How Would Marino, Montana Have Fared in 2021?

San Francisco 49ers QB Joe Montana
San Francisco 49ers QB Joe Montana
Photo: USA Today Sports Images

NFL Offseason - Guest column by Cole Jacobson


Most of my prior projects on this website have been dedicated to in-game strategies that can actually help teams win. This one is not. Instead, it's meant to help settle an ongoing debate within the football community over the past decade. It's no secret that the NFL is in a "Golden Age" of passing, with passing becoming both more common and more efficient in recent years. Of the 17 individuals in NFL history to throw at least 200 passes in a season with a completion rate of at least 70%, 14 have come since 2009. Thirteen of the 14 all-time 5,000-passing yard seasons have come since 2008, with Dan Marino's legendary 1984 campaign being the lone exception. The top eight quarterbacks in NFL history in career passer rating (minimum 1,500 attempts) were all active as recently as 2020, though Drew Brees has since retired.

It's a given that NFL quarterbacks are succeeding like never before, but what's not universally agreed upon is why it's happening. Is it primarily because it has never been easier to be an NFL quarterback, due to offense-friendly rule changes, more innovative play design, and better athletes lining up out wide, as has been argued by outlets such as The Ringer, Sports Illustrated, Yahoo, and The Ringer again? Or has some old-fashioned "Darwinism" led to this generation's crop of passers just being that much better than those that came in the 20th century, as has been pitched by outlets including The Herald Bulletin and Fansided? We'll never know the true answers to those questions without having human time travel, but with Pro Football Reference's data and R programming, we can piece together the next-best solution.


To take this topic on quantitatively, I'll use a modified version of a concept I first discovered in Wayne L. Winston's 2009 book Mathletics.

In that book, the writers were attempting to estimate what Ted Williams' batting average would be in 2006 Major League Baseball, if he were to be in his 1941 form (when he became the last player to hit .400 in a season). They took the combined batting averages of all players who played in 1941 who were not in their last seasons, and then compared those averages to the same players' collective averages in 1942 (i.e., no 1942 rookies), in order to see how much the league's pitching and defense—the factors outside the hitters' control—improved from 1941 to 1942. Then, they took all players who played in 1942 who were not in their last seasons, and compared that group's batting averages to the same group's stats in 1943 (i.e., no 1943 rookies). This process was repeated for every pair of seasons up to 2005-2006 to see how much better the MLB's pitching/defense had become year by year since the 1940s, without being skewed by the new batters entering the league each year. The core principle of Winston's methodology was that "since young players tend to improve with experience and older players tend to decline in their later years, it's a fair assumption that this group's batting abilities won't drastically change from year to year."

This assumption provides the starting point for my project. I use a similar concept with five common NFL passing "rate stats": completion percentage, touchdown percentage, interception percentage, yards per pass attempt, and yards per completion. As was the case with the Mathletics Ted Williams study, the goal is to see how much all of the "external factors" that aren't directly related to a quarterback's individual skill have evolved over time, and how much those factors have influenced passing stats. These factors include, but aren't limited to:

  • More innovative offensive play design (in particular, play-action becoming more common).
  • The inception of more offense-friendly rules.
  • Better athletes playing around the quarterback on offense (particularly at receiving positions).
  • Better athletes playing against the quarterback on defense.
  • More complex defensive coverage schemes.
  • Advances in sports medicine and nutrition.
  • Reductions in the legal number of full-contact practices per NFL team per season.

However, my methodology has two key modifications to the Mathletics format. One of them is the institution of a passing attempts minimum. When comparing any two seasons, the method of excluding all retirees in the first season and all rookies in the second season conceptually makes sense, so that the group of quarterbacks is (theoretically) unchanged between each season. But in practice, there are numerous instances like Patrick Mahomes, who only played one game in his rookie year of 2017 but played all 16 games in 2018. In this example, the quarterback group wasn't really the exact same in 2017 as it was in 2018, because even though Mahomes was a part of both, he had 35 pass attempts in the prior year and 580 in the latter. As a result, any jump in league-wide stats from 2017 to 2018 was artificially inflated by Mahomes (and Deshaun Watson, for that matter) playing far more in 2018 than in 2017. This phenomenon can work in the opposite direction too: e.g., Tom Brady only had 11 pass attempts in 2008 due to an ACL injury after having a then-record 50 passing touchdowns in his historic 2007 season. To counter this, my data collection for this project involved looking at Pro Football Reference's statistics for two seasons at a time, and only extracting data for quarterbacks who hit 150-plus attempts in both seasons (regular season only). While still not flawless (e.g., a quarterback could have had 153 attempts in one season and then 603 in the next one), it allows us to avoid the egregious examples like 2018 Mahomes and 2008 Brady. Using this format, I compiled all passing statistics for quarterbacks for every pair of seasons since 1960 and 1961. I started at this point because 1960 was the first season of the AFL (American Football League, i.e., what the current AFC was called before the 1970 AFL-NFL merger), significantly increasing our year-to-year sample sizes compared to the pre-AFL era.

The other modification concerns decision-making. In the Ted Williams project, the writers attributed all of a season's statistical changes to external factors—i.e., if players not in their final season in 1953 had a collective batting average of .270, and players who weren't rookies in 1954 had a collective average of .260, that means that pitching and defense improved by an estimated .010 points in that offseason. But playing quarterback is different than batting in the sense that there's much more decision-making involved. While there are some choices that come at the plate in baseball, the mental side of playing quarterback involves far more complex decision-making on a play-to-play basis, with audibles, pre-snap coverage reads, and post-snap improvisations all playing major roles in where (if at all) a quarterback throws the ball. Because of this, it isn't fair to exactly copy the Mathletics assumption regarding a group of players collectively not improving or regressing noticeably from one year to the next. While the purely physical quarterback traits like arm strength and accuracy likely follow that ideology, an extra year in the league can significantly influence a quarterback's mental capacity. Because of this, I modified Winston's formula so that half of the league's year-to-year statistical changes are attributed to the "external factors" such as play-calling, rules, and defense, while the other half are attributed to the quarterbacks' own change in performance.

