Passing in the NFL is as important as ever, as teams put all their resources into finding their franchise quarterback and allowing him to succeed. One desirable quality of a franchise quarterback is the ability to push the ball downfield and be efficient when throwing deep. Teams with a quarterback who can throw deep often and still be productive will have advantages like being more successful on worse down and distance scenarios and being more likely to make a late comeback in a game that the team is trailing. In this article, I will use the stats from NFL quarterbacks on deep throws to determine who the best quarterbacks are when throwing deep.

## Sample

The sample of data that I used included all plays since the 2016 NFL Season, which is five seasons’ worth of data. This data was filtered so that only passes of at least 20 air yards were kept. Air yards are “the total distance that a football is thrown beyond the line of scrimmage to the point of reception.” Therefore, air yards do not count yards after catch on any given play. This ensures that the sample only includes plays where the quarterback had to throw the ball a significant distance. Lastly, the quarterbacks I included in the final ranking had to have at least 50 deep pass attempts within the last five seasons.

## Methods

In order to determine the best deep passers in the NFL, I used the passer rating for quarterbacks on exclusively deep throws. However, raw passer rating has many flaws. The most significant is that it does not account for the difficulty of the throw. In the passer rating calculation, every completed pass counts has the same value. In real game situations, though, a pass on a throw that traveled 60 air yards while being hit is far more difficult than an attempt that traveled 20 air yards with a clean pocket. This drawback can be somewhat accounted for by using an expected completion percentage model, similar to the way Next Gen Stats evaluates pass difficulty.

A similar problem arises with passing yards, touchdowns, and interceptions. Passing yards accounts for both air yards and yards after catch, even though a quarterback cannot directly affect the yards after catch. Therefore, when calculating yards, we should penalize quarterbacks that gain lots of yards from their receivers making plays after they have caught the ball. Sometimes, passers have bad touchdown luck. For example, a quarterback may throw to a receiver at the one yard line, but if the receiver is tackled immediately the quarterback is robbed of a potential touchdown. Thus, when calculating touchdowns, we should only look at where the ball was caught, not if the play actually resulted in a touchdown. Lastly, the problem with interceptions is comparable to the problem with completions. Interceptions are more likely on throws that are more difficult and farther down the field. We should use a model to account for the likelihood of an interception when calculating interceptions on deep throws instead of the actual number of interceptions.

The final aspect that has to be included after finding the efficiency of deep passes is the frequency of deep passes. Quarterbacks who are good at throwing deep and do so often are more valuable than those who are good at throwing deep but do so infrequently. Therefore, the last thing we have to account for before determining the best deep ball throwers in the NFL is the deep pass frequency.

## Models

### Expected Completion Percentage

The first problem with raw passer rating is that the simple statistic counts all completions equally when, in reality, passes have varying difficulty. In order to determine the difficulty of a pass, I specified a model for expected completion percentage based on a variety of factors, such as air yards, yard line, time remaining in the half, down and distance, score differential, the pass location (middle of the field or towards the sidelines), and whether the quarterback was hit while throwing. Since completing a pass is a binary result (1 for complete, 0 for incomplete), I used a logit probability model. The results of the model are displayed below.

The sample of the logit model was all passes of at least 20 air yards since the 2016 NFL Season. The p-values of each variable is statistically significant, with 6 of the 7 variables being significant at the 0.001 level. Each of the coefficients seem to make sense as well. Passes with higher air yards are the ones that are thrown farther down the field, and are therefore more unlikely to be completed. The variable “yardline_100” can be interpreted as the number of yards from the line of scrimmage to the endzone. Therefore, deep passes on plays that begin farther from the endzone have a greater probability of being complete than plays that begin closer to the endzone (likely because there is less space as an offense gets closer to the endzone). If there is more time remaining in the half, the pass comes on an earlier down, or the team is leading by a large amount, then the pass attempt will be more likely to be completed. The variables “Pass_Middle” and “qb_hit” are dummy variables signifying whether the pass was towards the middle of the field and whether the quarterback was hit while throwing, respectively. From the coefficients, we can see that passes towards the middle of the field and when the quarterback is not hit are more likely to be complete.

