Fantasy Football: Running Back Sample Sizes

"What state produces the most professional athletes per capita?" he inquired. I didn't know the answer, so we sat and speculated for a while.

"Texas," my brother said. I wasn't so sure. It seemed to me that while we knew that Texas, California and Florida all produced a lot of athletes, there also just a lot of people there. My gut told me the winner was not going to be one of these larger states.

Hawaii. That was my first guess. The small set of seven islands seemed to send a good number of players from its tiny population; players like Osi Umenyiora, Kila Ka'aihue and Shane Victorino. I figured that Hawaii wouldn't need that many players to overcome California--with its large populous.

It was a question of extrapolation, and I just didn't know. Hang on to that thought, it will be back.

But the more I thought about it, the less I was sure Hawaii was the one. I couldn't think of any NBA or NHL players that came from the 50th state in the Union. And what about the NHL? With so much of the league coming from Canada, I realized that Minnesota might have a huge leg up. What if Minnesota took the cake, simply from dominant numbers in hockey with below average numbers in every other sport? Was that possible?

No. Or if it is, it isn't the case. Fortunately enough there are people who do legitimate research on such pressing questions, and from sportsgeography.com I was able to learn that Louisiana is the winner (Washington D.C. actually has a higher rate, though it isn't a state). Alas, it was not my day. Though I will have you know that Hawaii ranked fourth on the list of states, so a small amount of my pride was left intact.

But back to my thought about Hawaii. I knew a small number of players from there, but that was offset by the fact that there are a small number people in the state. My question was, knowing such a small number of players, how accurate was my projection for the rate as a whole? In this case, fairly accurate. But what about football players with small sample sizes? How sure are we of their success or failures?

Let me preface this by saying this piece of writing is based off data published by Chase Stuart of Pro-Football-Reference.com. If you'd like the detailed version I recommend checking out his story. But in short, it's based on variance in yards per carry for running backs, and what an average back might be able to accomplish in a limited sample size.

Consider this the opposite exercise.

We can look at backs (and backs with less opportunities are generally more interesting here) to gauge the odds of them being simply an "average" running back that got lucky over a stretch last year.

Let's start with Felix Jones, who finished second in the league in YPA, with a whopping score of 5.9 over 116 carries. From Stuart's work, this puts him well clear of 95^th percentile, despite the low number of carries. Essentially, the odds on Jones being an "average" running back with a flukey 116 carries? Probably in the neighborhood of 1-2 percent—very low. This is fairly unsurprising, the knock of Jones has never been ability; it's that he is injury-prone.

A couple of other backs that check out by this system? Justin Forsett, Pierre Thomas and (surprisingly) Correll Buckhalter. Honestly, I don't know what to make of that last one.

Shonn Greene leaves us a little under 90% "certain" that he is an above-average back.

What about Michael Bush, who is looking increasingly likely to be the main rusher in Oakland? Bush averaged 4.8 yards per rushing attempt, over 123 carries. What does that make Bush? A little less certain. Looking only at this data, Bush would appear to have a 16-17 percent chance of being just an average tailback.

And on the other end? Now that may be even more interesting.

Matt Forte's rushing YPA last year was 3.6 and 3.9 in his rookie campaign. Both years he had a high sample for rushing attempts. Not a good sign for the 2009 first rounder. His 2008 stats give him a 25% shot of working his way up to an average rusher, with the number plummeting to five percent in 2009. Of course, Forte is a threat because of the aerial attack as well, but it isn't encouraging for those hoping for a rebound.

Other running backs who did poorly enough, despite a small sample, to be seriously concerning for their owners? Justin Fargas, Steve Slaton and Darren McFadden.

Remember to only put as much stock into this as deserved. Think Mike Martz will help Matt Forte? That's not calculated in here. There are many other factors to consider when evaluating players, and losing sight of them would be a mistake. But knowing how reliable the sample you are working with is worth of your time too.