Today’s post is a follow-up to my recent article on adjusting quarterback stats for schedule length and passing environment. In the original piece, I provided you with single-season stats with various era adjustments made. While my main goal was to glean as much as I could from your opinions, I noticed that some readers also liked looking at the different results based on which adjustments I made. With that in mind, I figured it only made sense to submit the career list as well.

When measuring single seasons, I think value over average is the way to go. However, I believe a lower baseline is in order when looking at entire careers. It seems to me that average play is an overlooked aspect of quarterback evaluation, and guys like Brett Favre or John Elway are significantly underrated by statistical models that compare to league average instead of replacement level. I would say that using a higher threshold shows us who was the most dominant, while using a lower threshold shows us who contributed the most value over an extended period.

The Method

There are a few ways to measure “average” and even more ways to determine replacement-level, so I’ll take a moment to tell you my methodology. For starters, I used Total Adjusted Yards per Play as my base stat. To find a general league average, I used the passing stats of quarterbacks only for every three year span with year N in the middle. ^[1]The exceptions, of course, are years that begin and end leagues, as well as a few seasons when stats weren’t available one year but were available the next. For example, from 2013-15, there were 62899 quarterback plays for 355743 Total Adjusted Yards. That means the number used for 2014’s average is 5.66 TAY/P. ^[2]This produces different results than you’d find if you used pass plays from all players. It also yields different results from the one’s PFR uses to find league average for their passing index … Continue reading Using three seasons gives us a larger data set and smooths data into several small eras. It is also especially helpful when measuring standard deviations later.

For replacement-level, I couldn’t decide what I liked best, so I used two different methods (which produce two very different sets of results). I’ll leave it to you to decide for yourself which you prefer. The first method is straightforward: just use 75% of the league average as the replacement baseline. Going back to 2014, that number would be 4.24. The other method is just as simple in theory but slightly more tedious in practice. First, I find the weighted standard deviation of TAY/P over the same three-year span. ^[3]I use a weighted standard deviation instead of just throwing everything into the stdev.p formula in Excel because I don’t want crazy outliers like Matt Moore and Scot Tolzien to artificially skew … Continue reading Next, I set the replacement-level baseline for each year at one standard deviation below average (an index score of 85, for those familiar with the PFR stats). This makes a pretty big difference the further back you go, as increased parity at the position has seen an ever-shrinking variance in TAY/P. ^[4]For instance, the standard deviation in TAY/P was 2.13 in 1950. It was just 1.67 in 1970, 1.45 in 1990, and 1.15 last year. In practical terms, this means that the threshold for replacement-level was much lower when variance was high than it is in more recent times when the margin for expected performance range has decreased.

With that out of the way, I’ll refresh you on the different ways I adjust for era. There are two methods I use to prorate seasons to the 16-game schedule: I call one prorating and the other lowrating. Prorating is simply slapping the number of scheduled team games in a season in the denominator under sixteen. Lowrating is the number you get when you find the average of the prorated number and one. ^[5]So a 14 game season has a Pro of 16/14, or 1.14. It has a low of 1.07. There are three methods I use to adjust for passing inflation (quarterback plays per game): I call those hard, soft, and weak inflation adjustments. To find hard, put the season’s QB plays per game in the denominator under the historical average (34.7). For soft, find the average of hard and one. For weak, add hard to two and divide by three. ^[6]Example time: In 2015, the league average QB plays per game was 40.8, so hard is 34.7/40.8, or 0.85. Soft is (0.85 + 1)/2, or 0.93. Weak is [(0.85 + 2)/3], or 0.95. All you need to do once you find these numbers is multiply them with quarterback values in order to find their era-adjusted values. As you’ll see, the compounding effects of modifying scores based on both schedule expansion and usage inflation can be significant.

I’m sure you’re tired of reading about methodology and want to see some results by now. There is much information, so get your popcorn ready.

