Recently there was a very spirited response to my article "The Case Against Keeping Adrian Peterson." In that article I made the claim that Peterson may already be in decline as an older running back that will turn 30 years old before the start of the 2015 season, and that he is most likely going to decline in performance over the next 2 years. My use of his one game in 2014 in the statistical charts I included showing his overall yards per game and yards per carry declining with a linear trend line was rightly criticized, because I weighted that one game equally against his previous seven seasons. If you missed it, I included another "yards per carry" chart deep in the comments section of that article with the 2014 season removed and that chart also showed a slight declining linear trend line (albeit much shallower). In short, those graphs were probably not the best ones to use to show Adrian Peterson's past or future performance as a running back.
Rather than boiling down an entire season's worth of carries into one averaged data point, a better analysis of Adrian Peterson's yards per carry, would be on a per game basis. One of our users "CCHOF5yearstoolate" put together a spreadsheet of Adrian Peterson's rushing data, pulled from Pro Football Reference, and shared that with everyone in the comments of the previous article linked above. I owe him a bit of thanks for compiling such a large set of data from all of Peterson's 107 career games and making it easy to use in excel, so thank you "other CC"! In any case, I began pouring over the numbers from that spreadsheet and running a bit of analysis myself.
The chart below shows every yard per carry average from all 107 games, given equal weight over the course of his career, which allows us to more accurately use his one game from 2014 to compare against his previous games. The X-axis (horizontal) goes out to 123, because I've included several different "trend lines" to help predict what we can expect for his next 16 games (or his 2015 season).
The first trend line is the black, linear trend line, which for this data set isn't very helpful, actually. Because the data set has a large number of peaks and valleys, the linear trend line shows not much more than the overall average (Peterson's career YPC career average is 4.96). While at first glance the linear trend appears to be a flat line, careful inspection reveals an ever so slight decline over Peterson's 107 games. Its predictive nature is virtually worthless though. When looking at the predictability of trend lines their R^2 can range anywhere from 0 (not reliable at all) to 1 (totally reliable). The R^2 of his linear trend line is 0.0002 (virtually 0) for predicting the next 16 games. In other words: it's useless.
Again, because this data set has a HUGE variety from as high as 11.2 and as low as 0.21, a better trend line to show his actual performance is the green, "moving average". I set the period of average to 16, because there are 16 games in an NFL season. This trend line evens out the peaks and valleys a bit to make the overall trend over his career easier to see. If nothing else, it helps to show how incredible that 2012 season was (the huge hump near the end), especially compared to the rest of his career. A moving average trend is by nature not predictive, hence there is no R^2 value shown and the line does not extend past 107. Notice though, this rolling average trend line seems to hover around 4.5 yards per carry during most of his career, then spikes up over the games for 2012, followed by a decline over the last 16 games.
The last trend line I included is perhaps the most convincing and most predictive in this graph: the orange polynomial line. I set the order of polynomial at its highest rating of 6, and therefore it's most predictive. It has an R^2 rating of 0.1, which is pretty bad in terms of being predictive, but a lot better than the linear trend line of 0.0002. In other words, the Linear Trend is 0.002% reliable, while the Polynomial trend is 10% reliable. Notice there is not only a predicted decline over Peterson's next 16 games with this trend line, but a MASSIVE decline over his next 16 games. I do not expect that prediction to be accurate, but it is interesting that the more massive decline in rushing production also happens to be more predictive, given Peterson's history of performance.
There are a couple of other things worth pointing out about his yards per carry in particular. If you look at his most recent stats as being the most relevant for future performance, it doesn't paint a particularly bright picture. Over the last 16 games, Peterson is averaging only 95.6 yards per game and 4.32 yards per carry, a bit less efficient than his career average of 98 yards per game and 5.0 yards per carry. I think it's correct to state that his most recent performance is showing a decline when compared to his career averages.
