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# Fantasy Football Advice: How To Predict Chris Johnson's Yards-Per-Carry

June 3, 2010

If you missed it (which is likely, since we have yet to talk about it), we recently launched our 2010 Fantasy Football Package .  It is a collection of everything I use to dominate fantasy football leagues each year, including my personal projections, rankings, draft plans, players to target, and so on.  You can read more about the service by following the link above.

I understand it is a risk to take another person’s advice on a subject as serious (<— is that a joke?) as fantasy football, so I think it is important to detail the methodologies I implement to arrive at my final projections.

In my bio on this site, I wrote:

"I have always been fascinated by the way mathematics and statistics, if used properly, can thoroughly explain seemingly complex phenomena.  Like the motion of the planets or the path of an ant, I truly believe football can be perfectly represented by numbers (the difficult part is determining which numbers are significant and why ). . . I implemented the same sort of approach to playing (and winning) fantasy football.  Fantasy football is nothing more than risk analysis; like playing the stock market, a sound use of game theory can work wonders for your team."

This particular article is a sample of how I implement statistical analysis to determine future performance.

Running Backs’ Yards-Per-Carry

I recently visited New York City and passed a psychic in Times Square.  She told me she could tell me anything about the future that I wanted to know (for \$99, of course).  I asked her if she could tell me how likely it is that Chris Johnson will repeat his stellar 2009 yards-per-carry (YPC).  She walked away, and I never got my answer.

Nonetheless, I think statistical analysis and film study will give me a far more accurate prediction of Chris Johnson’s YPC than any psychic.  Predicting the future isn’t about knowing conclusively what will happen, but rather deciphering the chances that a particular event will occur.

Not to get too philosophical (hey, it’s what I do), but if the universe does not run through deterministic events, but rather random happenings, then it is impossible to “know” the future.

### Stats gathered from Pro-Football-Reference.com

That doesn’t mean accurate predictions cannot be made, however. Weathermen often get a bad rap, but they are generally very good at what they do.  Weather systems don’t function in a deterministic manner, such as balls on a pool table, but through random occurrences.

Likewise, the 2010 YPC for each running back in the NFL is not somehow “determined” beforehand—but the probabilities of certain averages for particular players, I believe, are already written in stone.

So how are we to determine these probabilities?

While they may “just come” to the New York psychic, I, unfortunately, have to do a lot more work.  My methodology includes statistical analysis, so let’s take a look at some numbers.

First, we must note that the league-wide YPC average has skyrocketed in the past 13 years.  After remaining relatively steady from 1974-'96, the YPC average has increased .2 yards since—a 5.11 percent increase.  That number might not appear large, but it is rather staggering for a sample size of carries as large as the entirety of NFL running backs over an extended period of time.

Thus, there is a difference in YPC among eras, meaning if we are going to use the statistics from prior eras to broaden our sample size, we must account for this disparity.

After correcting the YPC of “the old-timers” to more appropriately relate to the league-wide averages during their eras, we see that there is a rather significant correlation between a player’s YPC in year N and his YPC in year N+1 (the next season).

Pro-Football-Reference (excellent site, by the way) concludes that this correlation is best represented by the formula:

YPC_n+1 = LgAvgYPC -0.04+0.43*(YrNDiff)

As PFR writes:

"Another way to think of this is that any starting running back’s YPC projection next year should be roughly equivalent to about three-sevenths of his YPC average last year and four-sevenths of 4.2 YPC (i.e., the league average)."

The chart above displays projected 2010 YPC.  While these numbers are based upon league-wide YPC statistics over the past 35 years, the primary catalyst for these changes is a term we discuss a lot—regression to the mean.  I discussed this concept ad nauseam in another fantasy football article detailing the myth of overworked running backs .  There, I wrote:

"The key is in a statistical term known as ‘regression toward the mean . Mathematics is a beautiful thing.  Given a large enough sample size, numbers always win.  Flip a coin 10 times, for example, and the number of heads you obtain could realistically be anywhere from one to 10.  Flip it 100 times, though, and you are very unlikely to acquire more than 70 percent of either heads or tails.  Flip it 1,000 times, and it is a virtual certainty that you will have flipped no more than 60 percent of heads or tails (and much more likely, less than 55 percent).

This predictability through which the universe manifests itself is not irrelevant to football.  Two-point conversion rates and onside kick recovery percentages, for example, remain relatively stable from year to year.  There may be blips in the data from time to time, but the overall statistics always (always!) regress back toward the mean."

Likewise, running backs’ YPC, even if they are extremely talented, tend to regress back toward the mean.

Still, the above chart is by no means a definitive source for fantasy projections, but rather a base off of which to work.  Other factors come into play when assessing a running back’s fortunes, such as coaching changes, personnel alterations, his contract situation, and so on.

Understanding and utilizing "regression to the mean," though, is an excellent way to begin projections for not only YPC, but a vast array of fantasy football statistics.

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