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
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.