Since this all sounds confusing, here's a specific example of how it works, using completion percentage. Let's start with the 1960 and 1961 seasons as our baseline. There were 16 quarterbacks who had 150-plus pass attempts in each of those seasons. In 1960, those quarterbacks had a collective completion rate of 50.75%. Those exact same quarterbacks then had a collective completion rate of 51.10% in 1961. That's an increase of 0.35%. Our methodology splits that 0.35% right down the middle, so 0.175% is attributed to a collective increase of those quarterbacks own performances, and the other 0.175% is attributed to the external factors discussed above, making it an estimated 0.175 percentage points easier to complete passes between 1960 and 1961, thus combining to make the +0.35% gap.

To phrase the latter part about external factors more succinctly, we would say EXT_CompPct_1960to1961 = +0.175. Repeating this process for 1961 and 1962, we find that EXT_CompPct_1961to1962 = +0.895. Because our eventual goal is to find EXT_CompPct_1960to2021, we simply have to repeat this process over and over again: EXT_CompPct_1960to2021 = EXT_CompPct_1960to1961 + EXT_CompPct_1961to1962 + EXT_CompPct_1962to1963 … + EXT_CompPct_2020to2021. As you'll see below, it turns out that this number is +13.2, meaning that it was approximately 13.2 percentage points easier to complete a pass in 2021 than in 1960 by our logic.


While we saw a taste of our data in the Methodology section, below is the real final data, with explanations to follow. This data only shows results by decade rather than by individual seasons to save space, but I can share the year-by-year data to anyone interested.

Change in Rate Stats Since 1960
Year Cmp%, 1960
to Year X
YPA, 1960
to Year X
TD%, 1960
to Year X
INT%, 1960
to Year X
YPC, 1960
to Year X
1970 0.13 -0.33 -0.51 -0.31 -0.66
1980 4.06 -0.43 -1.12 -0.69 -1.79
1990 5.84 -0.42 -1.09 -1.19 -2.16
2000 7.65 -0.76 -1.53 -1.29 -3.11
2010 9.86 -0.83 -1.80 -1.36 -3.65
2021 13.18 -0.76 -1.83 -1.52 -4.14

These numbers show us that it has overall become easier to have success passing the ball over the past 60-plus years, but that doesn't mean that each individual statistic has necessarily seen a reduction in difficulty. By our project's logic, it has actually become slightly more difficult to throw touchdowns in today's league, and passing yards per attempt have been relatively stable, with a slight increase in difficulty. In contrast, completion percentage and interception percentage have been consistently and steeply trending in quarterbacks' favor throughout the past six decades. If we look at our far right column, yards per completion, we get a good explanation why. Yards per completion has collectively taken an extremely sharp decline in the NFL since 1960, which leads us to one major conclusion: quarterback statistics in the NFL are better today largely because of a systemic league-wide embracing of shorter, less dangerous passes in recent years. Completion percentages are higher and interception rates are lower because the league has shifted toward shorter passes, whereas touchdown percentage and yards per attempt haven't seen the same upward vault because they largely depend on increased downfield aggressiveness from quarterbacks. (Notably, there hasn't been a qualified passer to have 10-plus yards per attempt in a season since Norm Van Brocklin in 1954).

With that being said, while progress has been noticeable in several quarterback metrics since 1960, that progress hasn't been linear. In order to take a deeper look into how the difficulties of being an NFL quarterback have changed year-to-year, we can use R graphs. Again, we can start with completion percentage to explain our methodology. The following graph details how much easier it has been to complete passes based on external factors, going one year at a time, to allow us to see which specific seasons took jumps or declines from the immediately preceding one. In other words, the bar you see on the far right (just over 0.0 pct) represents EXT_CompPct_2020to2021, while the vertical red lines mark the start of each decade (excluding 2020):

2. Year-by-Year Comp Pct Change Since 1960

In contrast, the ensuing graph (and the one I find more informative) details how much easier it has been to complete passes in the NFL, but on a cumulative basis since 1960 rather than looking at one year at a time. So, the bar on the far right here, at just over 13 percent, represents EXT_CompPct_1960to2021, rather than EXT_CompPct_2020to2021:

3. Cumulative Comp Pct Change Since 1960

One interesting phenomenon that becomes evident from these graphs is that the whole is greater than the sum of its parts; in other words, while any given year-to-year jump might be minimal (and in fact, many of them are negative), we still have a drastic upward trend when we look at a longer span of time. I ran some two-sample T-tests to further verify this point, which I cut here for space but can share to anyone interested. Before getting into further observations, I'll throw in the same style of graph as the immediately preceding one—i.e., going cumulatively since 1960, instead of year-by-year—for the other statistics we have measured.

Yards per pass attempt:

4. Cumulative YPA Change Since 1960

TD percentage:

5. Cumulative TD Pct Change Since 1960

INT percentage:

6. Cumulative INT Pct Change Since 1960

Yards per completion:

7. Cumulative YPC Change Since 1960

You can scan the graphs to find your own observations, but these stood out to me:

In addition to being the first-ever 16-game season, 1978 is known for being when a year where two significantly pro-offense rule changes were enacted: contact between defensive backs and receivers was restricted more than 5 yards downfield, and offensive linemen were given more freedom to use their hands on pass plays without being called for holding. As expected, these made a noticeably positive impact on quarterback stats. Among 20 quarterbacks to have 150-plus attempts in both 1977 and 1978, they collectively improved in completion percentage, yards per attempt, and interception percentage in 1978, with a particularly large +2.37% jump in completion percentage. To clarify, those are the full statistical increases between the 1977 and 1978 quarterbacks, not the versions that are cut in half to account for just the impact made by our external factors.

In 2004, the NFL further cracked down on restricting contact by defensive backs more than 5 yards beyond the line of scrimmage, and that led to an absolute boom in passing stats between 2003 and 2004, including the largest year-to-year jumps in yards per attempt (+0.45) and touchdown percentage (+0.64) for any pair of seasons since 1960, excluding the strike-shortened season of 1982. This season is particularly known for Peyton Manning's historic output, as he set then-NFL records in passing touchdowns (49) and passer rating (121.1). Broadly, most quarterback stats, particularly completion percentage and interception percentage, have seen noticeable improvements over the past 20 seasons.

2011 was known as the "Year of the Passing Game," still standing as the only season all-time to have three 5,000-yard passers (Drew Brees, Tom Brady, Matthew Stafford)—none of whom even won NFL MVP, as that honor went to Aaron Rodgers and his still-standing record 122.5 passer rating. Unsurprisingly, this came after a rule change as well, as 2011 was when the NFL changed rules to further define and protect "defenseless receivers." While touchdown percentage and interception percentage weren't actually positively impacted between 2010 and 2011, the jump of +0.211 yards per attempt between the seasons is the fifth-largest since 1960.

