LT, TD big winners on 'rusher rating' list

Cold, Hard Football Facts for Aug 03, 2011



By Ken Crippen
Comparing players across eras is always difficult. Some say it can't be done. But it can be done. You simply need to compare how all players performed for a given year and then compare the average yearly performance across eras. It's called normalizing the statistics.
 
The NFL passer rating system (NFLPRS) provides an example of the need for normalization. It was implemented in 1973 – and has proven an incredible indicator of team success year after year, as the Cold, Hard Football Facts discussed this week on SportsIllustrated.com.
 
But it really only gives us a chance to measure the performances of quarterbacks for a given game or season. To truly compare quarterbacks across eras, you'd have to normalize the numbers, especially because passer ratings have skyrocketed over the years. Several football historians have tackled the subject over the years (more on that effort below*).
 
But we wondered: can you come up with a similar statistical rating system for positions other than quarterback? Can you compare running backs, for example? And then, more interestingly, can you then normalize the numbers to compare, say, Gale Sayers to Marshall Faulk?
 
The answer is 'Yes!' And we've just done it, with what we call rusher rating. Our effort yields some fascinating results:
  • Terrell Davis produced what may have been the greatest season ever by a running back in 1998, the year he powered Denver to its second consecutive Super Bowl title.
  • It may be sacrilege, but you can argue that LaDainian Tomlinson has had a better career than even the great Jim Brown himself.
  • Brandon Jacobs of the Giants and BenJarvus Green-Ellis of the Patriots were the two most effective ball carriers in football last year.
Here's how we did it: Using the same philosophy as the NFL passer rating system, we factored into the rusher rating equation the following factors:
  • yards per attempt
  • touchdown  percentage
  • fumble percentage
We selected 1973 as the control year (the same year that the current passer rating system was implemented), and the league-wide averages for each component were calculated to be one point on a scale of 0 to 2.375 (the same as the current NFLPRS). Results of each component are clamped at these minimum and maximum values. This yields the rusher rating. The entire formula is found below in the footnotes.
 
Terrell Davis and the 2,000-yard club
To put the normalized rusher rating system to the test, we sized up the six 2,000-yard rushing seasons in NFL history. Here are the players ranked by yards:
 
The NFL's Six 2,000-Yard Rushing Performance (ranked by yards)
 
YEAR
ATT
YARDS
YPA
TD
FUM
Eric Dickerson
1984
379
2,105
5.55
14
14
Jamal Lewis
2003
387
2,066
5.34
14
8
Barry Sanders
1997
335
2,053
6.13
11
3
Terrell Davis
1998
392
2,008
5.12
21
2
Chris Johnson
2009
358
2,006
5.6
14
3
O.J. Simpson
1973
332
2,003
6.03
12
7
 
Now let's apply our rusher rating formula to these six seasons. You'll see the list looks quite a bit different.
 
Six 2,000-Yard Rushing Performances (ranked by non-normalized runner rating)
 
YEAR
ATT
YARDS
YPA
TD
FUM
RTNG
Terrell Davis
1998
392
2,008
5.12
21
2
125.47
Chris Johnson
2009
358
2,006
5.6
14
3
113.85
Barry Sanders
1997
335
2,053
6.13
11
3
110.95
O.J. Simpson
1973
332
2,003
6.03
12
7
107.54
Eric Dickerson
1984
379
2,105
5.55
14
14
106.98
Jamal Lewis
2003
387
2,066
5.34
14
8
103.95
 
Those ratings are quite interesting. But, as mentioned, they don't take into account the differences in eras until we normalize the list.
 
Six 2,000-yard Rushing performances (ranked by normalized runner rating)
 
YEAR
ATT
YARDS
YPA
TD
FUM
RTNG
Terrell Davis
1998
392
2,008
5.12
21
2
132.05
Chris Johnson
2009
358
2,006
5.6
14
3
124.08
Barry Sanders
1997
335
2,053
6.13
11
3
115.21
Jamal Lewis
2003
387
2,066
5.34
14
8
111.74
Eric Dickerson
1984
379
2,105
5.55
14
14
110.53
O.J. Simpson
1973
332
2,003
6.03
12
7
107.54
 
Davis, the former Broncos great, clearly thrives in our rusher rating formula.
 
He was fourth in total yards and sixth in average per attempt. Those numbers look to put his 1998 season behind the likes of Dickerson or Sanders.
 
But Davis fumbled just twice in 392 attempts, easily the lowest fumble rate of the six players on the list. And his 21 total touchdowns and touchdown rate topped all others.
 
Dickerson clearly suffers in the rating fomula. He's still the single-season yardage leader with 2,105 yards, but his 14 touchdowns were offset by his 14 fumbles. In fact, fumbles haunted Dickerson throughout his otherwise tremendous career: 49 in his first four seasons alone and 78 total. As talented and as productive as he was, those fumbles clearly impacted his effectiveness – and rusher rating measures that impact.
 
