Does "the law of diminishing returns" apply to passing?

by Jim Glass
Does "the law of diminishing returns" apply to passing? If so, does it mean anything for team strategy?

Does diminishing returns apply to passing? As a QB passes more, should the effectiveness of his passing be expected to decline? Or do mismatches rule and quality win out in NFL contests, so a top-quality QB's performance should be expected to be consistent during an entire game – or even rise as he finds the weaknesses in a defense and maybe even "breaks" it?

Diminishing returns isn't really a law so much as the observation that people logically put a resource to its most productive use first, then to its second most productive, and so on, so the return from its use incrementally declines. This phenomenon is all around us in modern life.

In football the logic is that teams use the pass plays they can execute best for greatest results first. But when teams throw a lot they must move beyond those few plays -- so their AYA will fall to significantly below its level in few-attempt games.  There's lots of anecdotal evidence supporting this idea.

In my file of the last 15 years of playoff games Mark Sanchez has by AYA the 7th best of 326 playoff performances, 13.5 AYA (versus Cincinnati last year) and Trent Dilfer had a very superior run of 9+ AYA through the playoffs leading up to the 2000 season Super Bowl. Sanchez had another top performance of 10+ AYA against the Patriots a couple weeks ago. These are impressive playoff numbers for QBs who rated league-bottom during the regular season - and one thing all these game had in common was few passes attempted. NFL teams pass near 34 times per game on average, but Dilfer in his playoff run averaged only 16 while Sanchez threw 15 times in his 13.5 AYA game and 25 times against the Patriots this year.

Of course, in 16 years you'd expect a few bottom-rated QBs to have some top-rated games, and the fewer attempts tried the greater is the possibility of it happening by random chance, so that could be it. But there are many other examples more difficult to explain by invoking chance.

An historic one dates to the 17-0 season of the 1972 Miami Dolphins. Before the season they paid $100 to pick up 38-year old Earl Morrall off waivers as their backup QB. Then starter Bob Griese went down and Morrall QBed the team through most of the perfect season. He was named All Pro First Team and AFC Player of the Year after compiling an 8.4 AYA, far above the league's next highest of 6.9 put up by Joe Namath. Morrall averaged only 16 attempts per game as the Dolphins ran on more than 70% of their plays ñ yet it doesn't seem likely that random chance would produce one high-number game after another for him to earn him such honors for the full season.

If diminishing returns applies to passing one would expect the QBs with the fewest pass attempts to have the highest AYAs, other things being equal. Is that what's happened here?  To judge, we have to look beyond anecdotes.

Data
League-wide numbers over several years show a modest negative correlation between AYA and number of passes attempted. One might assume that in today's pass-friendly NFL the best pass offenses would pass the most, but the top five teams ranked by offensive AYA in 2010 (Pats, Chargers, Steelers, Packers and Bucs) by pass-run ratio ranked only 26, 17, 27, 14, and 21 (with a similar pattern is seen in reverse for the lowest-rated teams by AYA) quite consistent with diminishing returns.

But in league-wide numbers none of the other things are equal. One obvious point is that these five teams were all winners, and winning teams run more after getting ahead, so their numbers may show high AYA reducing passing rather low passing keeping AYA high. Since league-wide data are unconvincing I'll skip to the career numbers of individual quarterbacks, which are more interesting.

Quarterback career numbers
From the PFR.com database I took the career game logs of all QBs who started this year and had at least a five-year record (80 games) as a starting QB with 14 or more attempts in each game (then added Palmer and Garrard who just barely missed the cut). I divided their games into quartiles by number of passes attempted, and computed their AYA for their fewest-attempts and most-attempts quartiles.

For example, Peyton Manning had 204 games, thus 51 games in each quartile. In his fewest-attempts quartile of games he averaged 24.5 attempts and had an AYA of 9.3, while his most-attempts quartile he averaged 46.4 attempts and had an AYA of 5.8, a 37% decline. The results for all...