2018 was the year of Patrick Mahomes torching everything in his path in his first year as a full-time starter, but he wasn't the only reason that quarterback numbers spiked that season. Rule changes in 2018 included a penalty for any defender who lowers his helmet before contact, and the infamous "body weight" rule regarding defenders tackling quarterbacks. Subsequently, the group of quarterbacks with 150-plus attempts in both 2017 and 2018 collectively improved in the latter season in completion percentage, yards per attempt, interception percentage, and touchdown percentage. The jump of +3.16% in completion percentage is the largest between any pair of seasons since 1960, while the jump in yards per attempt (+0.28) ranks third in that span.

An obvious trend in these observations is that rule changes have directly led to improved quarterback stats. The NFL's Competition Committee even said the following in 2012: "If someone wants to accuse the National Football League of promoting offense to make the game more exciting, [the committee] believes the league should plead guilty." While other factors, particularly the evolution of play-calling, have likely also played a role in the offensive explosion, our data suggests that the NFL's rule changes have had the primary (and desired) effect of getting more points on the board.

Real-World Examples of Player Projections

With all of this data in our back pocket, now we can answer the titular question: just how good would the top quarterbacks of the past be in today's game? To start off in this task, here are the real statistics from five Hall of Fame quarterbacks in their MVP seasons:

Actual Statistics of Select MVP Quarterbacks
Player Team Year Cmp Att Cmp% Yards YPA TD TD% INT INT% Rtg
Johnny Unitas BALC 1967 255 436 58.5% 3,428 7.86 20 4.59% 16 3.67% 83.6
Terry Bradshaw PIT 1978 207 368 56.3% 2,915 7.92 28 7.61% 20 5.43% 84.7
Dan Marino MIA 1984 362 564 64.2% 5,084 9.01 48 8.51% 17 3.01% 108.9
Joe Montana SF 1989 271 386 70.2% 3,521 9.12 26 6.74% 8 2.07% 112.4
Steve Young SF 1994 324 461 70.3% 3,969 8.61 35 7.59% 10 2.17% 112.8

Now, here are the projected adjustments, based on external factors, regarding how much easier it got in each statistical category between those MVP seasons in question and 2021:

Yearly Adjustments of Select MVP Quarterbacks
Player Team Year Cmp%,
Year X
to 2021
Year X
to 2021
Year X
to 2021
Year X
to 2021
Year X
to 2021
Johnny Unitas BALC 1967 13.63 -0.55 -1.69 -1.59 -3.87
Terry Bradshaw PIT 1978 10.94 -0.24 -0.58 -1.13 -2.61
Dan Marino MIA 1984 8.08 -0.46 -0.87 -0.60 -2.36
Joe Montana SF 1989 7.51 -0.39 -0.57 -0.53 -2.09
Steve Young SF 1994 5.76 -0.16 -0.61 -0.23 -1.34

Fnally, here are what those old-time quarterbacks' projected stats would be in 2021, if we adjusted their MVP numbers to account for the external factors that have changed since those seasons. For the sake of comparison, we also include the real-life numbers for several big-name quarterbacks in 2021:

Adjusted Statistics of Select MVP Quarterbacks (with Select Modern Comparisons)
Player Team Year Cmp Att Cmp% Yards YPA TD TD% INT INT% Rtg
Johnny Unitas BALC 1967 445 617 72.1% 4,509 7.31 18 2.92% 13 2.11% 93.6
Terry Bradshaw PIT 1978 311 463 67.2% 3,558 7.68 33 7.13% 20 4.32% 95.8
Dan Marino MIA 1984 520 719 72.3% 6,151 8.55 55 7.65% 17 2.36% 113.6
Joe Montana SF 1989 360 463 77.8% 4,045 8.74 29 6.26% 7 1.51% 117.6
Steve Young SF 1994 365 480 76.0% 4,057 8.45 34 7.08% 9 1.88% 116.5
Aaron Rodgers GB 2021 366 531 68.9% 4,115 7.75 37 6.97% 4 0.75% 111.9
Tom Brady TB 2021 485 719 67.5% 5,316 7.39 43 5.98% 12 1.67% 102.1
Patrick Mahomes KC 2021 436 658 66.3% 4,839 7.35 37 5.62% 13 1.98% 98.5
Joe Burrow CIN 2021 366 520 70.4% 4,611 8.87 34 6.54% 14 2.69% 108.3
Dak Prescott DAL 2021 410 596 68.8% 4,449 7.46 37 6.21% 10 1.68% 104.2

We must view these projections for the old-timers with a grain of salt, because the real-life seasons we based those projections on, by virtue of being MVP years, are inherently major outliers. In other words, the takeaway shouldn't be that Dan Marino, Joe Montana, and Steve Young are all actually far better football players than Patrick Mahomes; rather, it should be that the absolute best seasons of each of those guys' careers compare favorably to what will surely end up being considered a below-average season in Mahomes' career. This phenomenon is largely my own fault for choosing to use some of the greatest seasons of all-time to analyze here, but I figured the average reader cares more about Marino and Montana than about Steve Spurrier or Doug Pederson.

With that disclaimer being said (and more to come in the bottom section on Sources of Error), these projected numbers are still largely impressive. 1984 Dan Marino's modern-day projections would set the all-time passing yards record and tie Peyton Manning's passing touchdown record, which makes sense given the discourse about his 1984 season. 1989 Montana and 1994 Steve Young both were projected to set single-season records in completion percentage and beat all 2021 starters in passer rating, which isn't too surprising given that they were the only qualified passers to have a 110.0-plus passer rating in the entire 20th century. However, as most fans would expect, the "average" quarterback of 2021 would be closer to the level of players like Montana and Young than their contemporaries were. For example, Steve Young's Passer Rating Index (a measurement of how one's passer rating compares to the rest of the league of that season, where 100 is standardized as league average, similar to OPS+ in baseball) in 1994 was a staggering 147. But his projected Passer Rating Index in 2021 would have been approximately 131, even though his actual projected passer rating would have been higher in 2021 than in 1994. These projections lead us to a reasonable conclusion: while the collective quarterbacks of today's game are still better than they have ever been, the vastly inflated statistics we see today are largely due to the external factors such as rule changes and play-calling. It isn't fair to call the "it's never been easier to be a quarterback" ideology correct and the "quarterbacks are just better nowadays" ideology incorrect, since both sides are right to an extent, but I believe the former trait is what ultimately has been more impactful on modern-day quarterback statistics.

