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By Jonathan Bales

“22 in 22″ Finale: Will Anyone Break Emmitt Smith’s Rushing Record? A Statistical View

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Jonathan Bales

A few weeks ago, I completed a study detailing Emmitt Smith’s chances of breaking college football’s all-time rushing record (had he stayed in school).  Using statistical projections and the normal distribution, I concluded Smith had a 3-5 percent chance of breaking Tony Dorsett’s then all-time rushing record (and just a 0.1 chance of gaining enough yards in his senior season to still be college’s all-time leading rusher today).

The nature of college football and the abundance of D-I running backs each season makes the college rushing record susceptible to collapse.  Two running backs (Ricky Williams and Ron Dayne) have subsequently broken Dorsett’s mark, and a few generally recent runners have come pretty close as well (DeAngelo Williams, Cedric  Benson, LaDainian Tomlinson, Garrett Wolfe, Mike Hart, and Darren Sproles).

Emmitt Smith’s NFL rushing record of 18,355 yards, however, seems much more unapproachable.  For starters, the method by which running backs are employed has altered drastically even since Smith’s career.  Gone are the days of workhorse backs.  Today, it’s all about two and three-running back rotations.  There’s simply no way for a running back to approach Smith’s record with only 225 carries a season.

Second, running back is, even more so than ever, a young man’s position.  Rookie running backs are frequently asked to contribute immediately, often taking the place of the savvy veterans with bigger salaries.  Colleges are preparing these runners for the NFL better than ever as well.

But are there any current running backs who possess even a glimmer of a hope of approaching 18,000+ yards?  That’s what I will try to answer today. . .

First, let’s take a look at Smith’s career numbers and the total for five current backs who I have deemed the most likely to break Smith’s record–Ray Rice, Adrian Peterson, Chris Johnson, Steven Jackson, and Maurice Jones-Drew.

Emmitt Smith
Years Pro: 15
Carries: 4,409
Yards: 18,355 (1,224/season)
YPC: 4.16

Ray Rice
Age: 23
Carries: 361
Yards: 1,793 (897/season)
YPC: 4.97

Adrian Peterson
Age: 25
Carries: 915
Yards: 4,484 (1,495/season)
YPC: 4.90

Chris Johnson
Age: 24
Carries: 609
Yards: 3,234 (1,617/season)
YPC:  5.31

Steven Jackson
Age: 27
Carries: 1,548
Yards: 6,707 (1,118/season)
YPC: 4.33

Maurice Jones-Drew
Age: 25
Carries: 842
Yards: 3,924 (981/season)
YPC: 4.66

As Smith showed, greatness isn’t flashing talent here and there.  It is about longevity and consistency.  There isn’t anything too special about his career 4.16 yards-per-carry average.  More amazing is the fact that he rushed for 1,000 yards in 11 straight seasons and 1,400 in five straight.

So as we analyze the numbers of the men below, keep in mind that longevity and consistency are (much) more important than yards-per-carry.  Also note that all of these projections assume near full health for each runner–something which is basically a necessity to break any all-time record.

Projected Seasons Left (Projected “Prime” Seasons)
Ray Rice:  12 (9)
Adrian Peterson:  8 (5)
Chris Johnson: 10 (6)
Steven Jackson: 6 (3)
Maurice Jones-Drew: 10 (6)

These numbers will undoubtedly be the most important in our evaluation.  The reason I project Steven Jackson and Adrian Peterson to have less seasons left in the tank (even when adjusting for their age) is due to their running style.  Neither player will be able to hold up much past the age of 30 due to the hits they take.

Ray Rice, in my opinion, is the most likely to have a long career.  He doesn’t rely solely on speed (like Chris Johnson), so he should still be effective after the age of 30 or so.  Remember, speed dissipates rather quickly in your late 20s.  Strength doesn’t.  If you think about it, Rice is also the most like Smith–not flashy, but consistent, utilizing vision and great balance to be a tremendous running back.  He’s got workhorse running back potential without being an above average injury risk.

