Marcus Allen was a master of scoring a touchdown or getting a first down in short yardage situations. He was not very big, but he got the job done. Also, like the fact that he handed the ball to the ref after he scored. Old-school: “Act like you’ve been there before.” Combine all that with his distain for weird Al and I’d go with him. Priest Holmes and Dontarie Poe were both fun. :-)
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My mother in law. Nobody can stop that bitch once she gets a full head of steam.
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Jamaal Charles is the all-time NFL leader in yards over expected per carry. He was actually 1.28 YPC over expected.

Only 4 backs in NFL history have even exceeded 1 YPC and Charles was a quarter yard better than that.

I mean I know he got stuck in the backfield sometimes...but not very often.

For me it comes down to Charles or Jim Brown. And I might just take Charles. His vision and balance through the hole was second to none.
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Lot of good answers, but I'm going with Marcus Allen
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Jamaal Charles on 12 career carries of 4th and 1-3 (unfortunately I can't find a simple 4th and 1 split) -- he converted 9 of them for 1st downs.

For perspective, Adrian Peterson was 17 of 28. Charles clearly better.

Emmitt Smith was 19/27 over the games when the stats were kept (post 1994) so Charles beats him as well despite Emmitt running behind the best line of all time.

I don't think we consider Charles short-yardage ability because he was so often breaking long ones, but the guy was a force even in short yardage situations.
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Ironhead Hayward
or
Bo Jackson (especially if we are talking Tecmo Bowl)
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He’s gotta be the most efficient back of all time, by any measure.

He was always moving forward, no wasted movement. It was like art.
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I mean just look at it this way -- if he averaged greater than 1.25 yards more than expected, then all your OL has to do is not lose BADLY.

Block the thing up for zero yards and Charles will probably bail you out and get that 1.25 for ya.
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Most efficient short yardage back was Marcus Allen
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It's awfully hard to argue otherwise.

3rd and 1-3: 58 first downs on 69 attempts over the course of his KC career (when he was no longer in his prime)

4th and 1-3: 14/18 converted.

So just simple combined probability, if he's about 84% likely to pick up the 1st down on 3rd and 1-3 yards, then about 77% likely to pick it up on 4th down, that means facing a 3rd down and 3, you'd fail to pick up a 1st down by giving it to him on both 3rd and 4th downs twice over 100 such scenarios.

A 98% success rate if you can pick up 7 yards on 1st and 2nd down? That's not half bad right there.
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Brandon Jacobs?
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