Possible Sources of Error/Other Comments on Methodology

While any football analytics project has some built-in risk of error, this one has particularly major caveats given that it attempts to deal with time travel. The biggest one is that the attribution of half of the changes in quarterbacks' stats to their own skill changing, and half to the external factors around the league, was a somewhat arbitrary allocation. While just about every other trait of this project was determined with a data-driven process, as shown by the barrage of R graphs and tables, the decision to go with a 50/50 split here was an intuitive call based on my beliefs on how quarterbacks benefit by having extra experience in the league. While that intuition fortunately led to reasonable projections (e.g., we weren't told that Johnny Unitas would have an 84% completion rate in today's league), there's still no way to ensure that it was the correct distribution. If anything, there probably was no single uniform correct distribution; i.e., perhaps attributing half of the changes to external factors was too low for a year with drastic rule changes like 1978, but too high in other seasons.

The other primary flaw, and one that is common across football analytics projects, is that every team in a certain year is treated exactly the same. We say that it's roughly 13 percentage points easier to complete a pass in 2021 than in 1960, but in practice, that would obviously depend on which team a quarterback was playing for. Those external factors suh as play-calling and skill position talent don't just vary from year to year; they also vary from team to team within a specific year, which this project doesn't account for. This distinction is particularly important when discussing guys like Joe Montana and Steve Young, since lining up next to prime Jerry Rice is an ideal asset for any quarterback. While we estimated it was roughly 6% easier to complete passes between in 2021 than 1994 for average teams, that gap wouldn't likely be as big if we compared the average 2021 team to the 1994 49ers specifically. As such, the modern projections for those two quarterbacks, and the other old-timers as well, were likely a bit inflated. By virtue of winning MVPs in those seasons, they inherently were probably in situations where their team's coaching and supporting cast made it easier to succeed than it would have been on another roster. Unfortunately, this was another systematic flaw we had to accept, since sample sizes would have been trivial if looking at one team at a time.

These are the primary sources of concern, though there are more minor ones as well (e.g., the flaws of passer rating as a stat have been well-documented for years, but you can't exactly access DVOA back to the mid-1900s.)

Pertaining to methodology, some readers may be wondering how I estimated the raw number of attempts for old-time quarterbacks in their theoretical 2021 statistics. The way I did it was a "scale" based on each individual season's leader in pass attempts. To elaborate, Joe Montana had 386 pass attempts in 1989, and the 1989 leader in pass attempts was Don Majkowski at 599, meaning Montana had 64.4% of the leader's attempts. The 2021 leader in attempts was Tom Brady, at 719. So, using the same scale, the theoretical 2021 Joe Montana would have (64.4% * 719) attempts, or 463. Of course, it's not a perfect assumption to make (largely because we can't assume each old-time quarterback's theoretical 2021 team would have the same play-calling tendencies as his real-life team), but it's a solid proxy in the sense that it gave numbers that are at least feasible for the 2021 season.

Thanks for the read, and I'm happy to hear any feedback or further questions about methodology.

Cole Jacobson is a Next Gen Stats Researcher at the NFL Media office in Los Angeles. He played varsity sprint football as a defensive lineman at the University of Pennsylvania, where he was a 2019 graduate as a mathematics major and statistics minor. With any questions, comments, or ideas, he can be contacted via email at and @ColeJacobson32 on Twitter.


77 comments, Last at 25 Mar 2022, 8:56pm

1 Wow

If the author of the book thought Williams hit .406 in 1944, when he was a USMC pilot in the Pacific, I would not trust his thinking on anything.

”The biggest one is that the attribution of half of the changes in quarterbacks' stats to their own skill changing, and half to the external factors around the league, was a somewhat arbitrary allocation.”

Only somewhat?  What would it take to be significant?  Making up ALL the numbers?

45 Yup, my fault here. The …

In reply to by Raiderfan

Yup, my fault here. The "Mathletics" author had Williams' .406 season correctly written as being in 1941, I just made a typo in the first draft of this piece. Embarrassing slip-up for sure.

As for the 50/50 allocation, as I said in the piece, there's no objective right way to do it. Any "comparing eras"-style piece, regardless of sport, will be incapable of providing exact answers, so the goal is instead to get the best approximation we can based on the data we have. The 50/50 isn't perfect, but it's better than throwing a dart at a board and letting the scale be determined from there.

2 Great Analysis

...and love the caveats at the end.  I think I'd also add that Steve Young and Joe Montana were already playing in what are "fairly close" to modern passing offenses in '89 and '94.   For instance, look at their YPC compared to the other 3 seasons highlighted--- Unitas checks in at 13.44 YPC, Bradshaw at 14.1 YPC, and Marino at 14.0 YPC.  Meanwhile, Montana and Young check in at 13.0 (Montana) and 12.25 (Young).  The personnel is only part of the story -- as the West Coast scheme (and variants of it) really are the forerunners of many of today's modern passing concepts and placed a strong reliance on shorter routes and horizontal concepts to open up the passing game.  Bill Walsh's scheme, which both of these QBs were operating in, (with modifications) serves as a template for most of the really explosive passing attacks today.

It'd be interesting to look at a couple of QB's not included in this list -- first, Ken Anderson, and his 1981 MVP season and the follow-up 1982 season.  It's often lost that the West Coast offense took it's seminal steps in Cincinnati, and that Ken Anderson had the most accurate season for a QB in 1982 that we'd see until Drew Brees broke the record in 2009.  That makes that 1982 season one of the biggest statistical outliers ever --and it'd be interesting to see what it'd look like today (of course, Anderson only played 9 games that season, so you'd also have to project his output to 16....).  It goes without mentioning that Anderson not being in the HOF is still a huge crime.

Another interesting look would be any of Ken Stabler's prime years (or even Dan Fouts), as those QBs were "push the ball down the field" types as opposed to the more modern West Coast descendants we have now.  Ken Stabler's 1976 season would probably look ridiculous when adjusted this way -- and for having 16 games.  For Fouts, either 1980 or 1981 would make for really interesting views, given how insanely productive the Charger's passing attack was during those years.

