Welcome back to another sticky stat piece!

This time, I'll be exploring the correlation of per game passing stats year-over-year. To be more explicit, I will be comparing the per game numbers in season Y (e.g. 2012) to season Y + 1 (e.g. 2013). The exploration will start with the unfiltered passing data from 2012-2022 and continue with various filters applied upon the data set.

Beyond general exploration, the intention of this analysis is to see if there are per game stats that strongly correlate on a year-to-year basis, such that they can be used as predictors for fantasy football performance.

I highly recommend checking out part one of the series to understand more of the motivation and background behind this analysis. Furthermore, it covers year-over-year season total correlation numbers for passing stats.

For those purely interested in the graphs and heat maps, I suggest seeing the comprehensive appendix of the blog.

I started by taking a look at all of the unfiltered passing data on a per game basis from 2012-2022. This yielded the following correlation heat map:

While the correlations are not quite as strong as the year-over-year season totals, we do see strong correlation across the board. The only real exception is with EPA, which still has moderate correlation year-to-year.

To help visualize the strength of the correlations from the heat map, a scatter plot of the strongest correlation statistic from the year-to-year stats, passing yards per game vs. passing yards per game of the previous season:

Similar to completions vs completions last for season totals (a strong correlation stat from the season total analysis), the scatter plot above shows us that the unfiltered data incorporates of noise, in regards to finding value from starting quarterbacks, and more importantly, starting fantasy quarterbacks.

So, while passing stats are generally very sticky on a per game basis, they are not as sticky as their year-to-year correlations on a season basis. An additional observation: the most predictable stats are still passing yards, passing attempts and completions, with passing touchdowns being more reactive from year-to-year.

Again, we will have to dig deeper to find something closer to the truth.

In order to make the data set more relevant, we apply a filter on it: starters only. Starters are defined by players who have played in at least 12 games in consecutive years.

This filter yields the following correlation heat map:

This is surprising... the correlations across the board are suspiciously strong, outrageously so, especially with the numbers we have seen so far.

That being said, the pattern of passing yards, completions and attempts having the strongest correlation continues to hold, moreover touchdowns year-to-year continue to have a weaker correlation compared to those three stats.

Let's take a look at the strongest correlation, passing attempts per game vs. passing attempts per game in the previous season, to investigate further:

Ah, there is the potential misrepresentation: Taysom Hill and some trick plays seep into this filter.

Let's apply an additional filter: at least 150 yards passing per game in consecutive seasons.

The new, more selective filter produces the following heat map:

This is more in line with the rest of the analysis we have done so far. This heat map very much resembles the season total one for starters.

Interestingly enough, the correlations for passing yards, attempts, and completions are a bit stronger on a per game basis season over season. However, the touchdowns on a per game basis, year after year, are slightly weaker.

This seems to suggest the pattern that quarterbacks improve passing yards, attempts, and completions at a higher rate on a per game basis than on a season basis, from year-to-year. Additionally, touchdown numbers are marginally harder to replicate on a per game basis year-over-year.

What to make of this? While I do find the above to be a bit strange, the water holds that passings stats are pretty sticky - bar touchdowns - for quarterbacks.

My explaination for touchdowns going down on a per game basis comes down to the number of games starters play from year-to-year. A starter can improve their touchdown numbers from season to season by playing more games, but the rate at which they throw touchdowns is slightly less likely to improve season to season.

For example, player X may throw 40 touchdowns in 15 games in year one, but then 42 touchdowns in 16 games in year two. The season total improves from 40 to 42 for X, but the per game numbers decline from 2.67 touchdowns per game to 2.63 touchdowns per game.

To wrap up this section, I will leave you with the scatter plot of the strongrest correlation from above, completions per game vs. completions per game in the previous season:

As a continuation from the Diving Deeper section in the first part of the quarterback passing stability analysis, I will look into starting quarterbacks by age.

Specifically, another filter will be added to our most stringent one from the previous section: young or old. Young is defined as quarterbacks who are thirty in season Y + 1 (i.e. the current season). Old is defined as quarterbacks who are thirty in season Y (i.e the previous season).

The following heat map is for our young bucks:

And this heat map is for the savvy vets:

Once again, there is a difference between young and old starters. The young quarterbacks have correlations of 0.56, 0.63, and 0.68 for passing yards, attempts and completions, respectively. Whereas, for the same stats, old quarterbacks have correlations of 0.52, 0.48, and 0.51.

Note, for futher comparison, all starters have correlations of 0.61, 0.61 and 0.66 for passing yards, attempts and completions. So, the year-to-year, average per game, performance of quarterback is slightly more predictable, and positive, for these bread and butter quarterback stats.

Another interesting observation: old quarterbacks are better than young ones in the passing touchdowns department (0.29 vs 0.25, respectively). Starters, on the all, have a correlation of 0.34 for average passing touchdowns per game, year-to-year. In all cases, this is pretty weak correlation, which, again, gives merit to the idea that touchdowns are a much more fluky stat.

Lastly, young quarterbacks have a moderate - almost strong - correlation in their per game fantasy numbers (0.55), year-over-year. This is better than old quarterbacks (0.27) and all starters (0.45).

This analysis seems to corroborate the ideas from part 1: quarterbacks continue to, reliably, improve up until about 30 years of age. The important thing here is that the improvement of their overall game also relates to their improvement from a fantasy perspective.