Projected Carries/Season
Ray Rice:  275 in prime, 150 thereafter (2,925 total)
Adrian Peterson: 295 in prime, 200 thereafter (2,075 total)
Chris Johnson: 305 in prime, 200 thereafter (2,630 total)
Steven Jackson: 285 in prime, 175 thereafter (1,280 total)
Maurice Jones-Drew: 280 in prime, 200 thereafter (2,480 total)

Projected YPC
Ray Rice: 4.7 prime, 4.2 thereafter
Adrian Peterson: 4.9 prime, 4.4 thereafter
Chris Johnson: 5.1 prime, 4.5 thereafter
Steven Jackson:  4.25 prime, 3.8 thereafter
Maurice Jones-Drew: 4.7 prime, 4.2 thereafter

When determining yards-per-carry, I like to use a combination of past results and regression to the mean.  I use this same method in fantasy football to project a running back’s yards-per-carry.

For example, Chris Johnson’s career 5.31 yards-per-carry mark is stellar, but I highly doubt he will be able to maintain it for even the next five years.  He had an incredible season last year–one of the best ever–but his YPC is likely going to take a tumble.  It will regress toward the mean, despite his talent.

Meanwhile, Maurice Jones-Drew’s 4.66 career yards-per-carry mark is more established.  He’s played more seasons, meaning we can probably expect him to maintain that mark for a little while.

Projected Yards Left (Total)
Ray Rice: 13,523 (15,316)
Adrian Peterson: 9,868 (14,352)
Chris Johnson: 12,933 (16,167)
Steven Jackson: 5,629 (12,336)
Maurice Jones-Drew: 11,256 (15,180)

The first thing we notice about these totals is that longevity really is more important than short-term greatness.  Peterson figures to have a greater rushing average than Rice and Jones-Drew over his career, but he falls short in the projected career yardage mark because he’s unlikely to be able to sustain that level of play.

Johnson leads the pack with a projected total of 16,167 yards–2,188 yards short of Smith’s total. Those 2,000+ yards would be awfully difficult to gain at ages 34 and 35.  Further, I’ve been fairly generous in my assumptions of both projected health and longevity.  Very few running backs play until they are 35 years old.

But what are the chances that, even if Johnson’s mean projected career rushing total is the 16,167 I have listed above, he would reach Smith’s record total simply by luck?  That is, if we were to simulate 1,000 careers for Johnson and 16,167 was the average total, how many of those 1,000 careers would he break the all-time rushing mark?

I did a very similar analysis in my article on Smith’s chances of passing Dorsett’s college rushing total.  In both studies, we must use a term I mentioned earlier–the normal distribution.  I gave a pretty in-depth explanation of it in my study on Smith:

The normal distribution is very relevant to football statistics and gives us an excellent base for making probability-based predictions.

Also known as the “bell curve,” the normal distribution is used to describe any set of variables that tend to cluster around the mean.

We see this all the time in football when there are a bunch of players with very comparable statistics and just a few players with “outlying” ones.   Of the 1,000 yards rushers in the NFL last season, for example, 14 of 15 rushed for within 220 yards of the 1,281 yard average.   The lone outlier? Chris Johnson and his 2,006 yards.

By calculating the variance among the runners, we can determine the “standard deviation.”  If a set of data possesses a low standard deviation, we know that nearly all of the data clusters around the mean.  A high standard deviation means just the opposite.

Calculating the standard deviation, or variance from the norm, is so important because the normal distribution is governed by standard deviations–even the distribution of football statistics.   In the example above, for example, we can determine that, of the 1,000 yard rushers, there is a standard deviation of about 160 yards.

Thus, according to the normal distribution, we would expect approximately 68 percent of 1,000 yard rushers to be within 160 yards, or one standard deviation of the mean.  In 2009, that would have been between 1,121 and 1,441 yards. In reality, only 9 of the 15 running backs were in this range (60 percent). Over a larger sample size, however, we’d expect these numbers to level out–they always do.

So, to more easily decipher Johnson’s chance of breaking the rushing record, we must determine how many career yards is equal to one standard deviation (as it relates to 1,000 simulated careers).  A simpler way to put it is, “Within what range of yards would 68 percent of Chris Johnson’s simulated seasons fall?”  You could also think of it as “Within what range of yards is there a 68 percent chance that Chris Johnson’s career yardage falls?”

Why 68 percent?  Well, if you look at the bell curve pictured above, you can see that in any given set of data which tend to cluster around the mean, about 68.2 percent will fall within one standard deviation of the average.  If we know the standard deviation, we can determine the likelihood of future events quite precisely.

