by Sam Waters

Last week we looked at expected production for running backs based on pick number in the NFL draft. Using a logistic regression, we found the price NFL teams currently pay in terms of draft picks for a given amount of expected defense-adjusted yards above replacement. Our next task is to compare expected production for each pick to expected salary, in order to find which draft position is most efficient in terms of purchasing as much production as possible with each dollar.

We start by finding the expected salary at each draft pick by regressing the total contract value (contract data from http://www.spotrac.com/) in millions of dollars against pick number. Since there is a break in salaries between the first and second rounds, I divided the data at the thirty-second pick. A logistic regression was the best fit for the first round data, while a cubic regression was the best fit for the second through seventh round data. These two regressions give us an expected rookie contract value at every pick in the draft:

y = -5.374* ln(pick) + 24.711, if pick ≤32

(.3923) (1.15322)

y = 1E-06* (pick)^{3} + 0.0006* (pick)^{2} – 0.0959* (pick) + 7.5197, if pick>32

(7.54e-08) (.0000344) (.0048361) (.204214)

**Robust standard errors in parentheses below equations*

Next, we turn back to Part I from Monday to get the expected DYAR values for each pick in the draft that we obtained through logistic regression. Even though rookie contracts usually only last about four years, we use career DYAR values, as this still works for the sake of comparison among picks. In order to find how much production teams get per dollar at each pick we divide expected salary by expected DYAR at each pick. The graph below shows the relationship between expected DYAR/million dollars and pick number:

The most noticeable feature of the graph above is its peak- teams maximize production per dollar when they select a running back at the beginning of the second round. It should be noted that some of this is due to the change in regressions I used between the first and second rounds, but is is also largely dependent on the salary drop-off between the 32nd and 33rd pick. We see that production per dollar increases as we go deeper into the first round and decreases steadily from the end of the first round to the end of the seventh round. In fact, by the end of the draft, teams should not expect any yards above replacement per dollar spent. This is not surprising, as we found in part one of this study that almost 90% of seventh round picks are at around replacement level. The low DYAR/$ values in the later rounds indicate that teams may overvalue these replacement level players- by the last few picks teams are actually losing yards above replacement per dollar spent. Of course, a replacement level player is not worth $0, as the ability to produce at a baseline level is still worth some small amount of money. It just seems clear that there is more value to be had in paying middle round backs with solid production than getting minimal value by drafting interchangeable assets in the later rounds.

The break in salaries at the end of the first round appears to create a clear buying opportunity at the beginning of the second round. Overall, second and third round picks seem to be the most financially beneficial. After that, the first and fourth rounds provide approximately equal financial benefits. The fifth through seventh rounds provide increasingly less value as we approach the last pick. Since teams are operating under a hard cap and need to maximize the value they get out of each dollar, it would be prudent to look at which picks maximize production per dollar when acquiring running backs.

I am still learning to understand DYAR, but from what I read at Football Outsiders, it seems that it is a function of both a running back’s effectiveness (as a rate) and his workload. So comparing the first running back drafted to the fifth or sixth (presumably a second-rounder) means you’re probably comparing two guys that got equal opportunities. So the evaluation of production / salary seems fair to me in that case.

But it seems to me like perhaps 7th-round running backs are low on this production / salary chart not completely because they are significantly worse, but maybe because they don’t get the same opportunities.

If, hypothetically, all running backs in the draft are equal, then those drafted in the 7th round may have lower DYARs simply because they never get a shot. If there are certain biases toward running backs that are unwarranted (I’m thinking kind of like pudgy baseball players), then maybe they are just as good, and a team could save an early pick by drafting one of these 7th round guys. I realize that hypothesis is not true, but maybe the rift is more of a sidewalk crack, or something in between. Have you tried the regression, by chance, with DVOA? I know there are shortcomings to that statistic, but it wouldn’t weigh the 7th-rounders down so much.

Just a thought. I might just not understand DYAR well enough….

Well as you know we as humans are not great at probability. Most NFL scots go by what they see and not what the player truly possess. If you look at this mathematical formula, it clearly states that some players will not play the way that certain experts predicted. So in the NFL’s game of drafting, some see it as what you see is what you get, but it is clearly not a trustworthy pattern. If we look at a # 1 overall pick what are the chances of that player being a success, well if you look at past#1 overall pick the pattern of production, will obviously not be the same. I believe this clearly states that and this should be a guide that scouts should use. As a 14 year old this is obviously not something I have mastered but wish to succeed in later in life.

Scouts*