There is some probability that a running back gets hurt when he carries the ball and when he catches the ball. For the sake of argument, let's say that all touches have the same risk of injury and it's 0.1%.
If a back gets 200 carries, we'd expect that he'd have ~ 82% chance of not getting hurt over the year and ~ 18% chance of getting hurt.
If that same back gets 300 carries, we'd expect that he'd have ~ 74% chance of not getting hurt and ~ 26% chance of getting hurt.
This doesn't mean that he's injury prone (i.e. the chance of getting injured per touch didn't change). But, his chances of getting hurt over a season went up because he's in a danger of getting hurt more often. I feel like I looked at this before and Bell's touches has him playing something like 1.5 games more than other highly used backs in the league. So, if every back had the same chance of getting injured every play you'd expect Bell's risk of injury to be almost 10% higher than other highly used backs.
That's a pretty simple analysis that assumes that getting hurt is random and occurs at a constant rate. My guess is that RBs get a little bit hurt every time they carry the ball. I think that's not unreasonable given the violence that can take place with every hit.
I think that those minor aches and pains probably add up over a season and make the chance of injury increase over time. I think that this is why most teams don't give their backs as many touches as they did in the past (kind of like how basketball stars get rested periodically and goalies in hockey don't play in back to back games).
I'm not the only one that thinks this. The NFLPA is very much against adding games to the season because they believe that it increases injury risk.
Because of that, I think he has a higher chance of being injured in a season even if his chance of being injured on a particular play is the same as every other back in the league.
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