## Adrian Peterson’s 2012 Season Lacked Some Juice

When I went on the Advanced NFL Stats Podcast in late December, I discussed my use of Z-scores to measure the Seattle pass defense. Host Dave Collins asked me if I was planning on using Z-scores to measure other things, like say, Adrian Peterson’s 2012 season. I told him that would be an interesting idea to look at in the off-season.

Well, it’s the off-season. So here’s what I did.

1) For every season since 1932, I recorded the number of rushing yards for the leading rusher for each team in each league. So for the Minnesota Vikings in 2012, this was 2,097.

2) Next, I calculated the average number of rushing yards of the top rusher of each other team in the NFL. In 2012, the leading rusher on the other 31 teams averaged 974 yards.

3) Then, I calculated the standard deviation of the leading rushers for all teams in the NFL. In 2012, that was 386 yards.

4) Finally, I calculated the Z-score. This is simply the difference between the player’s average and the league average (for Peterson, that’s 1,123), divided by the standard deviation. Peterson’s Z-score was 2.91, good enough for 15th best since 1932. The table below shows the top 250 seasons using this method from 1932 to 2013; it’s fully searchable and sortable, and you can change the number of entries shown by using the dropdown box on the left.

RkRunning BackYearTeamLgTmsRshYdLgAvgLgStDvDiffZ-Score
1O.J. Simpson1973BUFNFL26200382029611834
2O.J. Simpson1975BUFNFL26181780429210133.46
3Jim Brown1963CLENFL14186363935512243.45
4Walter Payton1977CHINFL28185278532010673.33
5Jim Brown1965CLENFL1415446382739063.32
6Joe Perry1954SFONFL1210494901735593.22
7Chris Johnson2009TENNFL32200696032410463.22
8Earl Campbell1980HOUNFL28193484534010893.2
9Jim Brown1958CLENFL1215275723029553.16
10Charles White1987RAMNFL2813746702267043.11
11Barry Sanders1994DETNFL2818839033239803.03
12Eric Dickerson1984RAMNFL28210595738211483.01
13Cliff Battles1937WASNFL108744381484362.95
14Barry Sanders1997DETNFL30205399935910542.93
16Jim Brown1957CLENFL129425571353852.84
17Steve Van Buren1947PHINFL1010084072136012.81
18Jim Brown1959CLENFL1213297032246262.79
19Jim Nance1966BOSAFL914586123088462.75
20Eric Dickerson1986RAMNFL2818218593569622.7
21Otis Armstrong1974DENNFL2614077192556882.7
22Emmitt Smith1995DALNFL3017739792977942.68
23Emmitt Smith1991DALNFL2815637892997742.59
24Jim Musick1933BOSNFL108093891634202.57
25Barry Sanders1991DETNFL2815487902997582.54
26Joe Perry1953SFONFL1210184842115342.53
27Terrell Davis1998DENNFL30200810353879732.52
28Jim Brown1964CLENFL1414466663137802.49
29Ricky Williams2002MIANFL32185310893077642.49
30Jim Taylor1962GNBNFL1414747432967312.47
31Steve Van Buren1948PHINFL109454571984882.47
32Eric Dickerson1983RAMNFL2818089923328162.45
33Leroy Kelly1968CLENFL1612397072195322.43
34Jamal Lewis2003BALNFL32206610844039822.43
36LeSean McCoy2013PHINFL3216078902967172.42
37Jim Brown1961CLENFL1414087252826832.42
38Dan Towler1952RAMNFL128944431874512.41
39Maurice Jones-Drew2011JAXNFL3216069382806682.39
