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3030
A good number played when running was the name of the game. Makes some of their numbers, like Youngbloods, even more impressive.

They did not start keeping official sack stats until 1982.

There have been people though who have gone over the film and can list unofficial sack stats from before 1982.

Youngblood had a lot more than 24 sacks. That's just the ones they counted from 1982 on.

Here are the unofficial totals for Rams that includes sacks from before 1982. Not every player on this list was a Ram his whole career, so factor that in:

Deacon Jones 173.5
Jack Youngblood 151.5
Coy Bacon 130
Fred Dryer 103
Larry Brooks 68.5