I did an analysis of QB's RushYards/Game vs. % of Games Missed, and came up with some interesting conclusions.
Rushing QBs those with >25 RushYards/Game historically missed 17.7% of their games, playing 461 out of a possible 560 games.
Vick
Culpepper
McNabb
Cunningham
McNair
Young
Scrambling QBs those with 10-25 RushYards/Game historically missed 6.5% of their games, playing 688 out of a possible 736 games.
Stewart
Garcia
Brunell
Brooks
Gannon
Plummer
Elway
Pocket QBs those with >10 RushYards/Game historically missed 6.6% of their games, playing 1366 out of a possible 1463 games.
Green
Montana
Favre
Moon
Leftwich
Hasselbeck
Aikman
Manning
Johnson
Brady
Bledsoe
Warner
Pennington
Bulger
Marino
I ran a regression of the data, they were positively corelated with a t-stat of 3.67 (for you statistic buffs). The sample included 27 QBs, and included 2759 possible games. I made adjustments for the games during seasons where the QBs in question were not official starters.
So, based on an admittedly small sample, you could draw the conclusion that rushing QBs are more likely to be injured than pocket passers or scramblers.

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