## Running Backs - YAA (Yards Above Average)

In a league of relativity, whenever a running back rushes he either helps or hurts his team. If a running backs aggregate rushes gain more yards than what an average back might have achieved, he has helped his team; If he gains less, he hurt it.

This would imply that Yards Per Carry is a valuable indicator of the value a player brings within his teams scheme. If a player is capable of achieving an above average YPC, it should be reasonable to assume he has pushed the overall rushing value of his team in an above average direction. The inverse should also hold true. While these assumptions are correct, YPC fails to establish the context in which the average was achieved. Marshawn Lynch and Joique Bell had essentially the same YPC however not a single person would suggest they're equivalent in value. Why? Because Lynch carried the ball ~250 more times than Bell and even though they were roughly as efficient on a per carry basis, Lynch had much more total value. In other words: Both Lynch and Bell were good, but Lynch was good more. Our dilemma however, is not comparing two like players, but rather two unlike players. To further this point, we'll need the help of our old friend Justin Forsett who In 2012 was actually significantly superior to Lynch on a per carry basis. As stated, Forsett had a much higher YPC but he achieved it over a much smaller number of carries. Additionally, both Lynch and Forsett were above average in terms of YPC, just not equally so. It is to this very situation that I have attempted to formulate a meaningful statistical comparator.

Our method of comparison will evaluate the relative value of the following 67 running backs. My cutoff was arbitrary but I feel this list hits all the staples with only a few notable omissions (Sproles).

