I’ve looked at the NFL Draft a lot since starting this
blog. As the draft was here in Chicago this year, I found myself running into a
number of jerseys on the street when I went out for lunch on Thursday and
Friday. Even more surprising than the fact that people had travelled – in some
cases from pretty far away according to the jerseys – was the fact that a lot
of them were wearing jerseys of players who were disappointments if not outright busts. It
got me thinking about sunk costs and whether teams are any better than their
fans about cutting their losses.
To try to get at this we’ll need to know how much teams
value their draft picks – conveniently we do know this via the Jimmy
Johnsonpopularized draft value chart – and then compare this to how much those
players are used. Usage is a bit tricky but I’m going to approximate it with
games started (1 full game) plus games played (2014 avg snaps nonstarter /
2014 avg snaps starter, by position).
Before even getting to questions of usage, there is a
significant disparity in the proportion of players from each round who end up
making a roster.
Round

%
on Roster Year 1

1

97%

2

94%

3

83%

4

81%

5

70%

6

62%

7

52%

I am guessing that most of this comes down to talent
disparity, but there is certainly some aspect of sunk cost at work here. Lots
of later round picks – to say nothing of undrafted players – never make it onto
a roster to get into the rest of this analysis. They are, however, not the
topic of this analysis. I want to see if a player’s draft value still impacts
playing time even after making a roster.
The first cut of this is simply to look at draft weight
and usage, checking how much the former impacts the latter. The regressions for
each of a player’s first 6 seasons are below:
Usage vs Draft Weight





Draft Weight


Year

R^2

Intercept

Coefficient

PValue

1

0.22

4.53

15.87

0.00

2

0.16

6.88

13.87

0.00

3

0.10

8.10

10.71

0.00

4

0.08

8.84

9.18

0.00

5

0.05

9.49

6.58

0.00

6

0.04

9.88

6.14

0.00

The draft weight is a significant variable throughout the
first 6 years of a player’s career, but the strength of that relationship
declines over time. The 1^{st} year model explains 22% of the variation
in usage while the 6^{th} year model explains just 4%.
Of course, this is highly stylized. While coaches will
always have more information than is reflected in statistics, there is some
additional quantitative data that can be added to the model. For the next round
we’ll add past performance, represented in terms of the square root of a player’s
AV over the past 3 seasons. The 3 is a bit arbitrary, but bear with me. The
square root allows us to make sure additional performance has diminishing
returns in predicting usage in year N. If, for example, a player is an allpro
for years N3 to N1, he can still only play 16 games in year N. On the other
hand, if a player has been injured for a year or two, a solid year will still
have a significant impact on predicted usage.
Usage vs Draft Weight
+ SQRT Prior 3 Years AV





Draft Weight

SQRT
 Prior 3 Yrs AV


Year

R^2

Intercept

Coefficient

PValue

Coefficient

PValue

1

0.22

4.53

15.87

0.00

N/A

N/A

2

0.29

4.89

7.28

0.00

2.29

0.00

3

0.29

4.11

2.46

0.00

2.26

0.00

4

0.26

3.77

0.97

0.13

2.00

0.00

5

0.26

3.40

0.78

0.24

2.02

0.00

6

0.25

3.45

0.24

0.74

1.93

0.00

Lots of stuff to unpack here. First, the Rsquared stays
roughly the same throughout the 6 seasons. The draft weight, however, drops
rapidly with the coefficient moving toward 0 and the pvalue coming up past the
0.10 threshold in years 46. The square root of the prior 3 years AV stays
pretty consistent around 2 for the coefficient and the pvalue is pegged at 0
throughout, indicating sustained significance.
It certainly isn’t controversial that recent past
performance has a strong effect, but it is a bit surprising to see draft weight
have an impact well into a player’s career. With one last set of regressions we’ll
try to get a bit of insight into a player’s future skill level by looking at
actual future performance. The methodology is the mirror image of our variable
for past performance as we’ll consider the square root of AV in the next 3 seasons
(e.g., years 24 for a rookie). This should serve as our proxy for how a coach
with perfect foresight will evaluate a player. If they can make a significant
impact in one of the next three years, or a moderate impact in all three, we
would expect to see that reflected in present year usage regardless of track
record.
Usage vs Draft Weight
+ SQRT Prior 3 Years AV + SQRT Next 3 Years AV





Draft Weight

SQRT
 Prior 3 Yrs AV

SQRT
 Next 3 Yrs AV


Year

R^2

Intercept

Coefficient

PValue

Coefficient

PValue

Coefficient

PValue

1

0.35

2.86

9.14

0.00

N/A

N/A

1.04

0.00

2

0.41

3.52

3.89

0.00

1.46

0.00

1.11

0.00

3

0.43

3.16

0.47

0.36

1.32

0.00

1.24

0.00

4

0.41

3.56

0.14

0.80

0.98

0.00

1.29

0.00

5

0.41

3.68

1.61

0.01

1.00

0.00

1.28

0.00

6

0.38

3.99

0.60

0.35

1.00

0.00

1.17

0.00

The overall model is improved from ~0.220.29 Rsquared
to ~0.350.43. With respect to draft weight, year one still shows a significant
impact, though the coefficient is reduced from the prior models, and year 2
holds up as well before years 36 drop to insignificance (I’ll put my money on
the 1% chance that the significance of year 5 is random). At this point draft
weight appears to be more a proxy for prior performance, as it should be, than
a lingering sunk cost impacting decision making.
My next post will look at the first couple years in a bit
more detail, to try to tease out whether relative usage is due to draft weight
or other factors.
What’s Missing?
The future performance serves here as a proxy for coach’s
judgment/underlying ‘true’ skill level, but there are a couple other factors
missing in this analysis. The two main ones are the particular situation –
whether a player is sitting behind a veteran at the same position – and injuries.
Both can have a big impact on playing time but represent a bit of a modeling
challenge. Feel free to use the comments if you have any ideas for
incorporating these into the model. As it stands, I’m pretty happy with a model
that has ~0.4 Rsquared (~0.250.30 with only data available prior to the
season).
Rookie wage scale probably impacts usage ,right? With 4 years guaranteed for top picks, and 2 for 2nd rounders, those guys would naturally have a bit of an artificial boost in usage.
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