Running Back Rating- An objective comparison of All-Time great NFL running backs

To occupy some time over my spring break while keeping my brain sharp (essentially doing some "productive procrastination") I came up with the idea of creating an "objective" measure of the overall quality of NFL running backs. My idea was based on the system of the NFL Quarterback rating, which takes into account accuracy, touchdowns, and interceptions.

I developed a formula very similar to the NFL QB rating, for running backs, which takes into account rushing yards, rushing touchdowns, receiving yards, receiving touchdowns, and fumbles. I used the data of the top 50 running backs from the 2001-2010 NFL seasons (found at Sports-Reference) to develop my formula. Since we're dealing with running backs, not wide receivers, I weighted rushing 87% and receiving 13% (based on rushing making up approximately 87% of the total touches for players in my data set.) The minimum score a player can receive is a zero, and the maximum is 100. My formula was designed to give an "average" (based averages from the data) player a score of 66.6 (So 2/3rds will be below and 1/3 will be above).

After a few failed attempts, oversights, and adjustments, I found some numbers that I was pleased with (the averages of the data earned a score of 66.25047...I'll go ahead and round). I've included my formula at the end of the post for anyone interested.

Now, comes the fun part. There are a number of running backs who are in the discussion as the "Greatest of All-Time": Jim Brown, Emmitt Smith, Barry Sanders, Walter Payton, Gale Sayers, among others. I wanted to see who (according to the formula) is, in fact, the greatest of all-time. Now, I know that there are some factors which are not included in the formula (and can't actually be quantified); with that being said, I'm just interested in people's relative ratings.

So, here's how folks came out:
Jim Brown: 94.8
Gale Sayers: 92.5
Barry Sanders: 84.7
OJ Simpson: 84.6
Marcus Allen: 73.7
Walter Payton: 73.5
Eric Dickerson: 69.5
Emmitt Smith: 65.7
Earl Cambpell: 65.3


According to this formula, Jim Brown is the Greatest of All-Time, followed closely by Gale Sayers. An interesting illumination (as much as it pains me to say this as a Cowboys fan) is that Emmitt Smith, the NFL career rushing leader, has only a slightly above average rating for his career, indicating that he was good, not great, and just hung around a long time (which is a credit to his toughness...not measured here).

I'll move on to looking at ratings for active players, and ranking the greatest single seasons of all time. In the meantime, I welcome your comments...

Murphy's Law (A probabilistic representation)

Let E={All possible things that can go wrong}
P(E) = 1

There you have it.

Heat Check

As a part of my daily routine, I was reading Dr. Andrew Gelman's Blog and came across an interesting post which he had been sent by Jarad Niemi. It is essentially using statistics to make a case that I have been stating for months (and had recently presented this video as evidence); that case being that Chris Bosh is incredibly overrated and should not be considered one of the "Big Three" in Miami. There's nothing I love more than when someone uses methods I enjoy to support my case.

Niemi's explanation of his graph and his methods (as posted on Gelman's blog) are below:
2010-2011 Miami Heat offensive (red), defensive (blue), and combined (black) player contribution means (dots) and 95% credible intervals (lines) where zero indicates an average NBA player. Larger positive numbers for offensive and combined are better while larger negative numbers for defense are better.

In retrospect, I [Niemi] should have plotted -1*defensive_contribution so that larger was always better. The main point with this figure is that this awesome combination of James-Wade-Bosh that was discussed immediately after the LeBron trade to the Heat has a one-of-these-things-is-not-like-the-other aspect. At least according to my analysis, Bosh is hurting his team compared to the average player (although not statistically significant) due to his terrible defensive contribution (which is statistically significant).