• Each player has their rushing ATT(attempts) divided by the sum of all players ATT to yield their %ATT(percentage of attempts).
• Each player has their rushing YDS(yards) divided by the sum of all players rushing yards to yield their %YDS(percentage of rushes).
• All runners being equal, you would expect a players %ATT to equal their %YDS. Since players are obviously not all equal, we can determine the difference between their expected contribution and their actual contribution by subtracting their %ATT from their %YDS. %YDS-%ATT can be interpreted as total value above average.
• We can then convert a players %YDS-%ATT into YAA(yards above average) by multiplying the percentage against the total number of yards. This is merely the same number presented in a recognizable fashion; it can also be interpreted as total value above average.
• Dividing YAA by a players ATT gives us their YPCAA (yards per carry above average)
EG: Peterson brought ~1.41% surplus value or in other words ~614 surplus yards on his 348 carries for a per carry average of 1.76 above your normal player.
 . PLAYER ATT YDS % ATT % YDS %YDS-%ATT YAA YPCAA . Adrian Peterson, RB 348 2097 3.41% 4.82% 1.41% 613.19 1.76 . C.J. Spiller, RB 207 1244 2.03% 2.86% 0.83% 361.39 1.75 . Jamaal Charles, RB 285 1509 2.79% 3.47% 0.68% 293.81 1.03 . Marshawn Lynch, RB 315 1590 3.09% 3.66% 0.57% 246.90 0.78 . Alfred Morris, RB 335 1613 3.28% 3.71% 0.42% 184.62 0.55 . Frank Gore, RB 258 1214 2.53% 2.79% 0.26% 113.93 0.44 . Justin Forsett, RB 63 374 0.62% 0.86% 0.24% 105.38 1.67 . Doug Martin, RB 319 1454 3.13% 3.34% 0.22% 93.84 0.29 . Andre Brown, RB 73 385 0.72% 0.89% 0.17% 73.74 1.01 . Bryce Brown, RB 115 564 1.13% 1.30% 0.17% 73.66 0.64 . Ahmad Bradshaw, RB 221 1015 2.17% 2.33% 0.17% 72.69 0.33 . Chris Johnson, RB 276 1243 2.71% 2.86% 0.15% 66.18 0.24 . Joique Bell, RB 82 414 0.80% 0.95% 0.15% 64.37 0.78 . Kendall Hunter, RB 72 371 0.71% 0.85% 0.15% 64.00 0.89 . David Wilson, RB 71 358 0.70% 0.82% 0.13% 55.27 0.78 . Maurice Jones-Drew, RB 86 414 0.84% 0.95% 0.11% 47.31 0.55 . Ray Rice, RB 257 1143 2.52% 2.63% 0.11% 47.20 0.18 . Matt Forte, RB 248 1094 2.43% 2.52% 0.08% 36.57 0.15 . Brandon Bolden, RB 56 274 0.55% 0.63% 0.08% 35.23 0.63 . Lamar Miller, RB 51 250 0.50% 0.57% 0.07% 32.55 0.64 . Stevan Ridley, RB 290 1263 2.84% 2.90% 0.06% 26.49 0.09 . Marcel Reece, FB 59 271 0.58% 0.62% 0.04% 19.43 0.33 . Willis McGahee, RB 167 731 1.64% 1.68% 0.04% 18.94 0.11 . Reggie Bush, RB 227 986 2.23% 2.27% 0.04% 18.11 0.08 . Robert Turbin, RB 80 354 0.78% 0.81% 0.03% 12.89 0.16 . Ben Tate, RB 65 279 0.64% 0.64% 0.00% 1.85 0.03 . DeAngelo Williams, RB 173 737 1.70% 1.69% 0.00% -0.64 0.00 . Montario Hardesty, RB 65 271 0.64% 0.62% -0.01% -6.15 -0.09 . LeSean McCoy, RB 200 840 1.96% 1.93% -0.03% -12.76 -0.06 . Shane Vereen, RB 62 251 0.61% 0.58% -0.03% -13.36 -0.22 . Shaun Draughn, RB 59 233 0.58% 0.54% -0.04% -18.57 -0.31 . Danny Woodhead, RB 76 301 0.75% 0.69% -0.05% -23.05 -0.30 . DeMarco Murray, RB 161 663 1.58% 1.52% -0.05% -23.48 -0.15 . Bilal Powell, RB 110 437 1.08% 1.00% -0.07% -32.02 -0.29 . Ronnie Hillman, RB 85 330 0.83% 0.76% -0.07% -32.43 -0.38 . Rashard Mendenhall, RB 51 182 0.50% 0.42% -0.08% -35.46 -0.70 . Jacquizz Rodgers, RB 94 362 0.92% 0.83% -0.09% -38.80 -0.41 . William Powell, RB 60 217 0.59% 0.50% -0.09% -38.83 -0.65 . Jonathan Dwyer, RB 156 623 1.53% 1.43% -0.10% -42.16 -0.27 . Toby Gerhart, RB 50 169 0.49% 0.39% -0.10% -44.19 -0.88 . Mike Tolbert, FB 54 183 0.53% 0.42% -0.11% -47.25 -0.87 . James Starks, RB 71 255 0.70% 0.59% -0.11% -47.73 -0.67 . Fred Jackson, RB 115 437 1.13% 1.00% -0.12% -53.34 -0.46 . Peyton Hillis, RB 85 309 0.83% 0.71% -0.12% -53.43 -0.63 . Steven Jackson, RB 257 1042 2.52% 2.40% -0.12% -53.80 -0.21 . Cedric Benson, RB 71 248 0.70% 0.57% -0.13% -54.73 -0.77 . Isaac Redman, RB 110 410 1.08% 0.94% -0.14% -59.02 -0.54 . Jonathan Stewart, RB 93 336 0.91% 0.77% -0.14% -60.54 -0.65 . Daniel Thomas, RB 91 325 0.89% 0.75% -0.14% -63.01 -0.69 . Mark Ingram, RB 156 602 1.53% 1.38% -0.15% -63.16 -0.40 . Knowshon Moreno, RB 138 525 1.35% 1.21% -0.15% -63.41 -0.46 . Felix Jones, RB 111 402 1.09% 0.92% -0.16% -71.28 -0.64 . Arian Foster, RB 351 1424 3.44% 3.27% -0.17% -72.60 -0.21 . Michael Bush, RB 114 411 1.12% 0.95% -0.17% -75.08 -0.66 . Ryan Mathews, RB 184 707 1.80% 1.63% -0.18% -77.54 -0.42 . Ryan Williams, RB 58 164 0.57% 0.38% -0.19% -83.30 -1.44 . Vick Ballard, RB 211 814 2.07% 1.87% -0.20% -85.67 -0.41 . BenJarvus Green-Ellis, RB 278 1094 2.73% 2.52% -0.21% -91.34 -0.33 . Jackie Battle, RB 95 311 0.93% 0.72% -0.22% -94.06 -0.99 . Alex Green, RB 135 464 1.32% 1.07% -0.26% -111.62 -0.83 . LaRod Stephens-Howling, RB 110 356 1.08% 0.82% -0.26% -113.02 -1.03 . Shonn Greene, RB 276 1063 2.71% 2.44% -0.26% -113.82 -0.41 . Mikel Leshoure, RB 215 798 2.11% 1.83% -0.27% -118.72 -0.55 . Beanie Wells, RB 88 234 0.86% 0.54% -0.32% -141.22 -1.60 . Michael Turner, RB 222 800 2.18% 1.84% -0.34% -146.57 -0.66 . Trent Richardson, RB 267 950 2.62% 2.18% -0.43% -188.44 -0.71 . Darren McFadden, RB 216 707 2.12% 1.63% -0.49% -213.99 -0.99 . Totals 10200 43491

To our earlier query, Lynch provided ~247 YAA to SEA while Forsett provided ~105 to HOU. It is incredibly unlikely Forsett will maintain a YPCAA nearing Spiller and Peterson but this past year he produced all you could ask of a back up. It's probably unsustainable but Forsett really did produce the 7th most surplus yards of these runners last year.

Additionally, I'm much less impressed With Fosters 1400 yard season. He performed below average and considering the surplus value of both Forsett and Tate, it seems he was overworked.

Lastly, I think these numbers should allow for some optimism regarding Shonne Greenes new role in TEN. He was really bad as a feature back, but his YPCAA indicates he might only be kind of bad (bad vs bad more). The same goes for Greene-Ellis.

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