After specifying the model, I applied the results to each deep pass attempt in the sample. Then, I calculated the expected completion percentage and actual completion percentage for each quarterback with at least 50 deep pass attempts. After that, I calculated the adjusted number of completions by subtracting the expected completion percentage from the actual completion percentage, then adding the average NFL completion percentage on deep pass attempts (35.9%), then multiplying by the number of attempts for the quarterback. The first step, subtracting the expected completion percentage from the actual value, found the completion percentage over expected for the quarterback. Then, the value computed by adding the average NFL deep ball completion percentage can be interpreted as the completion percentage the quarterback would have if they had an average difficulty of deep pass attempts. Lastly, multiplying by the number of attempts transforms the value from a rate statistic to an estimated total. The new value, adjusted completions, can be entered into the passer rating formula and accounts for pass difficulty.

### Adjusted Yards

The issue with using passing yards in passer rating is that passing yards includes both air yards and yards after catch. However, a quarterback is only responsible for air yards, not yards after catch. Therefore, when calculating the adjusted number of yards, I simply added the completed air yards to the number of completions multiplied by the average yards after catch on deep pass completions (5.96 yds) (adjusted Yds = AirYds + Cmp*avg_YAC). This method gives the quarterback full credit for the air yards, but no credit for yards after catch, instead assuming that every deep catch has the same yards after catch.

### Expected Touchdowns

Touchdowns are not always a fair metric for evaluating quarterbacks. A quarterback can throw a complete pass to the one-yard line, then a runningback can run in for the touchdown on the very next play and the quarterback will get no credit. We cannot just leave out touchdowns, though, since scoring is an integral part of a quarterback’s ability. Instead of using the number of touchdowns thrown by quarterbacks on deep balls, we can use a model to estimate the probability of a completed pass going for a touchdown based on where the ball was caught.

In order to estimate the probability of a completed deep pass being a touchdown, I used a one-variable logit model where the independent variable was the natural log of the distance from the endzone after the catch. The distance from the endzone after the catch can be easily calculated by subtracting the air yards from the original distance to the endzone, if the pass was completed. The regression output below gives the log odds for a touchdown given the distance from the endzone after the catch (Distance_from_TD), and the corresponding graph shows the probability of a touchdown at each distance from the endzone.

Unlike the completion percentage model, the touchdown model was only used in select situations. The model was only used on completed deep passes that did not have a distance from endzone after catch of 0. The model was not applied to incomplete deep attempts because incomplete passes have a 0% chance of ending in a touchdown, and it was not used on plays where the distance from endzone after catch was 0 because those are passes to the endzone, which are guaranteed to be touchdowns if caught. Therefore, incomplete passes were given a touchdown probability of 0% and passes to the endzone (Distance_from_TD = 0) were given a touchdown probability of 100%.

After applying the model to all complete deep passes that were not thrown to the endzone, I added the totals for each quarterback in the sample. This value became their adjusted touchdowns to be used in the passer rating formula. The adjusted touchdowns is superior to raw touchdowns because it accounts for the fact that some teams have better receivers than others and the teams that have better receivers are more likely to get touchdowns on passes caught farther from the endzone. The adjusted touchdowns stat gives quarterbacks no credit for extra effort by receivers and only credit for completed passes downfield based on where the ball was caught.

### Expected Interception Percentage

The way I accounted for pass difficulty in relation to interceptions was very similar to the method used to account for completion percentage. Since interceptions are more likely on more difficult throws, I constructed a model to estimate the probability of an interception given the situation. The regression output for the logit model is shown below. Inserting values into this equation will give the log odds of an interception on a play with the given situations.

The variables used to determine the probability of an interception were air yards, yards to go on the down, whether the quarterback was hit, whether the pass was in the middle of the field, and the score differential. All variables except the dummy variable for whether a quarterback was hit were significant at the 0.01 level. From the coefficients, we can see that passes that go farther down the field towards the middle with more yards to go until the first down are more likely to be interceptions. Additionally, deep passes thrown when being hit and when being down on the scoreboard are more likely to be picked by the opposing defense.

After applying the model to the sample of deep passes, I found the actual and expected interception percentage for each quarterback. Then, I took the difference to get the interception percentage over expected. By adding the average NFL deep pass interception percentage (5.9%) and multiplying by the number of attempts, I calculated the adjusted interceptions (this process was the same as the one used for adjusted completions). Just like adjusted completions, adjusted interceptions is better to use in the passer rating formula because it accounts for throw difficulty.