40Emmitt Smith1993DALNFL2814868652606212.39
41Spec Sanders1947NYYAAFC814326713237612.36
42Eric Dickerson1988INDNFL2816598563428032.35
43O.J. Simpson1976BUFNFL2815038362896672.31
44Leroy Kelly1967CLENFL1612056692325362.31
45Marcus Allen1985RAINFL28175910023347572.27
46Emmitt Smith1992DALNFL2817139083578052.25
47Dickie Post1969SDGAFL10873677871962.24
48Michael Turner2008ATLNFL3216999773247222.23
50Arian Foster2010HOUNFL3216169822876342.21
51Bill Paschal1944NYGNFL107374141473232.19
52Barry Foster1992PITNFL2816909093577812.19
53Shaun Alexander2005SEANFL32188010413848392.19
54Earl Campbell1979HOUNFL2816979403487572.17
55Jerome Bettis1993RAMNFL2814298672605622.16
56Gale Sayers1966CHINFL1512316882525432.16
57George Rogers1981NORNFL28167410113096632.15
58Gerald Riggs1985ATLNFL28171910043347152.14
59Larry Johnson2006KANNFL32178911023216872.14
60Earl Campbell1978HOUNFL2814509012575492.14
61Tiki Barber2005NYGNFL32186010413848192.13
62Beattie Feathers1934CHINFL1110044292705752.12
63Bill Osmanski1939CHINFL106993771523222.12
64Steve Van Buren1945PHINFL108323792144532.12
65Steve Van Buren1949PHINFL1011465482825982.12
66Jim Brown1960CLENFL1312576422916152.12
67Larry Brown1970WASNFL2611256612204642.11
68Jamal Anderson1998ATLNFL30184610413878052.08
69Rick Casares1956CHINFL1211266502294762.08
70Terrell Davis1997DENNFL30175010093597412.06
71Paul Robinson1968CINAFL1010237121523112.05
72Tony Dorsett1981DALNFL28164610123096342.05
73Whizzer White1938PITNFL105673281162392.05
74Thurman Thomas1991BUFNFL2814077952996122.05
75Bill Dudley1942PITNFL106963881503082.05
76Jim Taylor1961GNBNFL1413077332825742.03
77Alan Ameche1955BALNFL129616181733431.99
79Barry Sanders1996DETNFL3015539423096111.98
80Christian Okoye1989KANNFL2814808793046011.98
81Ahman Green2003GNBNFL32188310904037931.97
82Curtis Martin2004NYJNFL32169710573286401.95
83Shaun Alexander2004SEANFL32169610573286391.95
84Chris Warren1994SEANFL2815459163236291.95
85Barry Sanders1989DETNFL2814708793045911.94
86Frank Akins1945WASNFL107973832144141.94
87Priest Holmes2001KANNFL3115559872945681.93
88Terrell Davis1996DENNFL3015389423095961.93
89Walter Payton1978CHINFL2813959032574921.92
91Walter Payton1979CHINFL2816109433486671.91
92Barry Sanders1990DETNFL2813048362454681.91
93Herschel Walker1988DALNFL2815148613426531.91
94Walter Payton1976CHINFL2813908402895501.9
95Ottis Anderson1979STLNFL2816059443486611.9
96Edgerrin James2000INDNFL31170910693386401.89
97Gale Sayers1969CHINFL1610326621953701.89
98Joe Perry1949SFOAAFC77835001502831.88
99Thurman Thomas1990BUFNFL2812978362454611.88
100Paul Lowe1965SDGAFL811216722404491.87
101Roger Craig1988SFONFL2815028613426411.87
102Freeman McNeil1982NYJNFL287865211422651.87
103Marion Motley1950CLENFL138105611332491.87
104Eddie Price1951NYGNFL129715942023771.87
105Walter Payton1984CHINFL2816849723827121.86
106Abner Haynes1960DTXAFL88755731633021.86
107Frank Gore2006SFONFL32169511053215901.84
108Larry Johnson2005KANNFL32175010453847051.84
109Edgerrin James1999INDNFL3115539283436251.82
110Jerome Bettis1997PITNFL30166510123596531.82
