Last week, I wrote the following:
Ben Tate has four fumbles on the season in 154 touches, or one every 38.5 touches. Arian Foster has three fumbles in 284 touches, or one every 94.7 touches (and that includes the WTF fumble from Sunday -- otherwise it would be one every 142 touches). For everyone clamoring for Tate to take over for Foster because of his higher yards-per-carry stat, keep that in mind.
On Sunday, Arian Foster proceeded to fumble on the second play of the game, making me look like a jackass.
I don't even own him in Fantasy!
Then on Monday, I start seeing guys such as Paul Kuharsky talking about Foster's "sudden propensity to fumble."
All this after Foster was named to the USA Football All-Fundamental team for following blocks and ball security.
So what gives? Should Foster's new sponsor be Bananas Foster Butter (which sounds kind of gross)?
Anyone who's read any of my rants (and especially those very few who may have actually paid attention) should know by now that I'm generally not interested in talking averages or generic statistics. I want to know about variation and probabilities.
Note: Yes, I know I did it in the pre-jump quote, but that was a quick bulletized post as opposed to any actual analysis, so don't bother pointing that out.
Even though Foster's apparent "propensity to fumble" has not quite dominated headlines in the manner of, say, Tim Tebow not performing a miraculous comeback, I was intrigued by any mention of it because I recall that Foster had a bit of a reputation for putting the ball on the ground while in college at Tennessee. So, the first question I have is regarding his past. We need to know if the Texans have been lucky with Foster's ball security in the past year and a half or if they're just getting to an unlucky streak.
While at Tennessee, Foster definitely got some heat for his fumbles. He had some big fumbles late in some big games, and this reputation, deserved or not, may have been one of the reasons that he went undrafted. Thus, I decided to start by looking a little into his college career and came across this post, which essentially said that Foster didn't fumble at a particularly high rate, but that his fumbles were at very visible and very costly moments, thus preserving them in memory.
Well, that's good enough for me.
So the question, then is, "Has Foster suddenly developed a fumbling problem?"
Foster has had four fumbles in his last four games, so at first glance, it would appear so. If we ignore the non-fumble against Cincinnati, it's still three fumbles in four games. In his previous 24 games, Foster had three fumbles.
So for starters, let's look at Foster compared to some of the game's top running backs. I didn't have a strong criteria for selecting this list, except that in order to get a strong enough data set, I wanted to look at other top running backs who have had similar work loads since the start of 2010. Here's a summary of the data.
|Running Back||Fumbles||Touches||Fumble Rate|
If we were to stop our analysis here, we would say that Ray Rice is the most reliable back and Maurice Jones-Drew is the least reliable.
But you, the knowledgeable BRB reader, are smart enough to spit on such analysis and say that drawing such a conclusion is meaningless unless we test for statistical significance.
So I have. For you.
As it turns out, and as I'm sure you're completely anti-shocked to see, there is no statistical difference between these players' fumble rates. MJD is a bit higher, but we cannot statistically say that he is in fact more likely to fumble than Ray Rice.
To put that another way, if Ray Rice had just one more fumble over his past 685 touches, he would be at 0.43% and in the middle of the pack. Two more and he's at 0.58%. I don't think that any of us would consider two more fumbles over 685 touches to be a cause for concern, so we similarly can't say that he would suddenly be worse than Adrian Peterson.
This is a major point in the discussion that is often overlooked. It would not at all surprise me to hear some commenter (most likely Dan Deirdorf) make mention of the fact that Rice has only fumbled twice in the past two years while MJD has fumbled eight times, with nary a comment on the fact that we're talking about over 600 touches.
On a side note, I did a quick check of Ben Tate's numbers against these guys and even though he has far fewer touches, and thus a higher standard deviation, he is significantly higher than all these guys except MJD, so my Tate concern continues.
We can now say that over the course of the past two years, even including the recent fumblitis, Foster is not fumbling at a rate that should really be cause for concern.
This leads us to the second question: Is Foster's recent increase in fumbles statistically significant?
Again, the answer is no.
If I compare the two data sets of the first 23 games in my data set and the last 4, I find that I have a p-value of 0.267 which means that there's essentially a 26% probability that this just happened by chance.
The interesting thing is that for both analyses, even if I add the Cincinnati non-fumble back into the data set, the results are still not significant.
I can hear you right now.
Gee, thanks, Vega. You just spent a whole post telling me that I can't draw any conclusions on anything.
Well, to be honest, that's one of the main purposes of statistics (and one that's nearly always ignored) -- to tell you when drawing conclusions is actually valid. In this case, Foster's recent fumbles don't seem to be indicative of anything actually going wrong, but are more likely just random chance and ultimately will be nothing more than a blip on the radar.
So when somebody says to you, "Man, I'm worried about Foster's recent fumbling problems," you can calmly and confidently point out to them that the recent fumbles are statistically insignificant when compared to other top running backs and to his career fumbling rate, so there should be little cause for concern going forward.
Then you can tell that person to suck it.