I’ve been working on a model to evaluate Running Backs and thought that I’m at the point where I’d share it and see what others thought of it. It’s a work in progress and it currently gives general conclusions, although I’m trying to make the conclusions a bit more specific.
Warning that there is some math involved, but I’ll try to skip the technical parts as much as possible.
Quick Background: Most of us (hopefully all of us really) know that when a running back’s YPC is stated as say 4.4 it means that on average he’ll gain 4.4 every carry he gets. However, he doesn’t get 4.4 yards every time, but rather it varies sometimes getting 1 other times getting 7. In fact, generally his YPC is obtained through several short runs of 5 yards or less and then 1 longer run of 5 yards are more (on average it’s about 3 short runs to 1 long run).
In general, the distribution of yards gained on each carry follows a normal distribution, however using a single mean and variance doesn’t accurately reflect the running back’s ability to break off long runs. Basically, a back is more likely to gain 10 yards after he’s already gained 5 on the play, than he is to gain 10 yards before he’s gained any. Long story short, I’ve come up with and tested to my satisfaction a distribution that more accurately reflects the true distribution of yards gained on a carry. I’m not going to include that documentation here although if any one is interested and I have time I’ll be more than happy to post that analysis.
Anyway, the model used is called a Regime-Switching Normal Model, and basically it uses one average and variance for “Short” runs (those less than 5 yards) and another average and variance for “Long” runs (those greater than 5 yards).
OK, back to my analysis. I selected 64 running backs and determined 5 data points: 1) % of carries that went for less than 5 yards, 2) Average Rush on rushes less than 5 yards, 3) Standard Deviation on rushes less than 5 yards, 4) Average Rush on rushes greater than 5 yards, and 5) Standard Deviation on rushes greater than 5 yards.
I randomly created 50 “seasons” of rushes and kept it the same for all years and all running backs to create consistency. (I can explain this in greater detail if anyone wants me to). I did this for years 2004 through 2007 (although some running backs get left off in early years because they weren’t in the league yet).
The model projects (based on the previous years averages and standard deviations) the average rushing yards that should be expected in the current year assuming that the averages and standard deviations are accurate. Comparing these two numbers will give us an indication of whether the running back underperformed or over-performed. This can best be though of as examining a series of coin tosses. After say 400 coin tosses if there were only 190 Heads occurring you can say that Heads underperformed expectations.
A couple things to note as I move on, 1) Running backs were not included until their 2nd season in the NFL (I needed a year of input to project), 2) Projections were based on the given number of carries the player actually had in that year.
I ran the model using 2004 stats to project 2005 totals and then compared.
Here are the results, those with negative Differences indicates that they “Over-performed”, positive Differences indicated “Underperformed”.
Name 2007 Perf. 2008 Proj 2008 Proj (Adj for Performance) DiffChester Taylor -284 693 541 151Jamal Lewis -220 1179 1148 31LenDale White -126 889 868 21Edgerrin James -111 976 956 20Chris Brown -111 610 590 20Laurence Maroney -101 1026 1007 19Willis McGahee -95 1013 994 18DeAngelo Williams -91 808 790 18Jerome Harrison -89 232 214 18Maurice Morris -84 552 535 17Brandon Jacobs -82 1149 1132 17Ronnie Brown -67 760 745 15Correll Buckhalter -61 213 198 15Fred Taylor -61 975 960 15LaMont Jordan -59 192 177 15Leon Washington -50 435 421 14Michael Robinson -34 124 112 12Kevin Jones -33 289 277 12Sammy Morris -28 340 329 11Michael Pittman -15 230 220 10Marion Barber III -6 1084 1075 9Cadillac Williams -4 85 77 9Reggie Bush -3 576 567 9Michael Bennett 0 236 227 9Dominic Rhodes 5 283 275 8Steven Jackson 10 1155 1147 8Ahman Green 13 127 120 7Clinton Portis 21 1172 1166 6Deuce McAllister 23 345 339 6Tatum Bell 39 332 327 5Willie Parker 40 1015 1011 4Reuben Droughns 40 94 90 4Kenny Watson 58 228 225 3DeShaun Foster 70 158 157 1Jerious Norwood 77 623 622 1Julius Jones 78 529 528 1Michael Turner 94 939 940 -1Adrian Peterson(1) 98 211 212 -1Larry Johnson 98 1002 1003 -1Ladell Betts 102 295 297 -2Joseph Addai 111 1099 1102 -3Brian Westbrook 125 1145 1149 -4Warrick Dunn 147 276 283 -6Rudi Johnson 157 539 546 -7Maurice Jones-Drew 176 758 767 -9LaDainian Tomlinson 215 1353 1367 -13Thomas Jones 224 881 895 -14Frank Gore 292 1045 1067 -21FINAL THOUGHTS:This wasn’t really meant to be a predictive model but more of an attempt to remove “hidden” factors from the game that you can’t see in the box score, or what one might not even see if he were watching the game.
