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The Time Value of Draft Picks

by Chase Stuart on March 25, 2013

in Draft, Statgeekery, Theory

How do you compare the value of a draft pick this year compared to a draft pick next year? NFL teams have often used a “one round a year” formula, meaning a team would trade a 2nd, 3rd, or 4th round pick this year for a 1st, 2nd, or 3rd rounder next year. But to my knowledge, such analysis hasn’t evolved into anything more sophisticated than that.

So I decided to come up with a way to measure the time value of draft picks. First, I calculated how much Approximate Value each draft pick provided from 1970 to 2007 during their rookie season. Then, to calculate each player’s marginal AV, I only awarded each player credit for his AV over two points in each year. As it turns out, the player selected first will provide, on average, about 4 points of marginal AV during his rookie year. During his second season, his marginal value shoots up to about 5.5 points of AV, and he provides close to 6 points of marginal AV during his third and fourth seasons. In year five, the decline phase begins, and the first pick provides about 4.7 points of AV. You can read some more fine print here.1

Here’s another way to think of it. The 1st pick provides 4.0 points of marginal AV as a rookie, the same amount the 15th pick provides during his second year, the 17th pick produces during his third year, the 16th pick during his fourth year, and the 8th pick during his fifth year. So the 15th pick this year should provide, on average, about the same value next year as the 1st pick in the 2014 draft (of course, that player might have something to say about that, too).

The graph below shows the marginal AV (on the Y-axis) provided by each draft selection (on the X-axis) in each of their first five years. The graphs get increasingly lighter in color, from black (as rookies) to purple, red, pink, and gray (in year five):

pvc for first five years

Let’s say a team wanted to trade the 65th pick in the 2013 draft for a 2nd rounder in 2014. Assume that the 2nd rounder is the 48th pick in the 2014 draft. How much value would those draft picks provide over the next five years?

Year
#65
#48
Diff
10.800.8
21.61.10.5
31.82.1-0.3
41.72.3-0.6
51.32.1-0.8

The first pick in the third round provides value in Year N and is still the more valuable pick in Year N+1, when the future, higher round pick will only be a rookie. By Year N+2 the higher pick provides more value, but even after four years, the team trading the (future) higher pick will have received more value. Of course, in Year 5 the higher pick is more valuable, and they would also be more valuable in a hypothetical year six. But it does take awhile for the higher pick to pay off, and it might be as many as five years for the total value to flip.

This is separate from another important consideration: the time value of production. If I told you that you could win the Super Bowl this year or the Super Bowl in 2024, you wouldn’t view those two options as providing equal value. While the difference between a Super Bowl championship in February 2014 may not be much more valuable than one in February 2015, there is still *some* value in winning the Super Bowl earlier. From the perspective of a hypothetical regime in power — i.e., a GM and head coach who may be on the hot seat — this effect obviously becomes magnified.

The time value of production will be different for each team, as different organizations will have different discount rates. The Denver Broncos with Peyton Manning will have a relatively high discount rate, while a rebuilding team will have a low one. But we can measure the value each draft pick will provide over each of his first five years. That’s what the next table shows:

