In preparation for my series on the statistical production of every quarterback since 1932, I thought it would be helpful to publish today’s post as a reference for what will follow. The three tables below contain the historical Total Adjusted Yards averages for every season in NFL, AFL, and AAFC history (98 league seasons in all).1 Normally, I measure value based on TAY/P relative to league average, multiplied by total plays. However, for this series I decided to measure performance versus a three year average of league plays. I believe this gives a better approximation of the era in which a quarterback played and helps mitigate the effect of outlier seasons like 1995 and 2004.
In this quarterback series, I am going to be looking at output relative to both league average and replacement level. I have previously used two different methods of determining the replacement baseline: 75% of league average and one standard deviation below league average. I have not settled on a favorite, so I will use both. Because of that, I thought it would be prudent to provide you with not only the average TAY/P over each three year span, but also the weighted standard deviation for TAY/P among all quarterbacks over each three year span.2 This way, you can see the numbers for yourself and not have to take my word for it.
Of course, measuring quarterbacks against league average or replacement level is fine for comparing them with their peers, but it doesn’t always suffice for comparing across eras. I’m not convinced there is a perfect way to do this, but I thought a good place to start would be adjusting for the sheer volume of plays quarterbacks of today run relative to their predecessors. To account for this, the first thing I do is prorate every season to the 16 game one we know today. After this, I account for the per-game difference in quarterbacks usage rates. To do so, I found the average number of quarterback plays per league game for each individual season, as well as for the whole of NFL/AFL/AAFC history. I then give players from each season hard inflation multipliers based on the ratio of their year’s plays per game versus the historical average plays per game. The historical average is 34.7, so using 1932 and 2015 as examples:
In 1932, there were 16.1 QB plays per game. To reach the average of 34.7, we must multiply by 2.151, so that is the multiplier we use for each player in 1932.
In 2015, there were 40.8 QB plays per game. To reach the historical average, we must multiply by 0.854, which is 2015’s multiplier.
This straight up era comparison seems (to me at least) to give way too much credit to older players. So I have a modified version of that (SOFT in the tables) which takes the average of the original multiplier and 100%. Again, using 1932 and 2015 as examples:
1932’s 2.151 multiplier becomes 1.384 when averaged with 100%.
2015’s 0.854 multiplier becomes 0.925 when averaged with 100%.
We still have older players gaining ground and newer players losing ground, but the difference is not nearly as egregious. However, if you love the good old days, when gas was penny and children always obeyed their parents, then you may prefer the original version.
Historical Total Adjusted Yards: NFL
This table shows historical 3-year averages for every NFL season with recorded stats. Read it thus: For the three year window with 1933 in the middle, quarterbacks produced 14730 Total Adjusted Yard on 5279 plays, good for 2.79 TAY/P. The weighted standard deviation of TAY/P among quarterbacks was 1.85. There were 330 league games in this period, meaning quarterbacks gained 44.6 Total Adjusted Yards and ran 16.0 plays per schedule game. The hard inflation adjustment is 2.171, and the soft inflation adjustment (average of 2.179 and 1.000) is 1.585.
There are a few things to note when looking at this chart. The first is that not every season has a three year average. Obviously 1932 and 2015 don’t, as the former doesn’t have an antecedent, and the latter doesn’t have a descendant. For those seasons, only two year averages are used. However, those aren’t the only years with just two seasons in the sample.
Prior to 1945, I do not have fumble data for players. This means that the league average TAY/P actually decreases from 1944 to 1945, as those fumbles take their toll on the numbers. Because of this, neither season is included in the other’s calculation.
From 1947 to 1962, I have data for sack yardage lost but not for number of sacks taken. Before 1947, this seems to have been tallied in the rushing column, so this isn’t an issue. However, in 1963 the league began tracking individual sacks, separate from rushing totals. Because of this, 1962 and 1963 are excluded from each other’s totals.
From 1963 to present, all of the inputs or TAY/P are available. Thus, regardless of the merger or subsequent expansions of the league or its schedule, all seasons are treated the same (i.e., they are stuck in the middle of a three year average).
Historical Total Adjusted Yards: AFL
Read this table just like you read the first one.
The same caveats apply here as applied in the NFL section. The first and last year of the league only have two year averages. Unlike the NFL, there is no sack distinction between 1962 and 1963. Instead, there is a period up to 1966 with no sack data at all, followed by a period beginning in 1967 with complete sack data. Because of this, 1966 and 1967 are excluded from the other’s totals.
Historical Total Adjusted Yards: AAFC
Read this table just like the first two tables.
As before, the first and last seasons cannot be in the middle of three year averages and are, thus, only given two year calculations. Although there is sack data for the NFL beginning in 1947 and fumble data beginning in 1945, no published records exist for the AAFC (at least none that I can find). This doesn’t affect the calculations at all, but it is important to remember when looking at the higher TAY/P metrics for the younger league.
That’s it. Come back later for the first of many All Time Quarterback posts.3
- Keep in mind that, because I don’t have data for first downs gained prior to 1991 or air/YAC splits prior to 1992, I will just be using the most basic version of TAY/P: (Pass and Rush Yards – Sack Yards + Pass and Rush TDs*20 – Interceptions*45 – Fumbles*25) / (Pass Attempts + Rush Attempts + Sacks). ↩
- I think using weighted standard deviation instead of normal standard deviations makes more sense for this project. That way, low volume, extreme efficiency seasons won’t skew the data. For example, in 2015 Matt Moore averaged 23.00 TAY/P, but he only had one action play. Scott Tolzien averaged -9.67 TAY/P, but he only had three action plays. Using the normal calculation (=stdev.p function in Excel) means these extremes make the SD much higher than it should be. Instead, I weighed each TAY/P score by volume before finding the SD. Here’s an example: for 2014, the three year average TAY/P was 5.66. Aaron Rodgers‘s 8.04 was a difference of 2.38 from that number. Square that, and you come to about 5.68 (the variance). Multiply that by his 591 plays and you get about 3356 (the product). Do this or every player and find the sum of products for the three year span in question; in this case, that number is 92514. Finally, take the square root of (sum of products / sum of plays). That gives you the weighted standard deviation for your three year span. For 2014, it’s 1.21. Once you get the formulas entered into Excel, this is a pretty simple chore. ↩
- The data for these posts came, almost entirely, from here. It only includes seasons when the player’s primary position was quarterback, so Johnny Lujack loses some negligible production, as do a few others from the pre-modern era. ↩