A couple of months ago, I asked this question on Twitter:

Do you know the answer? I’ll give you a couple of moments to think about it. First, a graph showing the 200 players with the most pass attempts in NFL history (all have at least 1,325 attempts). On the X-Axis is completion percentage; on the Y-Axis is Yards per Completion. There are no era adjustments here, which can also make it kind of fun: over time, completion percentages have skyrocketed, while the average yardage gained per completion has decreased. As a result, a player with a very high yards per completion percentage almost certainly played long ago, and therefore has a low completion percentage (and vice versa). Take a look:

In this graph, I have put nine of the data points in red. Those points are the Pareto Efficient quarterbacks: there is not even one passer in NFL history who has both a better completion percentage and a better yards/completion average than those players.  Who are they?

Let’s start from the top. Ed Brown played for the Bears in the ’50s and the Steelers in the ’60s. He led the NFL in yards per completion in ’56 and also ’63, and had other sky-high yards per completion seasons (like 1960) where he failed to have enough pass attempts to qualify for the crown.  Brown retired in 1965 as the career leader in yards per completion at 16.4; he remains the career leader, and it’s never going to change.  Steve Beuerlein (12.7 yards per completion) has the highest career Y/C average among players who were active in the 21st century; Cam Newton (12.5) and Jameis Winston (12.4) are highest among active players, but nobody is ever going to knock Brown out of the record books.  As a result of being the career leader in yards per completion, he will be Pareto Efficient regardless of his completion percentage.  That said, he had a pretty bad completion percentage even for his era: his first three years in the NFL he had a great completion percentage teaming with Harlon Hill, but for the rest of his career his completion percentage was pretty ugly.

After Brown we get a stretch of Hall of Fame passers. Another Bears quarterback, Sid Luckman, is second all-time in yards per completion at 16.2, and his 51.8% completion percentage was better than Brown’s 47.8%.  Third on the all-time Y/C list at 16.1 is Browns great Otto Graham (AAFL stats included), and he (55.8%) had a better completion percentage than Luckman.

We have to drop about 30 spots on the yards/completion list to get to another quarterback with a better completion percentage than Graham. That man was Packers legend Bart Starr, who completed 57.4% of his passes and averaged 13.7 yards per completion.

Next up is Chargers icon Dan Fouts, who averaged an even 13 yards per completion but at a 58.8% clip.  Fouts is remembered as a quantity guy and a deep thrower, and he currently sits 62nd on the career completion percentage list. But when he retired in 1987, he ranked 7th on the career completion percentage leaderboard, including behind two guys who entered the league in 1983.

Now, do you remember the trivia question at the top of the post? Next on the Pareto Efficiency list is our first entrant with a completion percentage north of sixty. He completed 60.6% of his passes and still averaged 12.6 yards per completion.  Even at the 1,000 attempt mark, he is the only player in NFL history to complete at least 60% of his passes and average 12.5 yards per completion. That man is Trent Green, who spent the bulk of his career with the Chiefs.  In Kansas City, Green completed 61.9% of his passes and averaged 12.48 yards per completion; outside of KC, he completed 56.7% of his passes and averaged 12.85 yards per completion, with his time with the Rams being his most productive.  Green may not have been as good as his numbers indicated, but he does stand out in this list of Hall of Famers.

Up next is another all-time great in Steve Young – he averaged 12.42 yards per completion, but where Young really stands out is his 64.3% completion rate. Twenty years ago, Young was the clear king of this stat, but he has now dropped to 9th on the list.

After Young is Kurt Warner, who is third on the career completion percentage list at 65.5%.  Despite that, Warner has a still impressive 12.1 yards per completion average; he, of course, like Green, played on talent rich teams which boosts his career rate stats.  But with a 7.95 yards/attempt average, Warner ranks fifth (behind Graham (8.98), Luckman (8.42), Van Brocklin (8.16), and Young (7.98)) on the career Y/A list.

Finally, the last name on the list is the bookend to Ed Brown: by virtue of being the career leader in completion percentage, Drew Brees has to be Pareto Efficient.  Brees has a very low (by historical standards) 11.3 yards per completion average, which makes him a true counter to Brown.

And that’s it: those are the 9 men in NFL history who have such a good completion percentage and/or yards/completion average, that no player in history was better at them in both categories.