Pk
1
2
3
4
5
145.55.95.94.7
23.95.45.75.74.6
33.85.35.65.64.5
43.75.25.55.44.4
53.65.15.35.34.3
63.44.95.25.24.2
73.34.85.154.1
83.24.74.94.94
93.24.64.84.83.9
103.14.54.74.73.8
1134.44.64.63.7
122.94.34.54.43.6
132.84.24.44.33.5
142.74.14.34.23.4
152.644.24.13.3
162.63.94.143.3
172.53.943.93.2
182.43.83.93.83.1
192.43.73.83.83
202.33.63.83.73
212.23.53.73.62.9
222.23.53.63.52.8
232.13.43.53.42.8
242.13.33.53.32.7
2523.23.43.32.7
261.93.23.33.22.6
271.93.13.23.12.5
281.83.13.23.12.5
291.833.132.4
301.72.93.12.92.4
311.72.932.92.3
321.72.832.82.3
331.62.82.92.82.2
341.62.72.82.72.2
351.52.72.82.72.1
361.52.62.72.62.1
371.52.62.72.62.1
381.42.52.72.52
391.42.52.62.52
401.42.42.62.41.9
411.32.42.52.41.9
421.32.32.52.41.9
431.32.32.42.31.8
441.22.32.42.31.8
451.22.22.42.21.8
461.22.22.32.21.7
471.22.12.32.21.7
481.12.12.32.11.7
491.12.12.22.11.7
501.122.22.11.6
511.122.221.6
52122.121.6
5311.92.121.5
5411.92.121.5
5511.92.11.91.5
5611.821.91.5
570.91.821.91.5
580.91.821.91.4
590.91.821.81.4
600.91.71.91.81.4
610.91.71.91.81.4
620.91.71.91.81.4
630.91.71.91.71.3
640.81.61.81.71.3
650.81.61.81.71.3
660.81.61.81.71.3
670.81.61.81.71.3
680.81.51.81.61.2
690.81.51.71.61.2
700.81.51.71.61.2
710.71.51.71.61.2
720.71.51.71.61.2
730.71.41.71.61.2
740.71.41.61.51.2
750.71.41.61.51.1
760.71.41.61.51.1
770.71.41.61.51.1
780.71.31.61.51.1
790.71.31.61.51.1
800.71.31.51.41.1
810.71.31.51.41.1
820.61.31.51.41.1
830.61.31.51.41
840.61.21.51.41
850.61.21.51.41
860.61.21.41.41
870.61.21.41.31
880.61.21.41.31
890.61.21.41.31
900.61.21.41.31
910.61.11.41.31
920.61.11.31.30.9
930.61.11.31.30.9
940.61.11.31.30.9
950.51.11.31.20.9
960.51.11.31.20.9
970.51.11.31.20.9
980.511.31.20.9
990.511.21.20.9
1000.511.21.20.9
1010.511.21.20.9
1020.511.21.10.9
1030.511.21.10.8
1040.511.21.10.8
1050.511.21.10.8
1060.50.91.11.10.8
1070.50.91.11.10.8
1080.50.91.11.10.8
1090.40.91.11.10.8
1100.40.91.110.8
1110.40.91.110.8
1120.40.91.110.8
1130.40.9110.8
1140.40.9110.7
1150.40.8110.7
1160.40.8110.7
1170.40.8110.7
1180.40.810.90.7
1190.40.810.90.7
1200.40.80.90.90.7
1210.40.80.90.90.7
1220.40.80.90.90.7
1230.40.80.90.90.7
1240.40.80.90.90.7
1250.30.70.90.90.7
1260.30.70.90.90.7
1270.30.70.90.90.7
1280.30.70.90.80.7
1290.30.70.90.80.6
1300.30.70.80.80.6
1310.30.70.80.80.6
1320.30.70.80.80.6
1330.30.70.80.80.6
1340.30.70.80.80.6
1350.30.70.80.80.6
1360.30.70.80.80.6
1370.30.70.80.80.6
1380.30.70.80.80.6
1390.30.70.80.80.6
1400.30.70.80.80.6
1410.30.70.80.80.6
1420.30.70.80.80.6
1430.30.70.80.80.6
1440.30.70.80.80.6
1450.30.70.80.70.6
1460.30.60.80.70.6
1470.30.60.80.70.6
1480.30.60.70.70.6
1490.30.60.70.70.6
1500.30.60.70.70.6
1510.30.60.70.70.6
1520.30.60.70.70.6
1530.30.60.70.70.6
1540.30.60.70.70.6
1550.30.60.70.70.6
1560.30.60.70.70.6
1570.30.60.70.70.5
1580.30.60.70.70.5
1590.30.60.70.70.5
1600.30.60.70.70.5
1610.30.60.70.70.5
1620.30.60.70.70.5
1630.30.60.70.60.5
1640.30.60.70.60.5
1650.30.60.70.60.5
1660.30.60.60.60.5
1670.30.60.60.60.5
1680.30.50.60.60.5
1690.30.50.60.60.5
1700.30.50.60.60.5
1710.30.50.60.60.5
1720.30.50.60.60.5
1730.30.50.60.60.5
1740.30.50.60.60.5
1750.30.50.60.60.5
1760.30.50.60.60.5
1770.20.50.60.60.5
1780.20.50.60.60.5
1790.20.50.60.60.5
1800.20.50.60.50.5
1810.20.50.60.50.5
1820.20.50.60.50.5
1830.20.50.50.50.5
1840.20.50.50.50.5
1850.20.50.50.50.5
1860.20.50.50.50.4
1870.20.50.50.50.4
1880.20.50.50.50.4
1890.20.50.50.50.4
1900.20.40.50.50.4
1910.20.40.50.50.4
1920.20.40.50.50.4
1930.20.40.50.50.4
1940.20.40.50.50.4
1950.20.40.50.50.4
1960.20.40.50.50.4
1970.20.40.50.50.4
1980.20.40.50.40.4
1990.20.40.50.40.4
2000.20.40.50.40.4
2010.20.40.40.40.4
2020.20.40.40.40.4
2030.20.40.40.40.4
2040.20.40.40.40.4
2050.20.40.40.40.4
2060.20.40.40.40.4
2070.20.40.40.40.4
2080.20.40.40.40.4
2090.20.40.40.40.4
2100.20.40.40.40.4
2110.20.30.40.40.4
2120.20.30.40.40.4
2130.20.30.40.40.4
2140.20.30.40.40.3
2150.20.30.40.30.3
2160.20.30.40.30.3
2170.20.30.40.30.3
2180.20.30.40.30.3
2190.20.30.30.30.3
2200.20.30.30.30.3
2210.20.30.30.30.3
2220.20.30.30.30.3
2230.20.30.30.30.3
2240.20.30.30.30.3