At the end of the day though, I'm not sure that Peterson's past performance on a yards per carry basis will really tell us anything useful about his future performance as evidenced by the low correlation coefficient of his trend lines. Chase Stuart over at Football Perspective wrote about the predictability of yards per carry in a general sense and the bottom line is that "yards per carry" is not very predictive anyway, at least on a team basis, and year to year as it's correlation coefficient is only 0.31 (or 31%). It would stand to reason that "yards per carry" is not particularly predictive for individual running backs either, and the graphs above show that to be true as well. However, there is a slightly more predictive rushing stat than Yards Per Carry and that is "Success Rate". It's also not terribly predictive, a CC of only 0.39 (39%), but it's better than yards per carry.
So, using Success Rate, I decided to plot Adrian Peterson's career on a per season basis (because that is all that was available) and run regression analysis on this data. Because of the valid criticism against using 2014 in comparison to Peterson's other seasons, I've decided to show two graphs. The first graph has 2014 omitted, as if it never happened, while the second graph has it added back in, just for curiosity's sake.
The data in this chart is very different from the 107-game one above. With only 7 points of data, it is a pretty small chart, and notice most of the data appears to be in a straight line. In this case, the linear trend line actually is the best one to use. And notice, the R^2 rating has a very strong correlation coefficient at 0.648 (65% reliable). This first graph has 2014 omitted, so it is making a prediction that the success rating for Peterson's 2014 season will go up slightly from 0.378 to about 0.382 (we can check that accuracy below).
I once again included the green rolling average trend line, but this time I set the period to only 2, since there are only 7 data points. I almost left this one out again, since it shows pretty much the exact same trend as the data itself. But, I left it in for consistency and as above there is no prediction with the moving average.
The green polynomial trend line in this data set is probably not as relevant as it was in the large YPC graph above, because of the size and type of the data is smaller and not as wildly inconsistent, but I included it anyway. In this case, I set the period level to only 2, because of the small data set. Interestingly, the correlation coefficient for this trend line is much higher than it was for yards per carry, and nearly equal to the linear trend line. It is making the prediction that Peterson's 2014 season will be roughly equal to his 2013 in terms of success rating and then drop off quickly after that.
The chart below includes Peterson's success rating again, but this time including his one game from the 2014 season. There is a valid criticism that this one game shouldn't count with equal weight against his other 7 seasons, so take this next chart with a grain of salt.
There are a couple of things to notice. First, his 2014 success rating was quite a bit better than 2013, and therefore the trend lines also predict different things for 2015 and 2016 than the previous chart as a result. His linear trend line predicted a slight increase, just not on the level it turned out to be (although perhaps over the course of a full 2014 season it would have flattened out some?). Never-the-less, the linear trend line may not be as relevant in this graph, since the 2014 season breaks the nearly consistent descending trend. And notice, it's R^2 rating drops significantly in reliability to 0.1156 as a result. It's still way better than yards per carry, but overall not very reliable. Also, I left the rolling average trend line in, but again, I probably just should have left it out, since the data set is so small.
The most interesting change is the orange polynomial line. In this graph it is probably more relevant than the linear trend line, because the data points appear to resemble one giant upside down curve. And in this instance, Peterson's success rating data curiously appears to be trending up! The R^2 for his polynomial line is much more reliable than the linear trend too at 0.35. Still, that's less reliable than the previous success rating chart, and this makes sense since it is weighting only 1 game's worth of data from 2014 equally to his full seasons. So, take it all with a huge grain of salt.
So, what are we to make of all this? Well, I think there are multiple signs showing that not only has Adrian Peterson's performance already been in a steady decline, but his best years are also behind him. The regression analysis of his past performance based on yards per carry and success rating show that there is a chance his future performance is set for a decline. When you also consider that a study of the past found that half of all elite running backs over the past 25 years are essentially washed up by their age-30 seasons, further suggests that Peterson's best years are behind him. At the end of the day no one knows for sure what will happen in the future, but there are signs showing us more likely outcomes. We'll just have to sit back and watch it all unfold.