One of the most difficult tasks in projecting fantasy football statistics is determining which aspects of players’ games are repeatable, and which are a matter of luck. That is, what percentage of Matthew Stafford’s 5,038 passing yards in 2011 were due to skill and other factors that are likely to repeat in 2012? The more luck that was involved with Stafford’s passing totals, the more likely they are to regress this season.
This concept is known as regression toward the mean, and it should be a factor in all your fantasy football projections. Rather than simply arbitrarily guessing projections, there are formulas we can use to make more educated predictions (albeit still “guesses”) regarding players’ stats. To show just how much of an impact regression can have and exactly how to implement it into your projections, I’ll take a look at how to project running backs’ yards-per-carry.
The formula I will use is a basic one, but it can be applied to all rate statistics to effectively factor in regression. Note that regression can also be accounted for within cumulative stat projections, but the formula needed is a more complex one than that shown below. Nonetheless, stats like yards-per-carry, yards-per-reception, drop rate, and so on can all be projected rather easily with this idea.
The most taxing aspect of creating rate-based projections is uncovering the strength of correlation for year-to-year stats, i.e. the average percentage of each individual player’s numbers that transfers over to subsequent seasons.
I did some work and found a strength of correlation of right around 0.41 for running backs’ YPC over the past five seasons. For our purposes, this means that 41% of a running back’s YPC is due to skill, and the other 59% is due to fluky factors, such as opponents, field conditions, and so on. For other rate statistics, the most difficult aspect of the analysis, and the majority of your work, is spent uncovering the strength of correlation between Year X and Year X+1.
After all is said and done, we can accurately predict running backs’ YPC with the following formula:
YPC_x+1 = 0.59*(AvgYPC) + 0.41*(YPC_x)
In layman’s terms, this means multiplying the league average YPC (4.3) by 0.59, then adding it to the player’s YPC from the previous season (which is multiplied by 0.41).
Let’s use Reggie Bush as an example. Bush averaged 5.03 YPC last season. To obtain a baseline projection of Bush’s 2012 YPC, we can first multiply 5.03 by 0.41 (getting 2.06 as a result). When we multiply the league average YPC (4.3) by 0.59, we get 2.54. Adding the two figures together, we see Bush’s initial projected YPC in 2012 is 4.60. That figure is a lot closer to Bush’s 4.29 career YPC mark than his 2011 rate.
To save you some time, I projected the YPC for the top 20 backs (in terms of rushing yards) from 2011. Then, I projected their carries using a myriad of factors, including 2011 carries, scheme alterations, personnel switches, and so on. Without further ado, here are your 2012 rushing leaders (with YPC in parentheses):
1. Maurice Jones-Drew: 300 carries for 1,338 yards (4.46)
2. Adrian Peterson: 300 carries for 1,335 yards (4.45)
3. Ray Rice: 290 carries for 1,316 yards (4.46)
4. Ryan Mathews: 280 carries for 1,274 yards (4.55)
5. Michael Turner: 280 carries for 1,224 yards (4.37)
6. Arian Foster: 275 carries for 1,194 yards (4.34)
7. LeSean McCoy: 260 carries for 1,170 yards (4.50)
8. Chris Johnson: 275 carries for 1,150 yards (4.18)
9. Matt Forte: 250 carries for 1,138 yards (4.55)
10. Fred Jackson: 225 carries for 1,078 yards (4.79)
11. Marshawn Lynch: 250 carries for 1,068 yards (4.27)
12. Shonn Greene: 250 carries for 1,063 yards (4.25)
13. Reggie Bush: 220 carries for 1,012 yards (4.60)
14. Frank Gore: 230 carries for 989 yards (4.30)
15. Steven Jackson: 220 carries for 955 yards (4.34)
16. Willis McGahee: 210 carries for 949 yards (4.52)
17. Beanie Wells: 210 carries for 901 yards (4.29)
18. Cedric Benson: 150 carries for 621 yards (4.14)
19. Ben Tate: 125 carries for 594 yards (4.75)
20. Michael Bush: 100 carries for 411 yards (4.11)
After projecting carries and recalculating YPC, the big winners are Ryan Mathews, Matt Forte, Adrian Peterson, and Fred Jackson. Notice a trend there? None of those players completed a full season in 2011. Now you certainly need to be careful drafting running backs coming off injuries, especially one like Peterson's, but there is definitely some value there to exploit.
The big losers in 2012 figure to be Frank Gore, Marshawn Lynch, Willis McGahee, Steven Jackson, Cedric Benson, and Michael Bush. All of those players figure to see either a decrease in carries, a decline in efficiency, or for most of them, both. They're also all on their last NFL legs.
Note that the YPC figures I generated above are only initial projections. There is more that goes into predicting statistics than this, but we can obtain a foundation from which to work with a basic regression formula. Chances are the rushing totals above will be closer to the 2012 totals than the final 2011 rushing standings, and that's really what we're looking for out of a predictive formula.
When projecting other rate statistics, you can see a lower strength of correlation from year to year will result in greater regression toward the mean. If a statistic hypothetically had zero predictive ability, we would multiply the league average by 1.00, leaving every player with the exact same projection.
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