We can use this to take a look at how the Jets might fare under a trade with Tampa Bay for Darrelle Revis. The rumor is that the Jets want Tampa Bay’s 2013 first and second round picks, while the Bucs want to trade their 2014 first and second round picks.

Tampa Bay holds the 13th and 43rd picks in the 2013 draft. My guess is the 2013 Bucs with Revis finish around 10-6 or better. They had 7.9 Pythagorean wins last year, and by adding Darrelle Revis and Dashon Goldson, Tampa would be shoring up the weakest link on the team. Add in the fact that Josh Freeman is still on the left side of his age curve and in general, Tampa Bay was the third youngest team in the NFL last year, and the Bucs are a likely playoff team with Revis in 2013.

That would leave the Jets with roughly the 23rd and 56th picks in the 2014 draft. So while the media may say the sides are close, there’s actually a large chasm between the sides. Take a look:

Year
13/43 in 2013
23/56 in 2014
Diff
20134.104.1
20146.53.13.4
20156.85.21.6
20166.65.61.1
20175.45.30

With a new GM in John Idzik, perhaps discount rate due to the time value of production isn’t significant. But there is still a pretty significant difference between Tampa Bay’s first two picks this year and next year, if you think the Buccaneers will be one of the league’s better teams next year. Some have argued that this effect could be muted with a potentially better 2014 draft class, but the teams still have a lot of ground to close. And to the extent that it’s just the top of the draft class that’s better next year, a late first round pick doesn’t get that extra bump.

  1. The charts in this post are “smoothed” charts using polynomial trend lines of the actual data. I have only given draft picks credit for the AV they produced for the teams that drafted them – that’s why the values are flatter (i.e., top picks are less valuable) than they were in this post. Finally, astute readers will note that the draft looks linear in the second half; that’s because if I kept a polynomial trend line all the way through pick 224, some later picks would have more value than some early picks []

{ 4 comments… read them below or add one }

matt March 25, 2013 at 11:33 am

How about labeling the x and y axis on your chart? Really tough to tell what it is displaying out labeling the axis. Im guessing the y axis is the marginal av and the x axis is pick number but readers shouldnt have to guess.

Reply

Chase Stuart March 25, 2013 at 11:34 am

Your intuition is correct. Labeling the axes is a good idea.

Reply

Brian March 25, 2013 at 7:55 pm

So what is the discount rate in percentage terms (for all teams, rebuilding teams, win-now teams)?

Thaler and Massey did this pre-the new rookie wage scale. They didn’t use AV but rather less sophisticated metrics like games started, Pro Bowls, etc. if I recall and got a discount rate of 174%, which is a staggering number.

Reply

Lucinda December 27, 2013 at 6:48 pm

Hi there! This post couldn’t be written much better!
Looking at this post reminds me of my previous roommate! He constantly kept preaching about this.
I’ll forward this information to him. Pretty sure he will have a good read.
I appreciate you for sharing!

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