If you have a prediction as to the number of yards each RB will rush for, you could plug in this formula and get a pretty reliable estimate of 1st Downs:
1st Downs = {RuYds*.043) + 5.2
Example:
Adrian Peterson 2008: {1760 RuYds * .053} + 5.2 = 80.9 (Actual was 81)
Steve Slaton 2008: {1282 * .043} + 5.2 = 60.3 (Actual was 60)
You should be able to predict about 2/3rds of your RBs within 6 (+/-) using this formula (well, assuming you could accurately predict their yardage).
This might work but would completely ignore the short yardage / goal line type RB.This formula seems to want to make a linear fit to the top RBs that produced first downs.
I think the purpose of the OP's question is to how to find RBs that will produce 1sts, and probably at a higher rate than the norm. If I'm in a league like that, that's what I would want to know - who gives me above-average production?
Based on rushing alone, I took that formula and looked at the Top 50 players for rushing first downs in 2008. (Minimum was 24).
Then I flagged ones that were either 10% above or 15% below that "best fit" line.
Player Team Pos Efficiency
T.J. Duckett SEA RB 206%
David Garrard JAC QB 163%
Tim Hightower ARI RB 152%
Pierre Thomas NO RB 134%
Michael Pittman DEN RB 132%
Marion Barber DAL RB 132%
Ryan Fitzpatrick CIN QB 131%
Sammy Morris NE RB 123%
Peyton Hillis DEN RB 120%
Joseph Addai IND RB 119%
Mewelde Moore PIT RB 118%
Steven Jackson STL RB 116%
Le'Ron McClain BAL FB 116%
Maurice Jones-Drew JAC RB 116%
Fred Jackson BUF RB 114%
LenDale White TEN RB 112%
Brandon Jacobs NYG RB 110%
Clinton Portis WAS RB 108%
Brian Westbrook PHI RB 108%
Matt Forte CHI RB 108%
Ronnie Brown MIA RB 108%
Derrick Ward NYG RB 108%
Michael Turner ATL RB 107%
Marshawn Lynch BUF RB 107%
Ricky Williams MIA RB 104%
Kevin Smith DET RB 104%
Larry Johnson KC RB 103%
Thomas Jones NYJ RB 102%
Jonathan Stewart CAR RB 102%
Adrian Peterson MIN RB 100%
Willis McGahee BAL RB 100%
Steve Slaton HOU RB 99%
LaDainian Tomlinson SD RB 98%
Tashard Choice DAL RB 98%
Cedric Benson CIN RB 96%
Dominic Rhodes IND RB 95%
DeAngelo Williams CAR RB 94%
Ryan Grant GB RB 93%
Chris Johnson TEN RB 93%
Maurice Morris SEA RB 90%
Darren McFadden OAK RB 90%
Kevin Faulk NE RB 89%
Frank Gore SF RB 88%
Earnest Graham TB RB 88%
Edgerrin James ARI RB 88%
Jamal Lewis CLE RB 87%
Julius Jones SEA RB 82%
Warrick Dunn TB RB 79%
Justin Fargas OAK RB 76%
Willie Parker PIT RB 74%
Contrastingly, the players at the bottom often got yanked in those short yardage situations or on third downs on a regular basis.