Again, I find it hard to draw strong conclusions from just these correlation pieces, but it does seem that the best point to make profit off of a quarterback is around the time they turn 30.

Upon further exploration, I had a few more findings that felt worth sharing.

Before continuing, I do want to preface that this section is on data from 2016-2022, as that's when advanced stat tracking starts in my data set. Moreover, the strongest filter applied in the Starters Only section is used here too.

First, the two advanced stats with highest correlation year-over-year, are disappointing as indicators for fantasy points on a per game basis.

The heat map for average time to throw (ignore the mean - it is a redudant label from massaging the data):

0.7 is really strong correlation, indicating great year-over-year reliability, but all variations of the comparison of this stat to fantasy points on a per game basis are below 0.35 correlation. That's not reliable at all, unfortunately.

The other advanced stat that correlates quite strongly from season-to-season is aggressiveness (a PFF stat measuring how aggressive a quarterback is):

A similarly unfortunate story occurs here: the stat correlates strongly with itself on a year-to-year basis (0.63), but quite poorly with any variation of a fantasy point per game stat (all correlations are below 0 - that's poor).

One interesting thing I want to note from the second heat map. It indicates that starting quarterbacks have a pattern of getting more and more aggressive. However, the increased per game aggression leads to lower fantasy points on a per game basis.

There's more - fascinatingly enough, young quarterbacks become more and more aggressive, quite reliably (0.72); however, the punishment on a fantasy basis is not particularly strong:

Weirdly enough, old quarterbacks, whose progression of aggression slows down, are far more hampered - in a fantasy sense - by their aggression:

Does this fit with the other idea from this exploration that quarterback value depreciates over time, with the cliff being around 30?

Maybe to improve quarterbacks must become more aggressive - something along the lines of attempting harder passes leads to more reward. However, at a certain point (~30) the level of aggression cannot be improved upon much, but it the slight increases continue to harm fantasy points. Furthermore, there is less return after a certain amount of aggression. The combination of a lack of consistent improvement in the passing game from increased aggression and continued increases in aggression lead to more negative fantasy lines. Essentially, there seems to be a point where the level of aggression cannot redeem itself, and it appears to be around 30.

It is just speculation on my part, but perhaps we have a narrative... It's possible this is just coincidence, but I'm finding the repeating pattern of 30 serving as the breaking point is becoming harder to ignore. 30 might very well be the cliff before losing out on selling a quarterback for their maximum production value.

From a different perspective, it might also be the age of mastery for the position - meaning that the abilities are about as good as they will ever become by now, and what remains of the career, is in most cases, determined largely by luck (situation, supporting cast, coaching, etc.).

The last thought I want to part with comes from the two correlation heat maps below.

The first displays the only stats that, at minimum, have a a moderate correlation with fantasy points or fantasy points per game:

In other words, all of the above stats compared to either fantasy points or fantasy points per game are at least okay indicators of fantasy points and/or fantasy points per game.

The best part is that each of these stats - passing yards, average max air distance, completions, and passing attempts are all somewhat predicatable, as they each have moderate correlations on their year-to-year values:

What's even cooler is that the law of 30 applies again!

The same two correlation heat maps for young quarterbacks:

Now for the old heads:

All four of these stats are decent predictors for fantasy points and/or fantasy points per game, for both young and old quarterbacks.

Of the four, passing yards are by far the most reliable predictor for fantasy points/fantasy points per game for both old and young quarterbacks. However, the only reliable stat year-over-year for old quarterbacks is average max air distance. Passing yards, average max air distance, completions and pass attempts are pretty solid indicators of fantasy relevance for quarterbacks under 30, while being somewhat-to-quite predicatable metrics.

It's not the holy grail I desire from the results of my analysis, but that's not a bad starting point for indicators of quarterback fantasy success.

That's all for this analysis!

Here's the recap one more time:

• Passing stats on a per game basis, year-over-year, are sticky when examining unfiltered data, but less so, when compared to the season totals year-over-year.
• Passing yards, attempts and completions are sticky year-to-year on a per game basis, for starting quarterbacks. The correlations are actually stronger than the year-to-year equivalent.
• Passing touchdowns per game are much more variable than yards, attempts and completions season over season. The correlation for touchdowns per game is even weaker than the season total version.
• The correlation numbers for per game passing yards, attempts, and completions are stronger for young quarterbacks than all starters, and old quarterbacks. In fact, the young bucks even have a decent correlation (0.55) for per game fantasy performance, year-to-year.
• Quarterbacks get more aggressive year-over-year, especially younger ones. Aggression is negatively, albeit weakly so, correlated to fantasy performance.
• The four best stats for quarterback fantasy performance are: passing yards, average max air distance, completions and passing attempts. All of these stats have moderate correlation with each other on a year-to-year basis - meaning they are (somewhat) reliable stats. These predictors are even stronger for young quarterbacks.

Thanks for reading!

Cheers,
Alex

For those who want the full details on the all per game stats I looked at from season, please enjoy the massive heat maps below.

I do not have much more analyis to add from my side, as I feel I've covered what is contained in that heat map pretty well. However, I figured I would provide it for data junkies and the sake of being comprehensive. Enjoy!

Unfiltered (year-over-year)

Unfiltered (all)