Guest column by Kevin Kolbe

Every year, multiple teams in the league have to answer the question of "what is a player's value to our organization?" It's not an easy question for any position, but when it comes to quarterbacks, there doesn't seem to be a rational approach to determining that amount. Consider this: eight quarterbacks make between $18 and $22 million a year, an amount one might think is still a bargain for elite or even just very good players at the most important position in football, and I am not going to argue otherwise. After all, a reliable quarterback who can carry his offense against any defense does guarantee a certain level of success.

One might expect that between the best starters and the merely above average, however, there would be a significant drop-off, but this is not the case. After the top eight, there are another six quarterbacks making between $14 and $18 million a year.

Between $5.6 and $14.6 million a year, there is just one quarterback: Tom Brady. This is ridiculous for many reasons. Only one quarterback in a $9 million dollar range? This means that, aside from Brady -- who can "sacrifice" to give the Patriots cap room in part because he doesn't need to be the primary breadwinner in his family -- all quarterbacks fall into four categories:

1) A "top of the league" talent

2) An above average talent without whom the team would still suffer

3) A player on a rookie contract

4) A completely replaceable journeyman/borderline backup.

I find this logic to be flawed. After all, some players have to be "average." Is the gap between the "good" and the "just OK" really worth $9-plus million a year? Let's find out. Note that the following points do not take into account strength of schedule, quality of offensive "weapons," protection, or even coaching. This will be about production versus cost. Initially, I did this without taking rookie contract quarterbacks into account, as their pay is intended to be lower than their potential value. However, I knew that fans of teams with young passers would want to see how their young quarterbacks compared, and it would be interesting to see an objective assessment of those players' value before they sign their first big contracts (especially with many of them in talks for said contract).

[ad placeholder 4]

Before we begin, I would like to apologize to the Titans, Rams, and Redskins. None of your quarterbacks made it into this article, as I arbitrarily decided to look at only those quarterbacks who started more than eight games in 2014.

I began by using Adjusted Net Yards/Attempt, a reliable metric for passing efficiency, but pass attempts do not show a quarterback's entire role in the offense. For example, on a failed passing play, sometimes a quarterback will take the sack, sometimes he will throw out of bounds, and sometimes he will run for it. In addition to that, read-options and designed runs are a significant part of the game plan for some teams. Lastly, a few gimmick plays feature the quarterback as a receiver, and it would be unfair to ignore them given how exciting they are to watch. TANY/A (Total Adjusted Net Yards/Attempt) adds in rushing as well, and the formula is written out here:

TANY/A = {passing yards + rushing yards - sack yards + 20 * (TD passes + TD rushes) - 45 * (INT + 0.5 * Fumbles) } (passing attempts + sacks + rush attempts)

As you can imagine, most quarterbacks will see their average yards decrease with rushing numbers added in. A lot of this is due to fumbles, but rushing attempts tend to yield lower average gains than pass plays. For simplicity's sake, in the following table, I added interceptions to half of each quarterback's fumble total and listed them in one column called "TO." "Attempts/Game" includes all passes, rushes, sacks, and (if applicable) receptions. In the first column, "games," I rounded to the nearest half-game, since some quarterbacks entered or left games due to injury.

I followed this up by looking up the average cap hit for each quarterback displayed. After all, the point of this exercise was not to determine which quarterback was best, but to figure out what each quarterback's value was. The following scatterplot displays each quarterback's average cap hit by TANY/A.

As you can see, there are cap hits that seem to have no relation to performance. Let's see what things would look like if all of them did.

[ad placeholder 3]

Aaron Rodgers had both the highest TANY/A as well as the highest average cap hit. This is wonderfully convenient for me because it gives me a clear and objective starting point to the exercise. The difference between the highest cap hit (Rodgers, $22 million) and the lowest (Russell Wilson, $0.75 million) is $21.25 million. The difference between the highest efficiency (Rodgers, 8.17 TANY/A) and the lowest (Blake Bortles, 3.90 TANY/A) is 4.27 TANY/A. I'll be using those high and low values to determine quarterback value by efficiency. The better a quarterback's TANY/A, the higher his base value.

The problem with only using TANY/A to determine base pay is that it does not account for the demands placed upon a quarterback. It is easier to move on from a quarterback who rarely has to throw thanks to a strong running game or stout defense than it is from a high-volume quarterback who is forced to carry the offense and keep the defense rested, and I wanted the formula to reflect that.

To account for this, I created a new metric, which I have named PAYD (Pay by Average Yards and Demand). PAYD modifies base value by twice the percentage difference of plays per game (using Aaron Rodgers' 38.1 plays per game as the standard). For example, if a quarterback with a base value of $10 million per year averaged 41.9 plays per game (10 percent more than Rodgers' mark), his PAYD would be $12 million per year (20 percent more than his base value).

