Sunday, May 10, 2009

Rethinking the rushing crown

Question:
The 'rushing crown' is awarded to the player who gains the most yardage on the ground each year, and this is what is often used to determine who is the best RB in the league. Yet, when a RB fumbles the ball after a 20 yard gain on 3rd down, we don't cheer for the 20 yards that were 'gained', we lament the 20 yards that were lost on the punt had he fallen down at the line of scrimmage. If we take fumbles into account -- who is the top rusher in the league?

Method:
The difficulty here is figuring out how much to penalize a player for a fumble. A fumble on a first down is clearly worse than a fumble on 4th down (assuming equal return yards), but we don't have access to this data, so this is difficult. We can try to approximate this by deducting how much the average carry would have brought us (~4.2 yards). We then tack on to this how much field position we lost had we simply punted the ball, which is roughly 39.5 yards.

The number of fumbles also seems to inflate the penalty, given the recovery of a fumble is roughly a coin flip. Thus instead of taking the total number of fumbles, we take 50% of the total number of fumbles.

We calculate adjusted yards per carry as follows:
  • A.YDS = YDS - FUM * 0.5 * (4.2 + 39.5)
Results:
Using this formula we produce a new 2008 rushing leaders list:















































































































































































































































































































































































































































































































































































































2008 Rushing Leaders
RNKNAMEATTYDSA.YDSAVGA.AVGTDFUMLST
1M. Turner RB, ATL37616991,6334.54.341732
2A. Peterson RB, MIN36317601,5634.84.311094
3D. Williams RB, CAR27315151,5155.55.551800
4C. Portis RB, WAS34214871,4214.34.16933
5Thomas Jones RB, NYJ29013121,2684.54.371321
6Steve Slaton RB, HOU26812821,2384.84.62921
7Matt Forte RB, CHI31612381,2163.93.85811
8Chris Johnson RB, TEN25112281,2064.94.81911
9Ryan Grant RB, GNB31212031,1163.93.58443
10L. Tomlinson RB, SDG29211101,1103.83.801100
11B. Jacobs RB, NYG21910891,02354.671531
12M. Lynch RB, BUF25010369924.13.97621
13Derrick Ward RB, NYG18210259815.65.39220
14Jamal Lewis RB, CLE27910029803.63.51410
15S. Jackson RB, STL25310429334.13.69753
16Kevin Smith RB, DET2389769324.13.92821
17B. Westbrook RB, PHI23393691443.92910
18Frank Gore RB, SFO24010369054.33.77863
19Ronnie Brown RB, MIA2149168944.34.181011
20L. McClain FB, BAL2329028363.93.611030
21Marion Barber RB, DAL2388858193.73.44731
22J. Stewart RB, CAR1848367924.54.311021
23Willie Parker RB, PIT2107917913.83.77500
24Justin Fargas RB, OAK2188537873.93.61131
25Warrick Dunn RB, TAM1867867864.24.23200
26LenDale White RB, TEN2007737733.93.871500
27Larry Johnson RB, KAN1938747654.53.96551
28M. Jones-Drew RB, JAC1978247374.23.741242
29Sammy Morris RB, NWE1567277054.74.52711
30Cedric Benson RB, CIN2147477033.53.29221
31W. McGahee RB, BAL1706716273.93.69722
32Julius Jones RB, SEA1586986114.43.86242
33Pierre Thomas RB, NOR1296256034.84.68911
34Mewelde Moore RB, PIT1405885884.24.20500
35R. Williams RB, MIA1606595724.13.57442
36Fred Taylor RB, JAC1435565563.93.89100
37M. Morris RB, SEA1325745524.34.18011
38Fred Jackson RB, BUF1305715494.44.22311
39D. Rhodes RB, IND1525385383.53.54600
40Joseph Addai RB, IND1555445223.53.37511
41E. Graham RB, TAM1325635194.33.93422



The list ordering does not appear to change too drastically, but this is somewhat expected since most players fumbled about the same number of times (~60% of the players on this list did not fumble more than twice and ~80% did not fumble more than 3 times).


There are some noteworthy movers, however. Michael Turner is the 2008 rushing king and not Adrian Peterson, whose yards per carry drops from an excellent 4.8 to an average 4.31. NFC West running backs faired poorly as Stephen Jackson drops from 12th to 15th and Frank Gore drops from 13th to 18th.

On a positive note, running backs like DeAngelo Williams are now graded much more closely to Adrian Peterson. Instead of them being ~250 yards different, they are separated by ~50 yards. This makes sense to me at least. If the turnover battle is as big to winning football games as people say it is, we should take that into consideration before naming Peterson the league's best rusher.

References:
The data used above was taken from the 'rushing leaders' list from ESPN.com, meaning that players who were listed below 41 on the original list are not listed here.

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