### Deep Throw Rate

The last element to include in the final ranking is the tendency to throw deep. Players that throw the ball deep more often and are good should be rewarded more than those who throw deep less often.

In order to complete this step, I regressed the adjusted passer rating against the deep throw rate for each quarterback in the sample with at least 50 deep pass attempts. Deep throw rate is the percentage of pass attempts that are thrown deep for a quarterback, and the values typically range from 8% to 15%. The average deep throw rate for the sample was 11.9%. The expected adjusted passer rating can be estimated by a player’s deep throw rate (DeepP). Although there is a low correlation, quarterbacks that tend to throw the ball deep more often usually have a worse adjusted passer rating on deep throws. The linear regression is shown below, along with a scatterplot of deep throw rate against adjusted passer rating.

Note: The deep throw rate should be entered into the equation as a decimal. (Ex: 12.5% = 0.125)

After calculating the expected adjusted passer rating, I found the residual for each quarterback by subtracting the expected value from the actual rating. I added the average deep throw adjusted passer rating (83.7) to the residual to calculate the Difficulty Adjusted Rating, accounting for Tendency, which forms the acronym DART. From now on, I will use DART to rank the best deep passers in the NFL from the last 5 seasons.

## Rankings

**Deep DART** = **Deep** throw **D**ifficulty **A**djusted passer **R**ating, accounting for **T**endency

### 10. Kirk Cousins, Was/Min

Deep Throw Stats: 131/331, 4630 yds, 39 TD, 14 Int

Passer Rating: 108.8 (3rd) | Deep Throw Rate: 12.0% (23rd)

Adjusted Stats: 131.4/331, 4494.4 yds, 33.8 TD, 14.8 Int

Deep DART: 102.7 (10th)

Kirk Cousins may not be thought of as a good deep passer, but he has actually performed well in these situations over the past few years. This may be because he does not throw the ball deep that often, ranking just 23rd out of 51 passers in Deep Throw Rate. When using adjusted stats accounting for situation and throw difficulty, Cousins’ deep passer rating actually falls a significant amount. Cousins ranked 3rd in unadjusted passer rating, behind only Dak Prescott and Aaron Rodgers, but his adjusted rating was lower because he did not often throw deep and because his receivers helped him by gaining more yards after catch and scoring more touchdowns than expected.

### 9. Deshaun Watson, Hou

Deep Throw Stats: 106/250, 3608 yds, 31 TD, 18 Int

Passer Rating: 99.1 (14th) | Deep Throw Rate: 13.4% (11th)

Adjusted Stats: 110.0/250, 3644.5 yds, 30.1 TD, 17.6 Int

Deep DART: 103.5 (9th)

Deshaun Watson’s NFL future may be uncertain, but teams should be lining up to acquire him if his legal issues are cleared. Watson has been one of the NFL’s best deep passers (and passers in general) since his entry in 2016, posting the 4th highest completion percentage over expected on deep throws. His deep throws are some of the most difficult in the NFL, which is why his raw passer rating ranks lower than expected.

### 8. Patrick Mahomes, KC

Deep Stats: 105/267, 3815 yds, 36 TD, 13 Int

Passer Rating: 106.2 (9th) | Deep Throw Rate: 13.5% (10th)

Adjusted Stats: 105.0/267, 3659.5 yds, 27.2 TD, 12.6 Int

Deep DART: 103.6 (8th)

It may come as a surprise, but Patrick Mahomes has not been the best deep passer in the last five years. In both raw and adjusted passer rating, Mahomes ranks just inside the top 10. He has greatly benefitted from talented receivers and good play-calling, as his pass catchers have gained more yards and scored far more touchdowns than expected. Nonetheless, Mahomes is still one of the best in the league when it comes to the deep ball.

### 7. Dak Prescott, Dal

Deep Stats: 101/249, 3540 yds, 30 TD, 10 Int

Passer Rating: 110.8 (1st) | Deep Throw Rate: 10.4% (43rd)

Adjusted Stats: 102.7/249, 3428.7 yds, 25.5 TD, 9.9 Int

Deep DART: 103.8 (7th)

Dak Prescott was an interesting case in this study. He ranked first out of 51 quarterbacks in unadjusted deep passer rating, but had a deep throw rate ranking just 43rd. While he did have more touchdowns than expected, Prescott’s Deep DART was lowered primarily due to his low rate of going long. It would. be interesting to see if Prescott could keep up his gaudy stats if he threw deep at a greater frequency, especially with his talented receiving corps of Amari Cooper, Michael Gallup, and CeeDee Lamb.