Again, this was a great read, and very interesting to see the trends over time.  



46 Thanks for the read,…

In reply to by Ranger88

Thanks for the read, appreciate the kind words. Definitely a good point about the 49ers, which matches up with what I said in the Sources of Error section: "By virtue of winning MVPs in those seasons, they inherently were probably in situations where their team's coaching and supporting cast made it easier to succeed than it would have been on another roster. Unfortunately, this was another systematic flaw we had to accept, since sample sizes would have been trivial if looking at one team at a time."

Even though Walsh himself wasn't the SF HC anymore during the seasons discussed in this article (his last year with SF was 1988, and the piece looked at 1989 Montana and 1994 Young), he obviously still influenced the way SF operated under George Seifert, which can't be discounted. 

If you want to see how the numbers would play out for Anderson, Stabler, Fouts, etc., send me an email (either or and I'm happy to run the numbers with them. Can't put screenshots in these comment threads as far as I know, otherwise I'd go about it that way.


3 Because of this, it isn't…

Because of this, it isn't fair to exactly copy the Mathletics assumption regarding a group of players collectively not improving or regressing noticeably from one year to the next. While the purely physical quarterback traits like arm strength and accuracy likely follow that ideology, an extra year in the league can significantly influence a quarterback's mental capacity. Because of this, I modified Winston's formula so that half of the league's year-to-year statistical changes are attributed to the "external factors" such as play-calling, rules, and defense, while the other half are attributed to the quarterbacks' own change in performance.

Couldn't you validate expected career path by looking at something like the aggregate adjusted stats across QB group? (for instance: 

This is still susceptible to team changes, which are also probably a bigger factor in the NFL than in MLB. (Even God has poor adjusted stats if his receivers are Agholor, Austin, Chris Chambers, and Ebron.

62 That's a good thought for…

That's a good thought for sure, and something I have considered. But I think you hit the nail on the head with why one would be apprehensive about it. Take Matthew Stafford (age 33 during the 2021 season) for an example. If one was creating an expected career path model for QBs as they age, his statistics would suggest that he was a lot better at age 33 than age 32. But was he really that much better in 2021 than in 2020, or just in a situation with better play-calling, skill position talent, etc.? Likewise, on the flip side, was Jared Goff actually a worse player at age 27 (2021) than he was in his Rams years, or just in a more difficult position to succeed?

Over a big enough sample size, this would likely even out (e.g., maybe for every Stafford, there's also a situation where an older player gets traded to a weaker team, and his stats decline even further than they would have for age reasons alone). But team changes aren't the only potential pitfall for the "expected career path" idea. E.G., Roger Staubach's yards/att jumped from 7.3 to 7.7 between 1977 and 1978 (the latter being his age-36 season). Was that primarily because of any change in his game, or because of the notable rule changes that year? So ultimately, I felt there was more risk than reward in formally implementing this idea into the article.

64 ok

Cole------In your example using Stafford, he was no better in 2021 in the Reg. Season than he was way back in 2011, although I get it that you were more comparing it to 2020.

But the bigger picture for Stafford was this: he was being consistently outplayed in the playoffs by the opposing QB's in years past, which led to very little to no success for him and his team.

But that really changed this year in all 4 playoff games and it led to his ultimate success in the playoffs for himself and his team.

67 I do agree that playoff…

In reply to by Bob Smith

I do agree that playoff performance for QBs should be a major factor in how we evaluate their overall careers (and that Stafford's three playoff appearances with the Lions didn't go so well). But with that being said, I still didn't feel that including playoffs was the proper move for this article specifically. The goal of the project was to assess how the NFL as a whole has become easier for passers. By looking at the playoffs, which only include the top 14 teams (or 12, or 8, etc., depending on the year), we would get a skewed version of how the collective NFL has changed over time. So while no one's saying that the playoffs don't matter, I felt this wasn't the place to approach them.

4 I'm curious why instead of…

I'm curious why instead of cumulative summing you didn't run do a smoothing algorithm to generate a trend?

Actually, how I might have approached this would be to do a smoothing model that allows for mean shifts to account for rule changes, but also probable segmented by splices of the data  ie- it's assumed the passing efficiency changes have been similar across every kind of quarterback, but perhaps it's only the top and that are driving that increase or has it been everyone but the worst?u Bt that's mostly a technical footpoint.

I think the broad conclusions are correct, teams are throwing short more than ever and squeezing efficiencies that way.

6 One of the things he's…

One of the things he's looking for are discontinuous jumps, which smoothing functions will tend to obscure.

our data suggests that the NFL's rule changes have had the primary (and desired) effect of getting more points on the board.

It's interesting that *that* hasn't entirely occurred. We see more yards, but not a huge move in points. Because more yards (and fewer turnovers) also leads to a larger change in field position from drive to drive, so the opposing offense also has to move more yards to score.

The other hidden factor is kickers getting dramatically better.

10 Well, that's why its…

Well, that's why its flexible enough to handle mean shifts.

The other reason scoring as a whole may not have increased is because drives are fewer since most offenses are not going three and out as frequently.

I'd still like to see these numbers without aggregating them all away by year and do a composite by team. The binning can be done by hand or by algorithm. Either way, id be curious 

63 Good question here, as R has…

Good question here, as R has a stat_smooth() function and other similar ones that could be used for "trend" analysis. But Aaron Brooks G. nailed it with what I was aiming for. I wanted to see the year-to-year specific impact that certain rules were making. Broadly, if any year had a notable increase or decrease in QB production, I wanted to know why.

I'd also say scoring has increased more than one might acknowledge at first glance. Even when looking at points per game instead of total points (since the season obviously has more games now than ever before), 8 of the top 10 scoring offenses in the Super Bowl era have come since 2000 (with 1998 MIN and 1983 WAS being the only exceptions). 23 teams have averaged 30+ PPG in a season since 2010 (a 12-season span), which is only one fewer than the 24 teams that did so from 1966-2009 (a 44-season span).


65 Just to be clear, there are…

Just to be clear, there are trend fitting models that are flexible enough to handle mean shifts. 

One crude way is to pass it through a change point detection model and then smooth the intervals afterwards. But there are even models that are more general than that.

The change point way at least let's you test more rigorously if the rule changes did indeed cause a significant and permanent mean shift.