I believe throughout the course of a season RB’s (like anyone else) get lucky or unlucky or whatever you want to call it. They play in bad weather, their offensive line men get hurt, they slip, or the defender slips enabling the RB to break off a huge run. They receive good blocks, they received bad blocks, missed assignments on both sides of the ball. And so on.
The purpose of this model was to try and remove this and place each running back in a vacuum where they all receive the same exact scenarios, the same blocking, the same footing, the same defenses, and the only thing that differs is talent.
I truly believe that many fantasy footballers rely too much on memory and have a mentality of what have you done for me lately without considering contingencies that can affect the variation on a season. A defender that slips on a 3rd and 5 can add 60-plus yards to RB’s total that they would have never gotten if it weren’t for that fortunate break (an extreme example I know, but you get my point).
At the very least I hope that this list will help us determine future values and those to approach with a sense of caution. The model states that LT, Westbrook, LJ, MJD, Thomas Jones and Frank Gore all “underperformed” last year in relation to what “should” have happened and it’ll be interesting to see if they surpass expectations this year. (I’ve compared some of the projected numbers to Dodd’s and they all seem to be in the same ball park which I would expect since I used his projected number of carries.)
And it’ll be interesting to see if Lewis, James, Maroney, White among other become “underperformers” after overperforming last year.
I hope you enjoyed this, feel free to poke holes in the logic, or thoughts, comments and suggestions.
Warning that there is some math involved, but I’ll try to skip the technical parts as much as possible.
Quick Background: Most of us (hopefully all of us really) know that when a running back’s YPC is stated as say 4.4 it means that on average he’ll gain 4.4 every carry he gets. However, he doesn’t get 4.4 yards every time, but rather it varies sometimes getting 1 other times getting 7. In fact, generally his YPC is obtained through several short runs of 5 yards or less and then 1 longer run of 5 yards are more (on average it’s about 3 short runs to 1 long run).
In general, the distribution of yards gained on each carry follows a normal distribution, however using a single mean and variance doesn’t accurately reflect the running back’s ability to break off long runs. Basically, a back is more likely to gain 10 yards after he’s already gained 5 on the play, than he is to gain 10 yards before he’s gained any. Long story short, I’ve come up with and tested to my satisfaction a distribution that more accurately reflects the true distribution of yards gained on a carry. I’m not going to include that documentation here although if any one is interested and I have time I’ll be more than happy to post that analysis.
Anyway, the model used is called a Regime-Switching Normal Model, and basically it uses one average and variance for “Short” runs (those less than 5 yards) and another average and variance for “Long” runs (those greater than 5 yards).
OK, back to my analysis. I selected 64 running backs and determined 5 data points: 1) % of carries that went for less than 5 yards, 2) Average Rush on rushes less than 5 yards, 3) Standard Deviation on rushes less than 5 yards, 4) Average Rush on rushes greater than 5 yards, and 5) Standard Deviation on rushes greater than 5 yards.
I randomly created 50 “seasons” of rushes and kept it the same for all years and all running backs to create consistency. (I can explain this in greater detail if anyone wants me to). I did this for years 2004 through 2007 (although some running backs get left off in early years because they weren’t in the league yet).
The model projects (based on the previous years averages and standard deviations) the average rushing yards that should be expected in the current year assuming that the averages and standard deviations are accurate. Comparing these two numbers will give us an indication of whether the running back underperformed or over-performed. This can best be though of as examining a series of coin tosses. After say 400 coin tosses if there were only 190 Heads occurring you can say that Heads underperformed expectations.