QB	Fewest Attempts AYA	Most Attempts AYA	Decline
Roethlisberger	9.30	6.59	-29%
P Manning	9.26	5.84	-37%
Rivers	8.81	6.91	-22%
Brady	8.61	7.19	-16%
Garrard	8.10	6.42	-21%
Palmer	7.93	6.44	-19%
Brees	7.81	5.95	-24%
Pennington	7.60	5.59	-26%
Brunell	7.52	6.39	-15%
Favre	7.47	5.96	-20%
McNabb	7.31	6.48	-11%
Hasselbeck	6.63	6.14	-7%
Delhomme	6.53	5.60	-14%
E Manning	6.19	6.42	4%
Kitna	5.98	4.98	-17%

The numbers show a significant general drop in AYA with increasing attempts. For perspective on their size, Peyton Manning's 9.3 AYA in his "fewest attempts" games is higher than the highest regular season AYA for any QB in 2010, while his "most attempts" AYA of 5.8 matched Colt McCoy's this year, 26th in the league.

And the low AYA number for "most attempts" games may understate how low AYA performance actually falls. Since it is an average for the entire game, to the extent that passing effectiveness decreases during the game the final passes must have lower AYA than that. In his passes number 41+, Peyton Manning's career AYA is only about 4.3.

Surprisingly, it is the best QBs who incur the biggest declines in AYA with additional attempts. Of the QBs on the table, the top eight by career AYA have a drop of 24%, the bottom eight one of only 10%. (That the poorer QBs have lower, or no, AYA decline with increasing attempts is supported by looking at other low career AYA QBs who missed the 80-game cut, such as David Carr.) 

Declining AYA with increasing attempts is also most steady with the "pre-eminent" quarterbacks, as seen in their numbers for all four quartiles.

QB	Least Attempts AYA	2nd Least AYA	2nd Most AYA	Most Attempts AYA	Total Decline
Roethlisberger	9.30	8.63	7.17	6.59	-29%
P Manning	9.26	8.09	7.62	5.84	-37%
Rivers	8.81	9.19	7.95	6.91	-22%
Brady	8.61	7.43	7.37	7.19	-16%
Brees	7.81	7.76	7.12	5.95	-24%
Favre	7.47	6.97	6.25	5.96	-20%
Average	8.54	8.01	7.25	6.41	-25%

I'm not sure what to make of this pattern. My first guess is that perhaps superior QBs, when they can pick their shots, have a special ability to exploit defenses that they lose when forced into a broader range of passing, while lesser QBs don't have that special ability so they don't lose it. But you may come up with a better idea.

Causation
Causation is always a problem when interpreting football stats ñ it can run either way, both ways at once, or in several roundabout ways. For instance...

* Teams certainly throw more when they are losing, and facing a top defense is more likely to cause them to lose ñ so maybe facing tough defenses both forces more attempts and drives AYA down. But that's not inconsistent with diminishing returns. A top defense forcing a QB away from what he does best while throwing more than he'd prefer is a fine example of diminishing returns in action. The two causations can co-exist.

* A QB may come out and throw 4 TDs in his six first passes so his team barely has to pass again. That's luck giving high-AYA, low-pass numbers. But it is also entirely consistent with diminishing returns - the team started with its best passing plays and they worked great, giving it no reason to move on to its next-best plays.

One can think up many different variations of causation, but the fact of diminishing returns with increased passing is hard to avoid in them.

Implications
Some may think about all this, "So what? QBs who get behind and have to go chucking in the 4th quarter trying to come back throw a lot of picks. What's news about this?" And that's a fair enough point, the reader can decide if all this has any worthwhile meaning. But from it I draw three conclusions that aren't generally appreciated...

* Good defense improves offensive passing efficiency. The logic is simple: If the game is always no worse than close, and the QB is confident it will stay that way ñ he doesn't have to go chucking to keep it close ñ he can always stay within the realm of what he does best and never be forced to get beyond himself. I can think of no other explanation for the Morrall-Dilfer cases, and others like them going back to Bart Starr. A good running game helps too, but you can't run if you are 17 points down.

Defense and special teams do at least half the job of keeping a team ahead or close ñ so to the extent that being ahead or close helps passing efficiency, they can boost a QB's AYA. QED. (I have other data on this, perhaps for another time.)

