How Many Yards Until First Down Again
What is the value of a start downwardly? By that I mean, how many marginal yards is a first downwardly really worth? Here'southward some other fashion to word the question: If three offset downs and 80 yards are worth Ten, so ii first downs and [???] many yards are equal to X?
Computing the marginal value of a thou isn't like shooting fish in a barrel. In fact, information technology'south been bugging me for years, considering I've never quite been certain how to derive them. So, a light bulb went off in my head: I needed to reach out to Brian Burke. I had an idea, but not the data or the ways to execute.
Burke, of grade, runs the fantastic website Avant-garde Football Analytics (formerly Avant-garde NFL Stats). I asked him if he would run some queries, and Brian was kind enough to do then. Fortunately, Brian's non simply a guy with admission to lots of information, but ane of the smartest minds in the industry. I wholeheartedly endorse his methods beneath, and I'm very thankful for his help. On top of running the numbers, he also provided an fantabulous writeup on his work. What follows are Brian's words and assay.
To estimate the value of achieving a 1st down without counting any of the value of the yardage gained, we can use the Expected Points model. The value of the 1st down itself minus yardage value will exist the discontinuity in EPA when a play's proceeds crosses the threshold for a 1st down. That discontinuity represents the value of the conversion apart from whatever yardage gained.
For example, on 2d and 10, the EPA would increase smoothly for each k gained upwards to ix yards gained, and then jump to a much higher EPA crossing the 10-yard mark where the conversion occurs. Afterward that signal, the EPA should increase smoothly over again with each marginal g gained in a higher place what was needed for the conversion.
Here is an analogy. The Y-centrality represents Expected Points Added, the Ten-axis the amount of yards gained on the play.
The EPA for a 9-yd gain is 0.57, and the EPA for a 10-yd proceeds is 1.04. That's a discontinuity of 0.47 EP, meaning that the 1st down itself is nearly equivalent to the ix-yards gained upwardly to the indicate of conversion.
But we besides need to correct for the yardage value of that 10th m. 1 yard of field position is mostly worth 0.064 EP. So in this case the discontinuity itself is worth 0.47 – 0.064 = 0.41 EP.
If we wanted to assign a "bonus" of yards to a player who is credited with achieving the conversion over and above the yardage itself, we could utilize this value's yardage equivalent. 0.41 EP / 0.064 EP/yd = half-dozen.4 yds. That'southward the bonus for 2nd downwardly and 10, but in that location are many other down and distance situations to consider.
For case, on 3rd and x, the discontinuity is one.57 EP, equivalent to nearly 25 yds. Showtime and ten is very strange because the discontinuity is negative. This makes sense, nonetheless, because an offense should prefer a second & 1 to a 1st & 10 anywhere on the field. It would be empty-headed to penalize a player for gaining the extra yard to convert, so my opinion would be to say the EP bonus for a conversion on 1st downwards is null.
Later on examining a smattering of 2nd and 3rd downward situations, the 2nd-down bonus EP is virtually 0.35 and tertiary-downward bonus EP is roughly 1.4.
4th down conversions would manifestly mean a very large bonus EP. They essentially have the value of a turnover–shut to 4 EP or so. Since 4th downs are qualitatively different (and relatively rare) I'grand going to gear up them bated.
In general, 32% of conversions come up on 1st downward, 38% come on 2d down, and 30% come on 3rd downward. So the weighted value of a conversion lone would roughly be:
[0.32 * 0] + [0.38 * 0.35] + [0.xxx * 1.4] = 0.55 EP
The conversion bonus of 0.55 EP can be translated into yards by dividing past 0.064 EP/yd, which ultimately makes the equivalent yardage bonus for a conversion: 8.7 yards.
Figuring out the value of a kickoff downwardly will have many applications for Football Perspective going forward. Please leave your thoughts in the comments, as I'd dearest to hear what you guys take to say. And cheers once more to Brian for his cracking work.
Source: http://www.footballperspective.com/the-value-of-a-first-down/
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