111Dan Towler1953RAMNFL128794962113831.81
112Joe Morris1986NYGNFL2815168713566451.81
114Clem Daniels1963OAKAFL810997392003601.8
115Floyd Little1971DENNFL2611337092374241.79
116Curtis Martin2001NYJNFL3115139892945241.78
117Tuffy Leemans1936NYGNFL98305311682991.78
118Leroy Kelly1966CLENFL1511416942524471.78
119Ace Gutowsky1936DETNFL98275321682951.76
120Rob Goode1951WASNFL129515962023551.76
121Corey Dillon2004NWENFL32163510593285761.76
122Walter Payton1980CHINFL2814608633405971.76
123Emmitt Smith1994DALNFL2814849183235661.75
125Tiki Barber2006NYGNFL32166211063215561.73
126Barry Sanders1995DETNFL3015009882975121.72
127Paul Lowe1960LACAFL88555761632791.72
128Curt Warner1986SEANFL2814818723566091.71
129Thurman Thomas1993BUFNFL2813158712604441.71
130Billy Cannon1961HOUAFL89486301873181.7
131William Andrews1983ATLNFL28156710013325661.7
132Don Woods1974SDGNFL2611627292554331.7
133Priest Holmes2002KANNFL32161510973075181.69
134Merl Condit1942BKNNFL106473931502541.69
135Curtis Martin1995NWENFL3014879892974981.68
136Jamaal Charles2010KANNFL3214679872874801.67
137O.J. Simpson1972BUFNFL2612518152614361.67
138John Brockington1971GNBNFL2611057112373941.66
139Jim Nance1967BOSAFL912166523395641.66
140Bill Dudley1946PITNFL106044071191971.65
141Ron A. Johnson1970NYGNFL2610276652203621.65
142DeAngelo Williams2008CARNFL3215159833245321.64
143Tony Dorsett1978DALNFL2813259052574201.64
144Cliff Battles1932BOSNFL85763831181931.63
145Wilbert Montgomery1979PHINFL2815129473485651.62
146Walter Payton1985CHINFL28155110103345411.62
147Alfred Morris2012WASNFL3216139903866231.62
148Doug Russell1935CRDNFL94993101171891.61
149Whizzer White1940DETNFL10514371891431.61
150Thurman Thomas1992BUFNFL2814879173575701.6
151Hoyle Granger1967HOUAFL911946553395391.59
152Marion Butts1990SDGNFL2812258392453861.58
153Tony Dorsett1982DALNFL287455221422231.57
154Jerome Bettis1996PITNFL3014319463094851.57
155Eddie Price1952NYGNFL127484561872921.56
156Dick Bass1966RAMNFL1510906982523921.56
157Marshawn Lynch2012SEANFL3215909913865991.55
158Clinton Portis2008WASNFL3214879843245031.55
159Curtis Martin1999NYJNFL3114649313435331.55
160Earnest Byner1990WASNFL2812198392453801.55
161Matt Snell1964NYJAFL89487241452241.55
162O.J. Simpson1974BUFNFL2611257302553951.55
164Jim Taylor1964GNBNFL1411696873134821.54
165Jim Taylor1960GNBNFL1311016552914461.53
166Larry Brown1972WASNFL2612168162614001.53
167Ricky Watters1996PHINFL3014119473094641.5
168Stephen Davis2001WASNFL3114329922944401.5
169Ray Rice2011BALNFL3213649462804181.5
170Pug Manders1941BKNNFL10486341971451.49
171Matt Forte2013CHINFL3213398992964401.49
172Edgerrin James2004INDNFL32154810623284861.48
173James Wilder1984TAMNFL2815449773825671.48
174Lawrence McCutcheon1974RAMNFL2611097312553781.48
175Bobby Humphrey1990DENNFL2812028402453621.48
176Mark van Eeghen1977OAKNFL2812738073204661.46
177Eric Dickerson1987INDNFL2810116832263281.45
179Franco Harris1975PITNFL2612468272924191.43
180Ottis Anderson1980STLNFL2813528673404851.43
181Larry Csonka1971MIANFL2610517132373381.43
