When it comes to analyzing quarterbacks, some stats get all the attention. Flashy touchdown totals and beefy yardage numbers certainly impress fans and catch the viewers' eyes. However, these most basic of statistics are known to not be very "predictive",
that is, indicative of future success. Yards and touchdowns are good ways to describe a player's past accomplishments, but they have little value in predicting how said player will do in the future.
In fantasy sports, it is important to be able to recognize and predict how players will perform on a week to week basis. Large sums of money and admiration from peers is usually up for grabs. Thus, it is important to also take into consideration statistics that are meant to be predictive. A stat first described in "The Hidden Game of Football" and later refined by the experts at Pro-Football-Reference, Adjusted Net Yards Per Attempt is historically the statistic most correlated with wins. To understand this statistic, first we'll look at another metric, completion percentage.
Completion percentage is the measure of how often a quarterback completed a pass given the number of times he attempted a pass. It's a quick and dirty way to judge who is making accurate passes and who, for some reason or another, can't hit their targets. While a high completion percentage is usually a good mark of an accurate quarterback, it does not correlate with fantasy points very well, as a completion is not inherently valuable to a team. A pass that connects for a loss of 2 yards doesn't do anything for a player or team on the scoreboard, but it will boost that player's completion percentage all the same. Thus, we need a way to assign value to the player's throws, instead of this binary system. This is where Adjusted Net Yards Per Attempt comes into play.
Completion percentage can be thought of as "completions per attempt", which it is. To reward quarterbacks for making long, risky but valuable throws, we can replace the "completions" in that stat with their total yardage on the season, to get the stat "yards per attempt". Y/A gets us closer to this ideal predictive stat, but still has some shortcomings. In short, it does not reward quarterbacks for the high value of touchdowns, or penalize them for the negative value of interceptions and sacks. Adjusted Net Yards Per Attempt rolls all these factors into one, and as a result is the most predictive metric for a quarterback when it comes to team wins. Unsurprisingly, in my findings it also correlated highest with fantasy points.
As a note, there is a big difference in the R squared value when it comes to comparing the two graphs above, which illustrates the difference between rate stats and counting stats very well. As ANY/A is a rate stat, it is unfair to find the correlation between it and counting stats, which fantasy points are. In an attempt to offset this, I plotted ANY/A against both fantasy points and "fantasy points per game", to make up for the fact that some quarterbacks (e.g. Tom Brady) did not play a full season, and thus have lower than expected raw numbers. However, as ANY/A is a per attempt rate stat, comparing it to fantasy points per game might also be faulty, when fantasy points per attempt might produce a stronger correlation. More testing is required.
For one final comparison, these are graphs plotting raw touchdown numbers against fantasy points. As touchdowns are a counting stat, and one that factors into the calculation of fantasy points, it correlates with fantasy points very well. However, it correlates with our rate stat version of fantasy points significantly less well. We do not use touchdowns as a predictive statistic though as they have proven to be inconsistent year to year (i.e. the leaders in touchdowns thrown one year are rarely the leaders the next year). So, while touchdowns are a good explanatory statistic, they are a poor predictive statistic.