Player Games Plays/G ANY/A TANY/A Cap Hit Base Value PAYD PAYD - Cap A.Rodgers 15.5 38.1 8.65 8.17 $22.0 $22.0 $22.0 $0.0 B.Roethlisberger 16 41.8 7.82 7.26 $14.7 $17.5 $20.8 $6.1 A.Luck 16 44.2 7.28 6.68 $5.5 $14.6 $19.2 $13.7 P.Manning 16 39.9 7.68 7.10 $19.2 $16.7 $18.2 ($1.0) D.Brees 16 44.7 6.77 6.42 $20.0 $13.4 $18.0 ($2.0) M.Ryan 16 43.0 6.71 6.47 $20.8 $13.6 $17.0 ($3.8) T.Brady 16 39.9 7.01 6.50 $11.4 $13.7 $15.0 $3.6 E.Manning 16 41.1 6.67 6.43 $16.3 $12.4 $14.4 ($1.9) R.Wilson 16 38.3 6.72 6.56 $0.7 $14.0 $14.1 $13.4 T.Romo 15 32.7 8.11 7.49 $18.0 $18.6 $13.3 ($4.7) J.Flacco 16 38.3 6.66 6.20 $20.1 $12.2 $12.3 ($7.8) P.Rivers 16 40.2 6.45 5.96 $15.3 $11.0 $12.2 ($3.1) M.Stafford 16 42.4 6.03 5.74 $17.7 $9.9 $12.1 ($5.6) R.Tannehill 16 43.3 5.83 5.50 $3.2 $8.7 $11.1 $7.9 M.Sanchez 8.5 43.1 6.18 5.47 $2.3 $8.6 $10.8 $8.6 Player Games Plays/G ANY/A TANY/A Cap Hit Base Value PAYD PAYD - Cap A.Smith 15 37.0 6.14 5.94 $17.0 $10.9 $10.3 ($6.7) R.Fitzpatrick 11.5 33.3 7.15 6.51 $3.6 $13.7 $10.3 $6.7 K.Orton 12 41.3 5.69 5.41 $5.5 $8.3 $9.6 $4.1 B.Hoyer 13 37.4 6.11 5.70 $1.0 $9.7 $9.3 $8.3 D.Stanton 8 34.5 6.22 5.80 $2.7 $10.2 $9.2 $6.5 C.Kaepernick 16 39.6 5.58 5.42 $19.0 $8.3 $9.0 ($10.0) J.Cutler 15 42.5 5.57 5.17 $18.1 $7.1 $8.7 ($9.4) C.Newton 14 42.1 5.45 5.12 $5.5 $6.8 $8.2 $2.7 T.Bridgewater 12.5 39.0 5.46 5.27 $1.7 $7.6 $7.9 $6.2 A.Dalson 16 32.4 5.75 5.95 $16.0 $10.9 $7.7 ($8.3) D.Carr 15.5 42.1 4.82 4.40 $1.3 $3.2 $3.9 $2.6 G.Smith 13 32.4 5.13 4.63 $1.3 $4.4 $3.1 $1.8 B.Bortles 13.5 43.4 3.81 3.90 $5.2 $0.7 $1.0 ($4.2) J.McCown 10 38.8 4.30 3.93 $5.0 $0.9 $0.9 ($4.1)

As I mentioned earlier, 14 quarterbacks made between $14 million and $22 million last year. How did that cap hit compare to production? Poorly. Only six of those 14 quarterbacks saw production worth within $4 million of their average cap hit. Nineteen of 29 quarterbacks had a PAYD within the range of $7 to $15 million a year, whereas only two quarterbacks (Tom Brady and Ben Roethlisberger) see average cap hits in that range in real life.

Deciding whether or not to let a starting quarterback go is a difficult decision, one that I would compare to the decisions teams make on fourth-and-short. Coaches know that going for it and failing will earn them a lot of blame. Punting is just safer, and doesn't receive the same level of scrutiny, and so punts are called far more frequently. NFL general managers are doing the same thing. Look at the four quarterbacks under Andy Dalton, and you'll see exactly what I am referring to. The Bengals didn't pay Andy Dalton $16 million a year because he outplayed Brady, Philip Rivers, and Roethlisberger. They paid him because keeping him meant not risking his departure and getting stuck with someone much worse; it was the GM equivalent of a punt on fourth-and-short.

The best teams will always be the ones that know when to go for it and take a wise risk.

Kevin Kolbe is originally from Houston, Texas, and has been in the Air Force since December of 2001. This is his first article for Football Outsiders. If you are interested in writing a guest column, something that takes a new angle on the NFL, please email us your idea at Contact Us.