182Joe Perry1952SFONFL127254591872661.43
183John David Crow1960STLNFL1310716582914131.42
184Brian Westbrook2007PHINFL3213339712563621.41
185MacArthur Lane1970STLNFL269776672203101.41
186Marion Motley1948CLEAAFC89646692092951.41
187Michael Turner2011ATLNFL3213409462803941.41
188Eric Dickerson1989INDNFL2813118853044261.4
189Spec Sanders1946NYYAAFC87094401922691.4
190Calvin Hill1969DALNFL169426681952741.4
191Ron A. Johnson1972NYGNFL2611828172613651.4
192Tiki Barber2004NYGNFL32151810623284561.39
193Stephen Davis1999WASNFL3114059333434721.38
194J.D. Smith1959SFONFL1210367302243061.37
195Delvin Williams1978MIANFL2812589082573501.36
196Eddie George1996HOUNFL3013689483094201.36
198Steve Owens1971DETNFL2610357132373221.36
199George McAfee1941CHINFL10474342971321.35
200Emmitt Smith1999DALNFL3113979333434641.35
201Billy Sims1981DETNFL28143710203094171.35
202Deuce McAllister2003NORNFL32164110984035431.35
203Steven Jackson2009STLNFL3214169793244371.35
204Willie Parker2007PITNFL3213169722563441.35
205Garrison Hearst1998SFONFL30157010503875201.34
206Howie Ferguson1955GNBNFL128596271732321.34
207Lawrence McCutcheon1977RAMNFL2812388083204301.34
208Ahman Green2001GNBNFL3113879932943941.34
209Abner Haynes1962DTXAFL810496992623501.34
210Rueben Mayes1986NORNFL2813538773564761.34
211Jamaal Charles2012KANNFL3215099933865161.34
212Curt Warner1983SEANFL28144910063324431.33
213Michael Turner2010ATLNFL3213719902873811.33
214Curt Warner1987SEANFL289856842263011.33
215Clinton Portis2002DENNFL32150811003074081.33
216Bill Paschal1943NYGNFL85724011291711.33
217Gerald Riggs1984ATLNFL2814869803825061.33
218Marshall Faulk2001STLNFL3113829932943891.32
219Natrone Means1994SDGNFL2813509233234271.32
220Jack Hinkle1943PHINFL85714011291701.32
221Robert Smith2000MINNFL31152110763384451.32
222Swede Hanson1934PHINFL118054492703561.31
223Terry Allen1996WASNFL3013539493094041.31
224Jamaal Charles2013KANNFL3212879002963871.31
225Chris Johnson2010TENNFL3213649902873741.3
226Marshall Faulk1999STLNFL3113819343434471.3
227Steven Jackson2006STLNFL32152811103214181.3
228Thomas Jones2009NYJNFL3214029803244221.3
229Jamal Lewis2007CLENFL3213049722563321.3
230LeSean McCoy2011PHINFL3213099472803621.29
231William Andrews1980ATLNFL2813088683404401.29
232Paul Lowe1963SDGAFL810107522002581.29
233Eddie George2000TENNFL31150910763384331.28
234Walter Payton1986CHINFL2813338773564561.28
235Billy Sims1980DETNFL2813038683404351.28
236Neal Anderson1989CHINFL2812758863043891.28
237Maurice Jones-Drew2009JAXNFL3213919803244111.27
238Alfred Morris2013WASNFL3212759012963741.26
239Gerald Riggs1986ATLNFL2813278783564491.26
240John Henry Johnson1962PITNFL1411417682963731.26
241Andra Franklin1982MIANFL287015241421771.25
242Walter Payton1983CHINFL28142110073324141.25
243Frank Ziegler1950PHINFL137335671331661.24
244Lydell Mitchell1975BALNFL2611938292923641.24
246Dave Osborn1967MINNFL169726842322881.24
247Dan Towler1951RAMNFL128546052022491.24
248Mike Garrett1967KANAFL910876683394191.24
249John Grigas1944CRDNFL106104291471811.23
250Dalton Hilliard1989NORNFL2812628873043751.23

