If you asked this question to a mathematician who knew nothing about football (but had access to data), this is what he might tell you:
Over the last six years in the NFL, running back rush attempts have a mean of 4.16 and a standard deviation of 6.11. While the distribution of outcomes on a single carry is nowhere near a normal (bell-shaped) distribution,
the central limit theorem guarantees that if you have a large number of carries (I'm sure 100 is more than enough), the
average will very closely approximate a normal distribution with standard deviation 6.11/sqrt(number_of_carries).
So, if you take a totally average back and give him 100 carries in randomly-selected situations, his YPC average will be normally distributed with mean 4.16 and standard deviation 6.11/sqrt(100)=.61. I.e. if you perform this give-an-average-back-100-carries experiment a whole bunch of times, he will have a YPC between 3.55 and 4.77 about two-thirds of the time. He will have a YPC between 2.94 and 5.38 about 95% of the time.
This means, of course, that an average back with 100 random carries will, about 5% of the time, have a YPC lower than 2.94 or higher than 5.38 by sheer dumb luck.
Here's a chart that shows the percentage of the time a totally average back would be outside a given YPC range on a given number of carries:
Code:
outside this range outside this rangeCarries 1/3 of the time 5% of the time----------------------------------------------------- 100 3.55 -- 4.77 2.94 -- 5.38 150 3.66 -- 4.66 3.16 -- 5.16 200 3.73 -- 4.59 3.30 -- 5.02 250 3.77 -- 4.55 3.39 -- 4.93 300 3.81 -- 4.51 3.45 -- 4.87 350 3.83 -- 4.49 3.51 -- 4.81 400 3.85 -- 4.47 3.55 -- 4.77 450 3.87 -- 4.45 3.58 -- 4.74 500 3.89 -- 4.43 3.61 -- 4.71 550 3.90 -- 4.42 3.64 -- 4.68 600 3.91 -- 4.41 3.66 -- 4.66 650 3.92 -- 4.40 3.68 -- 4.64 700 3.93 -- 4.39 3.70 -- 4.62 750 3.94 -- 4.38 3.71 -- 4.61 800 3.94 -- 4.38 3.73 -- 4.59 850 3.95 -- 4.37 3.74 -- 4.58 900 3.96 -- 4.36 3.75 -- 4.57 950 3.96 -- 4.36 3.76 -- 4.561000 3.97 -- 4.35 3.77 -- 4.551050 3.97 -- 4.35 3.78 -- 4.541100 3.98 -- 4.34 3.79 -- 4.531150 3.98 -- 4.34 3.80 -- 4.521200 3.98 -- 4.34 3.81 -- 4.511250 3.99 -- 4.33 3.81 -- 4.511300 3.99 -- 4.33 3.82 -- 4.501350 3.99 -- 4.33 3.83 -- 4.491400 4.00 -- 4.32 3.83 -- 4.491450 4.00 -- 4.32 3.84 -- 4.481500 4.00 -- 4.32 3.84 -- 4.481550 4.00 -- 4.32 3.85 -- 4.471600 4.01 -- 4.31 3.85 -- 4.471650 4.01 -- 4.31 3.86 -- 4.461700 4.01 -- 4.31 3.86 -- 4.461750 4.01 -- 4.31 3.87 -- 4.451800 4.02 -- 4.30 3.87 -- 4.451850 4.02 -- 4.30 3.88 -- 4.441900 4.02 -- 4.30 3.88 -- 4.441950 4.02 -- 4.30 3.88 -- 4.442000 4.02 -- 4.30 3.89 -- 4.43
And this is if your average RB is getting the ball in a random array of situations. If you bias the situations toward short-yardage, or toward garbage time, or whatever, that's going to make the problem worse, not better.