This year I am going to try writing about the NFL with a sort of focus on the Falcons because I am a homer and OK with it. I have been anticipating this season way more than I have past seasons and been eating up a lot of media about the NFL and a lot more about the Falcons. Since I do statistics for a living, I figure I will put that sort of spin on this. Bill Barnwell is probably my favorite writer when it comes to the NFL. I am a big fan on how he uses and interprets numbers in his articles in a relatively easy/straight-forward/accessible way. He also gots the jokes.
Alright, lets do it then! Lets get in it with some classic over-reaction to week 1 action. We will start with the team I love. The Atlanta Falcons showed what was a dominant defense in the first half and a barely competent defense in the second half. Average that together and its still better than last year! So one of the statistics that I thought explained Atlanta’s defense best last year was the fact that we allowed a 46.8% conversion rate on third down to opposition which was good enough for dead last in the league. While not the only statistic to look at for defense, it has a weakly positive correlation with the defensive DVOA rankings (courtesy of football outsiders) of 0.53. Nothing to write home about, but enough to at least weakly illustrate my point without taking me down a rabbit hole. It is also of note that the Eagles were 9th in the league last year on offense in this category with a rate of 43.5%. The numbers definitely suggested a beatdown was going to occur in this category, but what is that? The Eagles converted 3 of 12 for a 25.0% rate. If we look at the dominant first half that number is actually 1 of 6 for a rate of 16.7%.
So this basically means Dan Quinn completely overhauled the defense and the new additions proved to be shrewd, intelligent acquisitions and we be #quinning. As much as I wish this is the case, lets slow down. Point estimates are very rarely informative. What we really care about is if there is enough data to suggest this is truly coming from a different distribution (which can be read as this defense is not last years defense). For those of you who know me, you know I subscribe to Bayesian statistics. So while many of you know about confidence intervals, I will be using the Bayesian interpretation of examining if something comes from another distribution. The following description and image shows the interpretation.
- Θ1 – Falcon’s third down conversion rate last year
- Θ2 – Eagle’s third down conversion rate last year
- Θ3 – Falcons vs Eagles third down rate last night
- Θ4 – Falcons vs Eagles third down rate in first half last night
So we can see the point estimates going diagonally from the top left to the bottom right. We can also see the differences between the distributions on the off-diagonals with the top right being a mirror of the bottom left. We also clearly see that theta1 and theta2 show much more certainty in their estimates because we had a lot more data last year than we did in one game this year. So what does this all mean?! Well… it basically means we don’t know enough about our defense to make real conclusions yet. If you look at the difference between theta1 and both theta3 and theta4. Which represent 2014 Falcons, First game, and First half of first game; zero is still very much a credible value. While it does seem to pull towards this being an improved unit, I wouldn’t put too much stock in it yet. To further illustrate this, the numbers seem to think we didn’t look much different in the first half versus the whole game (theta3 versus theta4). This is in large part because the credible intervals for the true value are so large. For anyone watching the game, the Eagles were giving us the business in the second half.
Well thats my statistically backed way to say we actually don’t know too much about the Falcons or any team just yet. Might be fun to look at all the crazy projections to see how many come true. I’m looking at you Skip.