77 Interesting, that's good…

Interesting, that's good stuff to know. I'll be the first to admit that I definitely don't know every function or graphing tool that's out there in R, as there's always more to learn. I'll toy around with the program and see what other, more complex functions might exist to make models like this.

7 interesting

Cole-----This is very interesting, but does it really matter in the long run?? This is still Regular Season information and the only success a QB can achieve in the Reg. Season is playing good enough to help their team to qualify for the playoffs.

The far more important information would be how stats and facts for QB's .were affected IN THE PLAYOFFS. I will remind you of a Dan Marino quote: "I'd trade every Record we broke to be Super Bowl Champs".  That is how a record breaking QB looks at it.

11 We can now add Stafford to…

In reply to by Bob Smith

We can now add Stafford to the list of QBs that's better than Dan Marino. At least that one doesn't hurt the brain as much as Dilfer and Brad Johnson.

15 That's accurate, but then…

In reply to by Bob Smith

That's accurate, but then what is the implication of that statement? Or is it simply that Marino has no rings and other qbs do?

Also, I bet if you gave Dilfer truth serum, he'd trade his ring in which he gets 0 respect for half the career of Marino.

18 ok

Have you ever heard a QB talk about winning the S.B. and saying that they have  now "Reached the Pinnacle of Their Profession".? Dilfer and Johnson (and others) can say that.

Marino can only say that he would trade his Reg. Season Records to be able to say that.

20 Dilfer passed for under 200…

In reply to by Bob Smith

Dilfer passed for under 200 yards and 1 td. If he reached the "pinnacle", it wasn't much more than what the center, slot corner, or backup wide receiver felt on that Ravens offense.

Also, think about how Dilfer is remembered...he's the poster child for the anti rings movement. I'd rather be remembered as a hall of fame QB who rewrote the record books rather than a passenger on a title team that didn't even keep me the next year. 

27 ok

Those are all good points you are making. Plus Dilfer went into the playoffs with the No.1 Defense for Least Points Allowed which probably helped him to play better.

The sad part about that-Marino went into the playoffs twice ('83 and '98) with  No.1 Defenses for Least Points Allowed and played even worse than Dilfer played in his S.B. winning year. 

Dilfer in his S.B. winning year was 4-0 in the playoffs and had 3 TD's and 1 INT. and a Rating of 83.7

Marino in his 2 playoff years with No.1 Defenses had a Record of 1-2 and had 3 TD's and 5 INT's and an avg. Rating of 76.2

41 Yeah, well. He was a rookie…

In reply to by Bob Smith

Yeah, well. He was a rookie in 1983 and in decline by 1998, when he was only 11th in DYAR. In 1983 as a rookie he was 7th in DYAR, but the defense was only 16th by DVOA, so not nearly as good as you might think.

44 ok

In '83 Marino was in the start of his prime ('83-'86) and in '98 a fellow '83 Draftee (Elway) played good enough to help his team win the S.B.  and played good enough to be named the S.B. MVP--something Marino never came close to.

And Marino played good enough to beat those '98 Broncos in the Reg Season by throwing 4 TD passers a few weeks before the playoff game. Dan was very good in the REGULAR SEASON. 

In the playoffs Marino  was not nearly as good.

49 Are you being serious right…

In reply to by Bob Smith

Are you being serious right now? Yeah, he was in the start of his prime because he was a rookie! He was great, for a rookie, but still a rookie. No rookie is in his prime. Not even Marino. And like I said, his defense was 16th by DVOA, so there's nothing there, anyway.

Meanwhile, if his prime ended in 86, in 98 he was 12 years past his prime. It's not that he was bad in 98. He was ok. Did he play well against Denver? I'll take your word for it but I don't see how it matters. I'm sure he had some good games. But he overall he was far from the player he used to be. In fact, he only had one more season left in him, and not a good one.

50 He's not serious. The shtick…

He's not serious.

The shtick of "Bob Smith" is two items:

  1. Dan Marino sucked, because playoffs. (This is a modified RINGZ argument)
  2. NFL points allowed counting stats = defensive efficiency

No one who seriously follows this site actually believes either argument.

53 ok

Noahrk-----I have bought in to the studies that P-F-R has done concerning the Value that a QB gives to his team. They did a study for the Regular Season and a separate study for the playoffs.

In the Reg. Season Marino is still in the Top 10 for Value given amongst QB's. In the playoffs Dan is not even in the Top 100.That is what P-F-R has determined. I had nothing to do with either of those studies.

In the '98 Reg. Season game against the Broncos Marino had 4 TD's and led his offense to 31 points and a win. A couple of weeks later Marino led his offense to only 3 points in a playoff loss to those same Broncos. 

52 He also ran into the…

In reply to by Bob Smith

He also ran into the dynastic 49ers; a different quality of opponent vs the 2000 NY Giants.

54 ok

In '83 the Dolphins got beat by the Seahawks if that is what you are searching for ??

55 I was referring to the…

In reply to by Bob Smith

I was referring to the reason why he played worse than how Dilfer did in the super bowl.

I think it would be easier for everyone if you just stated the implicit point you're making behind all of this. We can all agree that Marino played worse in the playoffs than he did in the regular season. And therefore what do we conclude from this?

Because you haven't said it so far, I'm inferring from this that you think Marino is a choker. That somehow the regular season was all pressure free and in the playoffs it revealed who he really was as a quarterback. And therefore we should all stop pretending like Marino is some all-time great and probably throw him into the dustbin of quarterbacks you want on your team. Since all that matters is the regular season, he is no more valuable a player than Mark Sanchez and frankly worse than Joe Flacco Brad Johnson and Trent Dilfer.

56 ok

The P-F-R study said that Marino gave his team a Negative Value in 75% of his Championship Games (3 of 4). You can conclude whatever you want. I have made no conclusions.

57 But you bring it up. And not…

In reply to by Bob Smith

But you bring it up. And not the first time. And never because you were being prompted. That's suggests a motive beyond, "Hey, here's an interesting fact folks"

58 ok

Go back and read your 1st line in your post number 55. You were talking about each guys S.B. Marino's S.B. game was 1 of his Negative Value Championship  Games.

47 Luckman's 1943

Luckman's 1943 always finishes on top of the Value metric derived from TAY/P+ adjustments for single seasons by QBs, though there's huge amounts of adjustments in tow for all of those.

