The NFLPA announced today that the arcane and mystical formula that spits out the compensatory pick numbers has awarded no picks to the Minnesota Vikings, as was to be expected. The Green Bay Packers were awarded a third-round pick and a fifth-round pick, while the Detroit Lions received two fourth-round picks.

These compensatory picks are given at the end of the rounds they are tagged as part of, which means the four third-round picks that were awarded (Pittsburgh, Green Bay, Baltimore and San Francisco) take place at the end of the third round and before the fourth round.

The formula is secret, but it’s not quite as mystical as all that.

Generally speaking, the picks are awarded based on the net flow of free agents: the players a team loses to free agency measured against the players added to the team in free agency. This doesn’t always mean “more” free agents are added than lost, because the quality of player matters, too. In fact, the formula takes into account, the salary, playing time and postseason honors of the total free agent net a team has

Losing Jasper Brinkley in the 2013 offseason did not compare to gaining Greg Jennings. Up to 32 compensatory picks are awarded every year, which means teams that qualify for a compensatory pick through the formula may not end up receiving one.

In the NFLPA document, there is an implication that every player who hit free agency is ranked at the end of the year due to these considerations (or in some way is given a value).

I don’t know what the formula is, but after looking at the compensatory gains and losses listed in each NFLPA document, I can guess that one of the processes that plays out is a ranked ordering where values are added and subtracted. It could be that the addition/subtraction process is not ordinal (top-ranked gain vs. top-ranked loss), but rather that players with the most similar value are put up against each other, which San Francisco’s 2013 offseason can demonstrate. The four marginal additions (Phil Dawson, Craig Dahl, Glenn Dorsey and Dan Skuta) eliminated the four marginal losses (Ted Ginn, Ricky Jean Francois, Isaac Sopoaga, Delanie Walker), leaving Dashon Goldson standing alone and giving them a high pick (end of the third round).

An alternate method that would make sense to me, but I don’t think is used, is an ordinal ranking. The top-ranked eligible player lost by any given team is (in my estimation) subtracted against the top-ranked player gained by that team, and a positive value means a compensatory pick (usually). Then the process continues down the line for each eligible player gained and lost.

Then, I imagine, because teams are limited to four compensatory picks at the max, residual positive value is first added to the highest-ranked negative values (say, if the second-ranked player lost was worth less than the second-ranked player gained, but the top-ranked player lost was worth more than the top-ranked player gained) continuously until either that second ranked value is near the original gross value (of the lost player) or they run out of eligible ranked players to add in to the rankings. After that, they add to the highest-ranked positive value.

This bit is more speculation than most, because I recall only one team losing five or more net free agents in the past three years: the Green Bay Packers, who lost Daryn Colledge, Korey Hall, Brandon Jackson, Cullen Jenkins and Jason Spitz to the market in 2012 while adding no new FAs. They gained two fourth-round picks and two seventh-round picks for their trouble.

After that, I assume the negative values are then subtracted against the highest-ranked remaining positive value. Alternatively, negative values are thrown out and teams are awarded picks based on their remaining positive value slots. I think the first idea is more likely because of the following observation:

To my knowledge, no teams have gained compensatory picks while netting a gain in the total number of players in free agency, though teams have earned compensatory picks when they have not suffered a net loss or gain in the total number of free agents (all very low-round picks). That is, a team that signs three players eligible for the formula, but loses two to other teams, does not gain picks. But a team that signs two players and loses two players can earn a compensatory pick (and to my knowledge has not earned more than one).

This has not come up for this year’s draft, because three teams suffered a net loss in free agents (the Chicago Bears, the Atlanta Falcons and the Cincinnati Bengals) but those losses ranked 33rd, 34th and 35th. The Oakland Raiders qualified without suffering a net loss (or, like I said, gain) but effectively ranked 36th and therefore was not awarded a compensatory pick, either.

In the case of the Packers, Greg Jennings saw ample playing time and a good contract from the Vikings, and Green Bay did not add any players in free agency (other than players who do not count, usually those given reserve/futures contracts, were on the practice squad or did not make the team. Players who declared for the draft that year and were signed afterwards as free agents also do not count). That means, the value lost on that free agent was very large, and was therefore worth the second-best compensatory pick (pick 98). Only the Steelers’ Mike Wallace ended up netting more (because Bruce Gradkowski was the only player lost).