The Z-score is a good substitute for something like “how crazy was that season?!” And it’s hard to argue with O.J. Simpson’s 1973 season as the craziest. John Brockington was second in the NFL in rushing…. with 1,144 yards. For perspective, consider that in 2012, Alfred Morris, Marshawn Lynch, and Jamaal Charles all topped 1500 rushing yards, so Peterson’s stellar season isn’t quite the outlier.

The Z-score is a nice way to compare across eras and give some love to some forgotten seasons. Joe Perry led the NFL with 1,049 rushing yards in the 12-game 1954 season; his San Francisco teammate John Henry Johnson was second in the league with 681 yards! One might find this sort of analysis useful in Hall of Fame debates. For example, Terrell Davis had three very good years, coming in at 1.9+ standard deviations from the mean in 1996, 1997, and 1998. Jerome Bettis rushed for more yards than Davis, but he has just one top-100 season by this method, and only two top-250 years.

Walter Payton leads the way with 9 top-250 seasons, while Jim Brown is the leader with 8 top-75 seasons (Eric Dickerson, Steve Van Buren, and Emmitt Smith are all tied for second with four). Barry Sanders, Payton, and Brown are the only players with seven top-150 seasons.

Among 2,000 yard seasons, Jamal Lewis receives the lowest Z-score. That’s because the spread among top running backs was very wide that year, which occurred in the heart of the stud running back era. Ahman Green rushed for 1,883 yards, and LaDainian Tomlinson and Deuce McAllister each rushed for over 1,600 yards, while the leading rusher on every other team but Baltimore still averaged nearly 1,100 yards.

• Daniel Jones

Trying to understand the logic behind Z-score as a metric.

The standard deviation is an odd thing to use to judge performances by like this. What are you trying to achieve by doing it? I think certainly for running backs, the standard deviation is large when about half the teams have a RBBC approach, and small when almost all teams have either a feature back or RBBC.

It’s interesting as a curios though, so I still enjoyed reading the article.

• Chase Stuart

Well, the reason for the Z-Score approach is that it was requested. This just proves that I listen to and take requests!

• Kibbles

• Richie

How come sometimes your posts are highlighted in blue, but not always?

• David

I think the most impressive player here is Jim Brown. 3 of the top 9, 5 of the top 18, and 7 of the top 37. That is above and beyond anyone else on the list. I knew he was good, but this shows he was consistently excellent.

• sn0mm1s

This is primarily because he was taking 40-80 more carries in a 12 or 14 game season than the next guy. If you did something similar like this for WRs Don Hutson would blow everyone out of the water.

Out of the top 50 seasons 33 also led the league in carries only 9 seasons weren’t #1 or #2 in carries (all non #1 listed below)

Adrian Peterson 2nd in 2012 and 2008, Jim Brown 2nd in 1957, and Sanders 4th in 1994 and 1997, 2nd in 1991, Dickerson 3rd in 1984, Armstrong 3rd in 1974, Lewis 2nd in 2003, Towler 3rd in 1952, Emmitt 6th 1993, 2nd 1992, Simpson 3rd 1976, Allen 2nd 1985, Post 4th 1969, Tomlinson 2nd 2006, Foster 3rd 2010.

I would really like to see 3 other z-scores:
1) same as the current one but only against the top 1/3 of RBs that season instead of all of them.
2) YPC vs all other RBs
3) YPC vs. top 1/3 of RBs

• Samuel Lang

One season doesn’t seem to provide a large enough data set to justify using the Z-Score to make judgments. Have you guys ever tried doing something like an exponential moving average of multiple seasons instead of the average yards of a single season? I’m not a statistician so I don’t know how this would affect the standard deviation, but I’m sure you could figure out a way to make it work.

• Pingback: Temporary Archive Page()