70 Yeah, that Luckman season…

In reply to by HitchikersPie

Yeah, that Luckman season was pretty absurd for its era. While it would have been theoretically fascinating to take this project to NFL history, I went with the 1960 cutoff to increase our year-to-year sample sizes (since 1960 was when the AFL began play). There may have been too much volatility if we looked at seasons that only had 12 or so teams. But gotta show respect to Luckman being ahead of his time.

33 There are 272 regular-season…

In reply to by Bob Smith

There are 272 regular-season games per year and 13 playoff games per year. A great QB who isn't named Tom Brady might play in 10-15 playoff games in their career. In my opinion, the number of playoff games is too small to draw any true statistical trends from it over any timespan shorter than decades.

61 ok

RickD is right, but that doesn't invalidate other studies that have been done to determine the Value that a QB gives to his team IN THE PLAYOFFS. For example the P-F-R study done by Chase Stuart. Since this thread is about Montana and Marino let's use them.

Chase determined that Montana's Playoff Value to his team was 1,292 while Marino's was only NEGATIVE 156. When we see that Joe ended with a 16-7 Playoff Record compared to Dan's 8-10, and then see that Joe played good enough to lead his team to 8 total Championships compared to only 1 for Dan, it certainly seems to pass the Common Sense Test.

On top of that Montana had a winning Record in Championship games while Marino had a losing Record in Championship games.

My point-there are studies to help us see how a QB played in the playoffs.


8 These factors include, but…

These factors include, but aren't limited to:

  • More innovative offensive play design (in particular, play-action becoming more common).
  • The inception of more offense-friendly rules.
  • Better athletes playing around the quarterback on offense (particularly at receiving positions).
  • Better athletes playing against the quarterback on defense.
  • More complex defensive coverage schemes.
  • Advances in sports medicine and nutrition.
  • Reductions in the legal number of full-contact practices per NFL team per season.

Three I think are worth adding to this (though I imagine they'd be captured in your data regardless) are:

  • The changing effect of weather (season runs later vs. more domes - which is dominant?)
  • The increased quality of playing surfaces (just look at old NFL games, the fields look like mud pits)
  • Moving the goalposts (Seriously, who in god's name thought it was a good idea to put metal poles in the playing field?)

16 All of those except for…

All except for lacrosse and hockey are on the end line or behind it. And lacrosse AFAIK doesn't secure the poles down so they come loose if struck, like a hockey goal. In the pre-1974 NFL they were on the goal line, so they physically interfered with play.

19 Not necessarily true.Tiger…

Not necessarily true.

Tiger Stadium, Forbes Field, and Yankee Stadium all had flagpoles in the field of play and in fair territory. Minute Maid and Comerica were built with ones as well, and Fenway had one through 1973.

Sub-MLB, baseball has allowed all kinds of oddities. Clark Field at Texas had a cliff in center field. The cliff was inside the fences and was in play.

Ponce de Leon field had a magnolia tree in dead center that was in play.

22 And all of them have been…

And all of them have been taken out, because it was a terrible idea as I said. Further, in baseball only a single player has to deal with a flagpole way in the outfield, whereas the goalpost on the goalline was smack in the middle of the action in Goal to Go situations. Put a flagpole in the infield and we can compare it.

42 Put a flagpole in the…

Put a flagpole in the infield and we can compare it.


This needs to happen immediately.  George Carlin and I are boycotting baseball until it happens.  If we can't have landmines, this is an acceptable substitute.

71 Some really thoughtful…

Some really thoughtful points here, both by IlluminatusUIUC in his initial comment and those after it. It's always hilarious to see what the early 20th century baseball facilities looked like. My list of the "external factors" was meant to be non-exclusive, since we could go on forever hypothesizing about them. But as the initial comment said, any others would be captured in the data regardless, and it's fun to see the other ideas that you've thrown out there

36 I would also add changes in…

I would also add changes in high school and college strategy that affected the pool of NFL-ready QBs.

Go back and watch college football games from the 1990s. Very few teams threw the ball more than 20-25 times per game. This meant that college QBs didn't get as much practice. And the ones who did were going against simplified defenses geared toward stopping the run, so they came into the league with next to no experience reading NFL-style defenses. Because of this, you'll see a lot of passes to receivers who are open by a number of yards, which is comparatively rare today. You'll also see QBs missing relatively easy passes with much greater frequency.

This is even more true in the high school ranks. I played high school football in the 90s, and there was maybe one team in our conference that ran anything close to what we'd consider to be a modern offense, featuring multiple receivers and a balanced mix of passing and running. This meant that the pool of potential college QBs was much more slim than today.

Compare that to the amateur football scene today. The vast majority of high schools run some version of a shotgun spread offense, which gives promising QBs a chance to develop early. Then, when they get to college, most colleges run an offense that is similar to an NFL offense in many ways, and go against defenses running sophisticated coverage concepts. This means that the NFL has a much larger pool of plausible QBs to draw from, and the QBs are much more projectible and experienced.

I think NFL QBs as a whole ARE better due to these changes. It was interesting to see this article conclude that while top QBs in each era may be similar, the overall pool of NFL QBs now is deeper, because that's exactly what I would expect.

37 good points

Those are good and valid points and while I agree, I would also add this---of the 9 QB's that have 8,000+ Career Pass Attempts , only 1 (Marino) did not play a game in the 2000's. So QB's are definitely throwing more.

72 Yeah, great points here for…

In reply to by Bob Smith

Yeah, great points here for sure. High school football definitely looked much different in the 20th century than it did when I was playing in the early 2010s. So in the debate between "external factors have made it easier for QBs to succeed" vs. "the QBs are just better nowadays", these points support the latter argument for sure. The QBs are simply getting a lot more reps before entering the pros these days, not just from having more modern offenses at the HS/college level, but also from the booming "7 on 7" culture. I think we're all in agreement that both sides of the "external factor vs. QB improvement" debate are true to some extent, which the data supports.

9 I wonder how much comp/atts…

I wonder how much comp/atts change if you assume a 2021 rate, versus a scaled within-year ratio.

For shame for not including Tarkenton's 1975 (or his non-MVP, but perhaps better 1969) season. What Tarkenton would have been like had he not toiled away in the deadball era is a long-favorite question.