* Balanced teams win more games. If you accept the prior point, this must follow. You want to balance your team's investments in offense and defense to equalize their return and thus maximize their value.

Say you are lucky enough to have a superior QB and you believe, credibly, that offense is more important to winning than defense. You may decide to invest your salary cap overwhelmingly in your passing offense to make the most of your strength. That seems logical enough, but diminishing returns shows a flaw in the idea: your eighth unit of payroll invested in your O produces less than your third invested in your D, so such unbalanced investing weakens the team overall.

The result can be what I think of as "Coryell Syndrome" ñ Don Coryell coached teams with historically high-scoring offenses that never won anything because of their all-time worst defenses. (Did his offenses so dominate because he was such a great offensive coach, or because he utterly depleted his defenses to invest more in offense than anyone else?)

That bad defense is not only bad in itself, but by putting the offense in bad positions it takes back some of your QB's AYA obtained by investing so much in the offense, wasting that investment. In contrast, investing to bring the defense up from the bottom also helps place your offense in better positions ñ and so provides a bonus in helpings its AYA.

Have the Polian-Manning Colts suffered from Coryell Syndrome? With the dominant QB of a generation and an offense famously built around him they are 9-10 in the playoffs, and Peyton has lost far more playoff games in which he put up winning-level numbers than has any other QB. Even in 2006 when they won they won they were lucky ñ their defense was ranked 31st by EPA and gave up 173 yards per game rushing, and Peyton put up his worst post-season numbers, though they won anyhow.

The obvious contrast is the Belichick-Brady Patriots. Their defenses over the last 11 years has been much better than the Colts, (average -6 EPA versus +41 for the Colts) and they won the Super Bowl with defenses ranked 2nd, 6th, and 8th by EPA. Brady has won more playoff games when he put up poor numbers than any other QB. By "attempts quartile" Brady's high AYA is not as high as Peyton's ñ but his low is not as low and his drop is much less. Is all this evidence of a more balanced team?

* Not all passing offenses are equally scalable.  A team's passing AYA is a stunning 9.3 (far ahead of #2 team's 7.8) while its average yards per run is a mere 3.5, second-worst in the league. Yet the team has the highest run-to-pass ratio in the league - it runs more and passes less than any other. Is its coach a dummy who somehow doesn't understand that 9+ yards per play is better than 3.5? Should he pass a lot more?

A "yes" answer assumes that with a lot more pass attempts the great AYA will remain stable or fall only slowly.  If the team's QB is one who can make all the throws ñ a Namath, Fouts, Warner, P. Manning ñ decline in AYA due to extra passing may be modest, so that might be right. But if the team's QB has a very limited skill set ñ he's a Morrall or Dilfer ñ you may want to think twice. Remember, declining AYA comes largely from the -45 charge for interceptions, which can be game-turners.

The numbers above are for Lombardi's last great, dominant Packers team in 1966. Bart Starr, its QB, was a 17th round draft pick who was Lombardi's third choice as QB, getting the job only after the first two were injured. He kept the job when Lombardi was impressed by his intelligence, leadership and accuracy passing off of play action behind the run ñ not because of his throwing ability. The Packers also had the #1 defensive AYA, so they had a huge total AYA edge over the rest of the league.

But none of Lombardi's contemporaries thought he was leaving anything on the table by not having Starr hurl the ball like John Unitas ñ and I see no good reason to second guess them.

Concluding opinions
For what these are worth:

* Passing is generally subject to diminishing returns, one way or another, though at rates that vary greatly by team.

* The quality of a team's defense helps (or hurts) its offensive passing efficiency.

* In the NFL teams needs to pass effectively to win consistently ñ but don't need to pass at high volume if they pass very efficiently.

* If a team isn't lucky enough to have one of the few superior passers in the league, it can build an efficient passing game in other ways.

* Although offensive passing is the single most important contributor to winning, it is still possible to over-invest in it.  (Yes, I suspect the Colts have suffered a bit from Coryell Syndrome.)  Balanced teams have the advantage.