Players cut by teams (like Letroy Guion), traded by teams (like Percy Harvin) or re-signed by teams (like Everson Griffen) do not count towards or against teams when it comes to compensatory free agents.

Another interesting quirk is that regardless of how well Jared Allen gets paid this offseason (or how much playing time he receives, or what his postseason honors are), the Vikings will not get more than a fifth-round pick in compensation. So, even if Allen plays every snap, gets paid $12,000,000 a year for five years and is awarded the league MVP after a 30-sack season with Pro Bowl and All-Pro honors, the Vikings would still only receive a fifth-round pick.

That is because the system is designed to protect teams from players leaving their rookie deals more than anything else. Players at the end of their second (or third) deals have a significantly smaller impact, unless that player was given their “second” deal as a restricted free agent (to a point, presumably). Specifically, the player’s age is a significant factor if they are entering their third (or sequentially later) deal.

Unless that player’s a quarterback.

Or if that player signs after June 1st.

It’s a complex formula, but it encourages teams to build through the draft, re-sign their players and keep their teams young. As if they didn’t need a reason to already.

While initially a mechanism designed to restore competitive equity for teams that lost free agents, it may actually be a system that enforces disparity. The teams most likely to spend on free agents are the ones who do not have adequate players on their roster, which means that teams that have ready replacements for free agents who will make serious money on the market will receive additional compensation. That is to say, teams that draft well are rewarded by getting more draft picks.

I am not a fan of this system.

Edit: As commenter Jordan points out, the fact that Jennings will net a third-rounder for Green Bay despite being 29 when signing his third contract while Jared Allen can only net a fifth-rounder if all things pan out for the Vikings (which is unlikely, given the free agents they have signed) as a 31-year-old signing his third contract reinforces the absurdity of the system. Presumably, there is a cut-off for 30-year-olds and the Packers squeaked by.

As commenter K0N points out, there is also the additional complexity of figuring in extensions vs. new contracts. Oh joy.

As an aside, there are two potential meanings to a specific player not being awarded more than a fifth-round pick. It could either provide generic validation to the concept of player-for-player pick accreditation and that the formula is caŕried out and a pick cap is applied, or it could mean that a players max value is capped at whatever the formula determines a fifth-round pick is worth. There is not really a way to prove it one way or the other.

This changes the Vikings picks, so that they now have the following picks: 8th (1.8), 40th (2.8), 72nd (3.8), 96th (3.32 from SEA), 108th (4.8), 148th (5.8), 184th (6.8) and 223rd (7.8). Green Bay ends up with these picks: 21st (1.21), 53rd (2.21), 85th (3.21), 98th (3.34), 121st (4.21), 161st (5.21), 176th (5.36th), 197th (6.21) and 236th (7.21). The Detroit Lions end up with these: 10th (1.10), 45th (2.13), 76th (3.12), 111th (4.11), 133rd (4.33), 136th (4.36), 189th (6.13), and 227th (7.12). They traded their fifth-round pick to Jacksonville for receiver Mike Thomas.

The Chicago Bears, like the Vikings, remain unchanged in the total amount of picks, but have their order changed in the later rounds as follows: 14th (1.14), 51st (2.19), 82nd (3.18), 117th (4.17), 156th (5.16), 183rd (6.7 from TB) and 191st (6.15). They traded their seventh-round pick to Dallas for tight end Dante Rosario and received Tampa Bay’s sixth-round pick for Gabe Carimi.

Green Bay earned a third-round selection because of Greg Jennings and a fifth-round selection because of Erik Walden. Detroit was awarded their fifth-round picks due to a net loss of two free agents. They lost Cliff Avril, Gosder Cherilus, Justin Durant, Drayton Florence and Sammie Lee Hill, while gaining Reggie Bush, Jason Jones and Glover Quin.

The last time the Vikings earned compensatory selections was in 2012, after losing Ray Edwards, Sidney Rice, Ben Leber and Tarvaris Jackson to free agency while gaining Charlie Johnson and Remi Ayodele. With those picks, they selected Rhett Ellison and Greg Childs. Compensatory picks may not be traded (a provision whose enforcement is suspect given the possibility of after-pick trades, but one that has not been violated by obvious loopholes as far as I can tell).