How much of the 1985 drop is Marino having a relative down year as compared to his legendary 1984 and his titanic 1986? (And the Bears laying waste to every other passing offense that year)

This is an analysis that probably cannot be pushed back past 1950. Free-substitution is such an apocalyptic change that I'm not sure most modern analyses generalize across the event horizon. I'm curious what the mid-50s passing boom looks like in this analysis, though.

73 What exactly do you mean by …

What exactly do you mean by "assuming a 2021 rate"? The method I went with tried to estimate how many attempts each player would have had in 2021. E.G., Marino was estimated to have 700+ attempts because he was already airing it out more than any other player in 1984, while the 2021 versions of Bradshaw and Montana weren't near that level, because their attempts numbers were low even for their own era's standards. If what you're suggesting is different from that, I'm open to ideas.

I'm happy to run the numbers with Tarkenton, as well. Can't put screenshots in here, but email me (either or if you're interested and I could send that over.

Marino and the Bears certainly each played a decent role in the statistical dips of 1985. With a league of 28 teams (at the time), any individual QB or team defense can make a non-negligible impact by having a particularly notable season in either direction. That same notion is why I didn't choose to look at any seasons before the 1960 AFL inception. With a league of 12 (or 10, or 8) teams, I figured some results might be especially noisy. If you'd like to see 1950s included, though, email me and I can cook that up.



17 One thing ive been tying my…

One thing ive been tying my brain in knots over it offense getting better or defense getting worse? I am not sure how you could quantify whether it's one or the other.







21 Would probably be more…

Would probably be more accurate to say defence is becoming more difficult.  They oppose each other so I don't think you can say it's one or the other. I.e offence getting better means defence gets worse since it's impossible for them both to get better at the same time. It's probably true play quality has increased on both sides but I dont think there is any way to measure that. 

25 But that should only show up…

But that should only show up in mean shifts and maybe some short persistence afterwards. Instead, it's been a trend which suggests it's harder for defenses even excluding the rule changes.

Maybe thats happening at the lower levels? The best skilled players are all heading to the offense? 

28 I'm not sure the assumption…

I'm not sure the assumption that information is perfect and adjustment is instantaneous is valid. Looking at the trends, it seems to well-correspond to rule changes (which are pretty frequent...) which have a spike and then a decay, as well as few tactical shifts (west-coast offenses) and the occasional epoch change (the merger; AFL and NFL teams had different baseline talent levels and playing styles).

74 The "offenses improving vs…

The "offenses improving vs. defenses declining" question is certainly a fair one. While it's very hard to distinguish how much the specific factors caused the statistical increases seen in this article, I personally believe that the evolution of play-calling makes an even greater impact than rule changes or individual athletes improving. The 1985 Bears might have been the toughest MFers on the planet, but they still would be totally lost if they had to defend even the most basic outside zone RPO with a backside pair of slants that's seen today. So while it's easy for us to say "offense has gotten better", it's more fun to dive into why that's the case (e.g., players getting better, rules being offense-friendlier, coaches being more innovative, and so on).

24 The fundamental element of…

The fundamental element of this game remains the violence of it, and the toll that violence takes on athletic performance, physical and mental. The qbs of today are subjected to such lesser violence than was previously the case (the 2009 NFCCG, when the Saints purposely dared the refs to honestly enforce RtP on the bludgeoning inflicted on Favre, was a real inflection point) than in the 00s, 90s, 80s, dont get me started on pre-80s stuff like...

...that it becomes almost impossible to compare. Players vary hugely, in their ability to absorb extreme violence without severe degradation in performance, and in how long they can absorb it. I have no idea which guys of today would handle it well, relative to guys in the past, and which guys in the past would benefit more than others, if they had avoided such battering.




26 I'm guessing anyone who…

I'm guessing anyone who wasnt adept at avoiding sacks would be much worse off in the past given the applicable violence. I think Rodgers probably has the same career length as Young in a prior era.

29 I just don't know. What…

I just don't know. What would Jeff George be like, if he knew the risk of getting hammered was greatly reduced? Cris Carter, I think, once said "I used to think there were no cowards in the NFL, but then I played with Jeff George".

34 In terms of physical courage…

In terms of physical courage, Carter played in an era, and ran a lot of routes, where it was no place for the timid. He also had a fair number of qbs throwing to him where ideal ball placement could not be assumed. He didn't get alligator arms much.

38 One of my favorite quote,…

One of my favorite quote, from 1960 Johnny U on a play where Doug Atkins broke his nose and sent him to the sideline bleeding prior to a return and a miraculous comeback.  "He got me with his shoulder and forearm . . . it was a clean hit."


75 Yup, it's no secret that…

Yup, it's no secret that defenders just can't get away with what they used to be able to do against QBs. I tried to incorporate this into the project as much as I could, such as discussing the 2018 "body weight" rule ( Needless to say, much easier for QBs to have success when they don't experience quite the same level of violence as in prior decades.

39 RE: Williams

I wanted to mention that Baseball Reference has the programmed ability to generate a past season not just in the current era but any other season.


I do not 'know' but I suspect this feature is the better resource versus the research mentioned only because of the group rigor applied to the exercise.  Many of us are always smarter than one or a few of us as the saying goes.



40 Many of us are always…

In reply to by big10freak

Many of us are always smarter than one or a few of us as the saying goes.

Ahh, but recall Pratchett's Axiom: The IQ of a mob is the IQ of its dumbest member divided by the number of mobsters

59 That and Vime's boot theory…

That and Vime's boot theory and two of the many great tidbits that Pratchett had that really stick with me.

And while I agree with the ignorance of the mob as pointed out. I also have to sadly admit to there being a difference between a mob and a crowd. So yeah, wisdom of the crowds is a thing too. I think the difference is how much emotion drives decisions. Mobs are emotional and hence dumb. If you keep the emotional response tamped down then you can get the wisdom.

So I can agree with Many of us, if emotionally distanced, are usually smarter than one or a few of us. But like you I can't agree with the statement as written because "mob mentality" is definitely a thing and smart people can become exceedingly dumb when swept up in the emotional flow of a mob and the whole can definitely be dumber than all the individuals.

76 Very interesting tidbit…

Very interesting tidbit about Pro Baseball Reference, can't say I knew that before. Unfortunately I don't have Stathead access for non-football sports, so I won't test it out myself any time soon, but it's awesome that they are capable of that. They do some awesome things over there, so I'm sure their mob is not an ignorant one.


68 Brilliant

Super interesting and accessible read even for a football newbie like myself. Good job, dude