The Results

The Dominant

The first table displays every quarterback in history with at least 1500 career plays, 194 players in all. Read it thus: Peyton Manning began in 1998 and ended his career with 10114 plays for 68574 Total Adjusted Yards at 6.78 TAY/P. For his career, his TAY/P was 1.71 above average. His career value is 17287. That becomes 15694 with a Pro/Hard adjustment, 16491 with Pro/Soft, 16756 with Pro/Weak, 15694 with Low/Hard, 16491 with Low/Soft, and 16756 with Low/Weak. The table is sorted by average rank in all categories of value, but you can search and sort as you wish. By default, only the top 10 players are shown, but the table lists all 194 quarterbacks, with the most recent being the three from the 2012 Draft. Andrew Luck, Russell Wilson, and Ryan Tannehill, of course. Blaine Gabbert with 1,273 plays, is just shy of missing the cut, but he’ll be worth watching for next year. He would certainly challenge for the bottom of several of these lists, even though he got to play with Football Perspective launch man Justin Blackmon for a couple of years.

I want you to decide for yourself what you find interesting, so I’m going to try to keep this brief. I enjoy looking at how each method of adjusting for era changes the ranks of certain players. For example, Milt Plum has the greatest range of ranks (32) of any quarterback. He ranks 97^th all time when ranked without adjustments, and he ranks as high as 65^th with the Pro/Hard combination. Ken Stabler and Charlie Conerly have large ranges too (19), with the former having a high/low of 83/64 and the latter having a high/low of 64/45.

Bob Waterfield ranks 59^th before making adjustments and as high as 41^st with the Pro/Hard modifier. Similarly, Bobby Layne has a low of 54 and a high of 38. As you can see, great quarterbacks of yesteryear move up significantly when we adjust for the length of their schedules and the passing environment in which they played.

Of course, one guy maintains the same ranking no matter what we do. That’s nice.

The Valuable, part one

The second table shows the same quarterbacks as above, this time with their values based on a replacement-level threshold set at 75% of average. Read it just like the first table.

When measuring against replacement-level, we start to see quarterbacks who weren’t as statistically dominant, but who played pretty well for a long time, start to climb the charts. Favre, who ranked no higher than twelfth by value over average, ranks fifth in almost every column here. This is where different opinions on value affect the way we interpret careers. I’ll pose a question I asked on my site recently: would you rather have 4787 uber-efficient plays from Aaron Rodgers or 11296 pretty efficient plays from Favre? 4817 highly efficient plays from Romo or 8540 less efficient, but still very good plays from Elway?

Fun fact: Peyton Manning and Dan Marino rank one and two no matter what adjustments you make. On the other end, Randy Johnson and Mike Phipps rank 194 and 193 regardless of adjustments.

The Valuable, part two

The third table shows the same 194 quarterbacks, now with values based on a replacement-level baseline set one full standard deviation below average. You know how to read these by now.

This is the table where you’re going to see some rankings that might blow your mind (check out what happens when you sort by the last column).

Changing course, let me say something about Drew Brees. Regardless of where I set my baseline, Brees ranks in the top nine in history. I’ve had many people tell me my stats (or any stats) are useless because of how high he ranks. Honestly, I think it says more about our perceptions than it does about the stats. He’s been overshadowed his entire career by the Manning-Brady-media-fabricated-rivalry, but he has clearly been one of the greatest passers in history since he arrived in New Orleans. We have a natural desire to demote him because he happens to play at the same time as Manning and Brady, ^[7]Even though we seem to have no problem naming Alan Page, Joe Greene, Bob Lilly, and Merlin Olsen the greatest defensive tackles of all time. but I think that’s silly. We can’t nullify his greatness because he happens to be a contemporary of two Rushmore quarterbacks.

Kyle Boller ranks last in every column. In fact, he’s the only quarterback in history to reach 1500 plays while maintaining a TAY/P more than a standard deviation below average.

Also, once again, no matter what I do Manning remains on top.

That’s all I have to say about that. What say you, fine citizens?