### 6. Gardner Minshew II, Jax

Deep Stats: 37/84, 1230 yds, 6 TD, 3 Int

Passer Rating: 99.8 (13th) | Deep Throw Rate: 10.6% (41st)

Adjusted Stats: 37.7/84, 1241.4 yds, 7.9 TD, 3.1 Int

Deep DART: 105.1 (6th)

Minshew’s inclusion on the list may be the most surprising result. His DART was much higher than his unadjusted passer rating, meaning that his receivers scored less than expected. Minshew had a high completion percentage over expected on deep throws, completing over 9% more throws than expected. While the Jaguars will likely turn to Trevor Lawrence, any team looking for a fill-in quarterback will find. a great deep passer in Minshew.

### 5. Daniel Jones, NYG

Deep Stats: 34/94, 1119 yds, 13 TD, 3 Int

Passer Rating: 108.1 (5th) | Deep Throw Rate: 10.4% (44th)

Adjusted Stats: 34.3/94, 1149.5 yds, 11.9 TD, 2.74 Int

Deep DART: 108.4 (5th)

Daniel Jones may not throw deep often, but he is efficient when he does. Turning the ball over on just 3.2% of deep throws, Daniel Jones ranks 5th in both unadjusted passer rating and DART. His best attribute on deep throws has been his ability to limit interceptions, throwing interceptions 2.99 fewer interceptions than expected.

### 4. Justin Herbert, LAC

Deep Stats: 24/65, 939 yds, 10 TD 3 Int

Passer Rating: 105.3 (10th) | Deep Throw Rate: 11.0% (35th)

Adjusted Stats: 25.7/65, 907.0 yds, 8.0 TD, 2.6 Int

Deep DART: 108.5 (4th)

While he had a small sample in comparison to other quarterbacks, Justin Herbert was a top 5 deep passer during his rookie season. Despite some of the most difficult deep attempts, Herbert put up great numbers. He had an expected completion percentage of just 33.1%, the lowest of all players in the sample.

### 3. Matthew Stafford, Det

Deep Stats: 123/303, 4484 yds, 31 TD, 11 Int

Passer Rating: 106.7 (7th) | Deep Throw Rate: 11.9% (24th)

Adjusted Stats: 125.5/303, 4356.7 yds, 31.0 TD, 9.8 Int

Deep DART: 109.2 (3rd)

Matthew Stafford was traded from the Lions to the Rams this offseason, and Los Angeles should be excited by his ability. Jared Goff, the Rams’ previous quarterback, ranked 28th out of 51 qualified quarterbacks in DART, whereas Stafford ranks 3rd, primarily due to his tendency. to limit interceptions of deep throws.

### 2. Aaron Rodgers, GB

Deep Stats: 151/409, 5379, 43 TD, 10 Int

Passer Rating: 109.8 (2nd) | Deep Throw Rate: 14.6% (4th)

Adjusted Stats: 149.2/409, 5249.5 yds, 40.7 TD, 9.8 Int

Deep DART: 110.1 (2nd)

The reigning MVP ranks 2nd in deep throw efficiency over the last 5 years. He has thrown the ball deep often, ranking 4th in deep throw rate, and has limited his interceptions by throwing 14.2 fewer picks than expected on these throws.

### 1. Russell Wilson, Sea

Deep Stats: 168/411, 5961 yds, 44 TD, 17 Int

Passer Rating: 106.7 (8th) | Deep Throw Rate: 14.9% (2nd)

Adjusted Stats: 175.6/411, 6220.8 yds, 45.5 TD, 15.7 Int

Deep DART: 115.4 (1st)

Far and away the best deep passer has been Russell Wilson. Wilson may not have the best unadjusted passer rating, but his deep throw tendency and lack of help from receivers boosted him to the number. 1spot in DART. He had some. ofthe most difficult throws, with an expected completion percentage of just 33.9%. Still, he completed 7.0% more passes than expected and threw interceptions on 2.3% fewer passes than expected. The Seahawks have the best deep passer in the NFL, and they could unleash him even more if they “Let Russ Cook.”