A couple things to note as I move on, 1) Running backs were not included until their 2nd season in the NFL (I needed a year of input to project), 2) Projections were based on the given number of carries the player actually had in that year.
I ran the model using 2004 stats to project 2005 totals and then compared.
Here are the results, those with negative Differences indicates that they “Over-performed”, positive Differences indicated “Underperformed”.
Name 2007 Perf. 2008 Proj 2008 Proj (Adj for Performance) DiffChester Taylor -284 693 541 151Jamal Lewis -220 1179 1148 31LenDale White -126 889 868 21Edgerrin James -111 976 956 20Chris Brown -111 610 590 20Laurence Maroney -101 1026 1007 19Willis McGahee -95 1013 994 18DeAngelo Williams -91 808 790 18Jerome Harrison -89 232 214 18Maurice Morris -84 552 535 17Brandon Jacobs -82 1149 1132 17Ronnie Brown -67 760 745 15Correll Buckhalter -61 213 198 15Fred Taylor -61 975 960 15LaMont Jordan -59 192 177 15Leon Washington -50 435 421 14Michael Robinson -34 124 112 12Kevin Jones -33 289 277 12Sammy Morris -28 340 329 11Michael Pittman -15 230 220 10Marion Barber III -6 1084 1075 9Cadillac Williams -4 85 77 9Reggie Bush -3 576 567 9Michael Bennett 0 236 227 9Dominic Rhodes 5 283 275 8Steven Jackson 10 1155 1147 8Ahman Green 13 127 120 7Clinton Portis 21 1172 1166 6Deuce McAllister 23 345 339 6Tatum Bell 39 332 327 5Willie Parker 40 1015 1011 4Reuben Droughns 40 94 90 4Kenny Watson 58 228 225 3DeShaun Foster 70 158 157 1Jerious Norwood 77 623 622 1Julius Jones 78 529 528 1Michael Turner 94 939 940 -1Adrian Peterson(1) 98 211 212 -1Larry Johnson 98 1002 1003 -1Ladell Betts 102 295 297 -2Joseph Addai 111 1099 1102 -3Brian Westbrook 125 1145 1149 -4Warrick Dunn 147 276 283 -6Rudi Johnson 157 539 546 -7Maurice Jones-Drew 176 758 767 -9LaDainian Tomlinson 215 1353 1367 -13Thomas Jones 224 881 895 -14Frank Gore 292 1045 1067 -21FINAL THOUGHTS:This wasn’t really meant to be a predictive model but more of an attempt to remove “hidden” factors from the game that you can’t see in the box score, or what one might not even see if he were watching the game.
I believe throughout the course of a season RB’s (like anyone else) get lucky or unlucky or whatever you want to call it. They play in bad weather, their offensive line men get hurt, they slip, or the defender slips enabling the RB to break off a huge run. They receive good blocks, they received bad blocks, missed assignments on both sides of the ball. And so on.
The purpose of this model was to try and remove this and place each running back in a vacuum where they all receive the same exact scenarios, the same blocking, the same footing, the same defenses, and the only thing that differs is talent.
I truly believe that many fantasy footballers rely too much on memory and have a mentality of what have you done for me lately without considering contingencies that can affect the variation on a season. A defender that slips on a 3rd and 5 can add 60-plus yards to RB’s total that they would have never gotten if it weren’t for that fortunate break (an extreme example I know, but you get my point).
At the very least I hope that this list will help us determine future values and those to approach with a sense of caution. The model states that LT, Westbrook, LJ, MJD, Thomas Jones and Frank Gore all “underperformed” last year in relation to what “should” have happened and it’ll be interesting to see if they surpass expectations this year. (I’ve compared some of the projected numbers to Dodd’s and they all seem to be in the same ball park which I would expect since I used his projected number of carries.)
And it’ll be interesting to see if Lewis, James, Maroney, White among other become “underperformers” after overperforming last year.
I hope you enjoyed this, feel free to poke holes in the logic, or thoughts, comments and suggestions.
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for all the work you did