Normalizing had only a minor effect on the list, as O.J. Simpson and Jamal Lewis swapped positions in the standings.
 
Heresy! LaDainian Tomlinson > Jim Brown?
The complexity of rusher rating increases if you want to compare careers: you need to not only normalize each year of a running back's career, but you also need to give the appropriate weight to each year as a percentage of the total.
 
We accomplish this by multiplying the normalized rusher rating by the number of rushing attempts for that year. Sum the total and divide by the total number of rushing attempts for his career. Now, you have a player's normalized career rusher rating.
 
We looked at arguably the 10 best running backs of all time (in alphabetical order): Jim Brown, Earl Campbell, Eric Dickerson, Marshall Faulk, Walter Payton, Barry Sanders, Gale Sayers, O.J. Simpson, Emmitt Smith, LaDainian Tomlinson.
 
In order to show no bias in the results, these running backs were polled from various all-time lists and are not necessarily any one individual's top 10. Here they are, ranked in order by their normalized rusher rating:
 
10 All-Time Great Running Backs (ranked by rusher rating)

 

ATT

YARDS

YPA

TD

FUM

RTNG

LaDainian Tomlinson

3099

13404

4.33

144

30

118.76

Jim Brown

2359

12312

5.22

106

57

113.62

Marshall Faulk

2836

12279

4.33

100

36

105.77

Barry Sanders

3062

15269

4.99

99

41

105.30

Emmitt Smith

4409

18355

4.16

164

61

105.26

Earl Campbell

2187

9407

4.30

74

43

100.91

Gale Sayers

991

4956

5.00

39

34

100.10

Walter Payton

3838

16726

4.36

110

86

94.69

Eric Dickerson

2996

13259

4.43

90

78

93.86

O.J. Simpson

2404

11236

4.67

61

62

92..03

 
It's no surprise that Brown's rusher rating was so high. He is widely considered the greatest running back of all time. The surprising result is that Tomlinson beats out Jim Brown by a wide margin.
 
The reason Tomlinson tops Brown is pretty obvious when you see it in black & white: LT is simply brilliant when it comes to holding on to the football, suffering a fumble on less than 1 percent of all attempts in his career. Brown put up incredible numbers, as we all know, highlighted by an incredible record of 5.22 yards per attempt. But he suffered nearly twice as many fumbles as LT on 740 fewer career attempts.
 
It will be interesting to see Tomlinson's numbers after he retires. His production appears to be on the decline by any measure, while Brown retired at the peak of his game, after one of the great seasons of all time in 1965.
 
Gale Sayers and O.J. Simpson are interesting studies. Sayers may be the most talented back among all those on the list. but he was seperated from the ball on 3.4 percent of career attempts, easily the most among the 10 backs on this list. He's remembers as perhaps the most gifted runner in NFL history, but few remember that he struggled to hold on to the ball. Simpson, meanwhile, is the only player on the list to suffer more fumbles than touchdowns scored.
 
In both cases, the super-talented Sayers and Simpson suffer as measured by rusher rating because they struggled to hold on to the football.
 
Surprise best of 2010: Brandon Jacobs, BenJarvus Green-Ellis
Naturally, armed with rusher rating, we wanted to know which ball carriers were the most productive in 2010. We don't have to normalize the numbers in this case, because we're looking at players from a single season.
 
Once again, the results are surprising.
 
Arian Foster, for example, was the break-out star of 2010, with a league-best 1,616 rushing yards. But he was not necessarily the most effective running back last season.
 
That honor goes to punishing ball carrier Brandon Jacobs of the New York Giants. He was followed by a true shocker: BenJarvus Green-Ellis, "the law firm" who unexpectedly handled the bulk of the work of the 14-2 Patriots last year; and then Michael Bush, who shared duties with Darren McFadden in Oakland's highly productive rushing attack.
 
Jacobs had an incredibly high ever per attempt and a great touchdown ratio: 9 scores in just 147 carries. Green-Ellis skyrockets up the list for obvious reasons: his 13 rushing touchdowns were second in the NFL (with 98 fewer carries than league-leader Foster) and he did not fumble once all year. That's a very effective effort. Bush also had a high touchdown percentage without a single fumble.
 
You'll notice from this list that rusher rating is much like passer rating in that it rewards players for efficiency, not for volume. Running more often doesn't make you more effective as a running back, just like passing more often doesn't make you more effective as a quarterback.
 