The answer to this question is the tricky part.  The standard deviation of total yardage won’t be that great because, although totals can vary greatly from season to season, those fluctuations tend to level out over the course of a career.  Since we don’t have any simulated season from which to gather data and because the statistics of others are basically irrelevant to Johnson’s future, we simply have to make an educated guess.

While it is by no means a totally objective number, I would presume that Johnson has a 68 percent chance of falling with approximately a 3,000 yard range.  If we are to believe that the mean rushing total of 1,000 simulated Johnson careers is 16,167 yards, then we would expect for there to be a 68 percent chance that Johnson totals between and 14,667 and 17,667 career rushing yards.

As you can see, the upper end of that estimate isn’t too far from Smith’s career yardage mark.  Actually, Smith’s record is less than 1.5 standard deviations away from Johnson’s average.

So, what are the chances that Johnson breaks the record?  Well, if an “average” Johnson career results in 16, 167 yards, then there is approximately a 5-7 percent chance that he eventually retires as the NFL’s all-time leading rusher. Not bad odds, really.

Of course, my estimates of his career rushing attempts are somewhat generous, as they assumed full health.  In reality, Johnson, nor any of the other backs on this list, will go through their entire careers unscathed.  Smith was an anomaly.

If Johnson alone has a 5-7 percent chance of breaking the record, though, what are the chances that any of the running backs listed above will break it?  Well, if we assume the same 1,500 yard standard deviation that we used for Johnson (3,000 total yards–one standard deviation in both directions), Rice would have approximately a two percent chance of breaking the record, Peterson a one percent chance, Jackson almost a zero percent chance (we’ll say .001), and Jones-Drew just under two percent.

The first thing that jumps out to me is that, despite less than 1,000 more projected yards than Rice or Jones-Drew, Johnson is about three times as likely to break the rushing record.  This is because, as you get closer and closer to Smith’s record, the yards become “more valuable.”  That is, the chances of falling two standard deviations from the mean  is exponentially lower than falling one standard deviation away, such that a small increase in projected average means big-time alterations in the probability of a player breaking the record.

Think about it this way: if one of the running back had a projected career rushing total of exactly 18,355, he’s have a 50 percent chance of breaking the record.  That’s a far great probability than even that of Johnson, whose mean projected total is just over 2,000 yards from Smith’s record.

Nonetheless, we can decipher the probability of any of these five running backs breaking Smith’s record using the following formula:

Let A=Rice’s chance of breaking the record, B=Johnson’s, C=Peterson’s, D=Jackson’s, and E=Jones-Drew’s

P(A or B)= P(A) + P(B) – P(A and B)= 7.88 percent
P(C or D)= P(C) + P(D) – P (C and D)=  about o percent
P(AorB or E)= P(AorB) + P(E) – P(AorB and E)=9.72 percent
P(AorBorE or CorD)= P(AorBorE) + P(CorD) – P(AorBorE and CorD)= 9.72 percent

Thus, the overall chance that one of these backs breaks Smith’s all-time mark is probably somewhere between 9-10 percent.  Johnson, of course, has the best shot at around 6 percent, while Jackson’s chances are basically nil.

The fact that perhaps the five best running back’s in the game today have just a one-in-10 chance combined of becoming the NFL’s all-time leading rusher is truly remarkable and speaks volumes about the magnitude of Smith’s achievement.

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3 Responses to “22 in 22″ Finale: Will Anyone Break Emmitt Smith’s Rushing Record? A Statistical View

  1. Pingback: Dallas Cowboys All-Decade Team: Tony Romo at the Helm | Dallas Cowboys Times

  2. Ben says:

    I completely disagree. Superbowls aren’t won over lots of years, they are won in one season. When you say longevity is more important than YPC, I completely disagree. It makes a nice career, and a good case for the HOF, but 4.17? That’s average. This opinion reeks of homerism.

  3. Ben–The article wasn’t an argument that Smith is the best RB of all-time or better than these guys…it was simply a study to determine if anyone could break his record. As far as career rushing yds go, it’s pretty clear that longevity is key. A high YPC certainly helps, but it’s clearly not 100 percent vital, as Smith showed. Meanwhile, you aren’t rushing for 18k without longevity.

    So I’m not sure I see the “homerism” you do. I actually think there are plenty of RBs better than Smith…that has nothing to do with the odds of a future RB breaking his record.

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