I’m short on time today, which means a lot of data and not so much theory. One of the more underrated statistics to measure running backs is the number of first downs they produce. I don’t like using Yards per Carry for running backs because that metric is pretty sensitive to outliers. But by using rushing first downs, perhaps we can smooth things out.
We know that the value of a touchdown is about 20 yards, but what is the value of a rushing first down? Being short on time, I took the easy way out. Pro-Football-Reference has produced Expected Points Added for each team’s running game going back to 2000. I decided to run a regression on the team level to best predict rushing EPA based on four rushing statistics. The R^2 was 0.77, but more importantly, here was the best fit formula:
EPA = -16.6 -0.58*Rush + 0.067*Rush_Yd + 1.43*Rush_TD + 1.08*Rush_FD
What interests me is the relationships between the variables. Rushing touchdowns are considered 21.3 times as valuable as rushing yards, which happens to fit in well with our previous assumptions. But more importantly, this tells us that a rushing first down is worth 16.1 rushing yards. That seems pretty high to me, and I reserve the right to adjust this later, but for now, let’s adjust down and say the value of a rushing first down is 15 yards. Now what?
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