2010 Ball Carriers Ranked  by Rusher Rating (min. 100 attempts)
 
ATT
YARDS
YPA
TD
FUM
RTNG
Brandon Jacobs
147
823
5.60
9
2
120.89
BenJarvus Green-Ellis
229
1008
4.40
13
0
117.88
Michael Bush
158
655
4.15
8
0
111.09
Arian Foster
327
1616
4.94
16
3
109.58
Mike Tolbert
182
735
4.04
11
5
105.71
Adrian Peterson
283
1298
4.59
12
1
104.59
Willis McGahee
100
380
3.80
5
2
99.08
Rashard Mendenhall
324
1273
3.93
13
2
97.72
LeSean McCoy
207
1080
5.22
7
2
97.59
Michael Turner
334
1371
4.10
12
2
95.09
Chris Johnson
316
1364
4.32
11
3
93.60
Marion Barber
113
374
3.31
4
0
93.13
Jamaal Charles
230
1467
6.38
5
3
91.74
Darren McFadden
223
1157
5.19
7
4
91.35
Ryan Mathews
158
678
4.29
7
5
91.21
Chris Ivory
137
716
5.23
5
4
90.66
Peyton Hillis
270
1177
4.36
11
8
89.42
Joseph Addai
116
495
4.27
4
2
89.34
LeGarrette Blount
201
1007
5.01
6
4
88.08
Matt Forte
237
1069
4.51
6
3
84.82
Ryan Torain
164
742
4.52
4
2
84.30
LaDainian Tomlinson
219
914
4.17
6
3
84.30
Knowshon Moreno
182
779
4.28
5
3
83.62
Tim Hightower
153
736
4.81
5
5
83.36
Justin Forsett
118
523
4.43
2
0
83.09
Ahmad Bradshaw
276
1235
4.47
8
7
81.77
Marshawn Lynch
202
737
3.65
6
4
80.53
Chester Taylor
112
267
2.38
3
0
80.49
Ray Rice
307
1220
3.97
5
0
80.00
Maurice Jones-Drew
299
1324
4.43
5
2
79.68
Thomas Jones
245
896
3.66
6
3
79.61
Jahvid Best
171
555
3.25
4
1
79.44
Steven Jackson
330
1241
3.76
6
1
79.04
Ronnie Brown
200
734
3.67
5
3
78.81
Donald Brown
129
497
3.85
2
0
78.64
Fred Jackson
222
927
4.18
5
5
75.82
Brandon Jackson
190
703
3.70
3
1
75.54
Chris Wells
116
397
3.42
2
1
73.69
Cadillac Williams
125
437
3.50
2
1
73.30
Cedric Benson
321
1111
3.46
7
7
71.61
Frank Gore
203
853
4.20
3
4
70.51
Mike Goodson
103
452
4.39
3
5
70.35
Shonn Green
185
766
4.14
2
3
68.36
Felix Jones
185
800
4.32
1
2
67.20
Jonathan Stewart
178
770
4.33
2
4
66.76
Ricky Williams
159
673
4.23
2
4
66.14
 
Obviously, running backs are more than just rushers. They are also receivers. In our next article, we'll include a receiving component to the equation in order to give a complete Normalized Running Back Rating System.
 
FOOTNOTES:
*The concept of normalization of the NFLPRS is not a new one. Historian Bob Carroll broached the subject back in the 1980s ("Bucking the System: Or, Why the NFL Can't Find Happiness with its Passer Rating System", The Coffin Corner, Volume 8, Number 9, 1986).
 
More recently, historian and mathematician Rupert Patrick devised his own formulas for normalizing the passer rating ("Normalized Passer Rating", The Coffin Corner, Volume 33, Number 3, 2011), which yielded similar results as Carroll's. I applied a normalization concept to the rusher rating system to calculate the normalized rusher rating.
 
There have been a couple of attempts to come up with a Rusher Rating System, but their calculations were slightly different from mine. However, there has been no attempt to normalize the results across eras. If an attempt has been made, I have been unable to find it.
 
How to Calculate Rusher Rating
The current passer rating system consists of four components: completion percentage, yards per attempt, touchdown percentage and interception percentage.
 
To modify this for running backs, the rusher rating system consists of: yards per attempt, touchdown percentage, fumble percentage.
 
Here is how each component is calculated:
  • Average Yards Gained per Attempt (YD) = [Total Yards/(4.05 * Rushing Attempts)]
  • Percentage of TDs per Carry (TD) = [(39.5*Touchdowns)/Rushing Attempts]
  • Percentage of Fumbles per Carry (F) = [2.375-((21.5*Fumbles)/Rushing Attempts)]
Adding these components together and adjusting to a scale of 158.3 (the same as the NFLPRS) yields:
  • Rusher Rating = [(YD) + (TD) + (F)] * (100/4.5)
The Normalization Factor is the difference between the Average Rusher Rating for the league that season and the Average Rusher Rating for the control season. The Normalization Factor is added to the Rusher Rating of that year to give the Normalized Rusher Rating.
 
To calculate a career Normalized Rusher Rating, take the Normalized Rusher Rating for each season and multiply that by the number of rushing attempts for that season to give the Normalization Factor for each year (a weighted number based on the number of carries). Sum the Normalization Factors together and divide by the total number of rushing attempts for the player's career. This gives you the Normalized Rusher Rating for their career.

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