's an innocent enough acquisition and you pay whatever price then low and behold there's an additional price. You can lose a supplemental draft pick. It's been an educational process for us. We are certainly aware of it now and we weigh it when we had a decision to be made."

In what seemed to be timed with the new collective bargaining agreement in 2011 that slots rookies at team-friendly salary cap numbers, the Bengals cut back their pursuit of unrestricted free agents with their eyes on the extra picks.  It's beginning to pay off. This is the first time since 2010 they've had compensation picks so high.

And it's a strategy just not confined to the Bengals, but teams like the Cowboys are starting to play the game that has been perfected by AFC North rival Baltimore.

 "Most clubs in general would value a pick more than they did many years ago," said Cowboys exec Stephen Jones. "I just think people understand the salary cap and young players are important. The players you draft become the core of your team. To me it's a flawed strategy to think you build a team through free agency. It's just too expensive and the efficiency isn't there."

Dallas is getting grilled for signing the most controversial UFA out there, defensive end Greg Hardy, but Jones points out the Cowboys have lost seven UFAs this offseason and may lose up to three more. They're looking at the net losses.

"We're very much in tune with them. We manage the situation in terms of the plusses and minuses," Jones said. "There are obviously some years you know you're not going to lose anybody significant. No harm, no foul if you want to look into doing something efficient in the free-agent market.

"Too many teams bidding on too few good players drives up the price. I'm not a huge fan of it. There are times you stick your finger in and look at it as we did this time. It makes sense every now and then, but for the most part you're out there paddling in treacherous waters. Those compensatory picks are strong."

The idea is you get a prospect at the lowest rate possible in exchange for losing a higher-priced veteran. The Ravens have been the masters of it. According to profootballtalk.com, they have received more compensatory picks than any other team since the NFL implemented compensatory picks in 1994. Seven of the eight compensatory picks the Ravens have had in the last two years are still on the roster, PFT said.

After Monday's announcement, the Ravens lead with 44 all-time comp picks and the Bengals are tied for ninth at 24 with Seattle. The good teams look to be doing it. Last year's playoff teams Denver and Seattle (four) and Baltimore (3) led the way with the number of extra draft picks. Contenders Kansas City (4) and Houston (3) were also in the mix. 

"The opportunity has to present itself," said Bengals vice president Troy Blackburn. "For instance, we knew last year when you lose a big contract on Michael Johnson and big contract on Anthony Collins we knew we were likely to have an opportunity to get one if not two compensatory draft selections. In that environment it's particularly weighted."

Now, this year, after Blackburn negotiated deals for left guard Clint Boling (five years, $26 million) and middle linebacker Rey Maualuga (three years, $15 million), the formula works the other way. But they also hedged their bets when they signed Johnson and Packers linebacker A.J. Hawk,

who didn't count against the formula because they were released by their teams and not UFAs.  The formula would suggest next year could be a year to take a flyer on a free agent, but don't look for that with so many of their own players heading into free agency.

"This year, we were fortunate enough sign our own quality starters," Blackburn said. "If Boling had gone and signed a $5.5 million contract somewhere else and Maualuga signed a $5 million contract somewhere else we would have then measured what we were doing because we knew we would have gotten a compensatory pick for them, but now we are not facing a tradeoff as we did last year."

The Bengals are still looking to hit gold with their high compensation picks, but the more they get, the better they have a chance of hitting.

The last time they had an extra third-rounder and fourth-rounder came back in 2010 after they lost wide receiver T.J. Houshmandzadeh, right tackle Stacy Andrews, and quarterback Ryan Fitzpatrick and his 12 starts in place of the injured Carson Palmer in free agency.

With the 96th pick they took Wake Forest cornerback Brandon Ghee, a guy that has struggled to stay in the league and returned to the Bengals last week after being cut last year by two clubs. With the 131st pick they took Texas linebacker Roddrick Muckelroy and his promising career was cut short by a knee injury.

After losing defensive end Justin Smith and four others, they were awarded in 2009 the 98th pick in the third round and 209th pick in the sixth round and the sixth-rounder, Abilene Christian running back Bernard Scott, turned out to be a valuable pickup while third-rounder Chase Coffman, a tight end from Missouri, played six games for the Bengals and caught three balls.

They got a good find at No. 97 in the third round of 2008 after they lost left guard Eric Steinbach in a mega deal to Cleveland. Florida wide receiver Andre Caldwell caught two winning touchdowns in the last minute of AFC North games that led to the 2009 division sweep and although the Bengals decided to not to re-sign him after four years, he caught 124 balls in his career.

"I think we just learned as time when along," Brown said. "Maybe when it first started we didn't focus on it as much as we came to focus on it in the following years."

You only have to look as far as Johnson himself to see what the third-round can give you. He arrived at the top of the third round with the 70th pick in 2009.