A Unified Theory of Yards Per Attempt in NFL Quarterbacks

In my first look at the Yards per Attempt statistic in National Football League quarterbacks, I found there was a general correlation between Football Outsiders’ offensive line rankings and Yards per Attempt. Although I’m happy to see that there was some correlation, it made future predictions near impossible because FO owns the offensive line rankings.

In this piece, I’m going to see if we can create a better formula for predicting YPA than the one discussed in this Pro Football Focus article. Jonathan Bales used the average of a quarterback’s previous three seasons to predict future YPA numbers. Let’s see how accurate his predictions were for 2012, and how we can improve them.

If we apply Bales’ predictions to the actual results of the following quarterbacks in 2012, we get these results:

NFL Quarterback YPA ResultsWhere “aDiff” is the raw difference of the given QB’s YPA, compared to his average of the previous three years. The spreadsheet shows that Philip Rivers under performed his YPA projection by 1.7 YPA on the season. Alex Smith led the league in over performing his YPA projection, which ended up around 1.2 YPA.

How accurate are these numbers? One way to measure them is by taking the standard deviation of the differences for each player. An easier way to think of this number is by volatility. Bales’ predictions for 2012 were off by about 0.68 YPA, on average.

How can we improve on this number? We can do the something he recommended against and use a mix of quarterback specific history AND league average at the position. Over the past four seasons, around 58% of QB YPA was repeatable.

If 58% of a given quarterback’s YPA is repeatable, what is the rest of it? Bales himself mentioned in his RB YPC predictions that it could be “fluky factors, such as opponents, field conditions, and so on.” Let’s apply that same rationale to our predictions. We get this formula as a result:

Predicted QB YPA = 0.58*(QB YPA Avg) + 0.42*(League YPA Avg)

The results:YPA Predictions Paul

Where “eDiff” is the raw difference of the given QB’s YPA, compared to the prediction of our new formula. Players’ names are kept in the same order for clarity. You can immediately see that the predictions are closer to the actual results using this new formula. The predictions average only 0.51 YPA difference to the actual results, which is an improvement on Bales’ formula.

Going back a few more years might helps us really get the most accurate predictor for YPA. Additionally, I’ll need to use more quarterbacks in the future to really make sure this isn’t a fluke for just 2012. At the very least, we now have a more accurate predictor of YPA in a given season. Hooray!

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