A Game-Theoretic Approach to Personnel Decisions in American ...

δ
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R* Coloring the Unit Square
0
0 0.2 0.4 0.6 0.8 1
x
Figure 1: R ∗ (δ,x) using 2008 Chicago Bears Data
As can be seen in Figure 1, the breaking point when δ = 1 (as in 2
our calculations) is approximately 0.775. This implies that to be justified
in playing a pure pass strategy, the expected yards per play would have to
increase by approximately 2.178 yards. This is a large increase, and supports
our claim that it is unrealistic to anticipate that Chicago would ever pursue a
pure passing strategy.
In order to examine how Jay Cutler impacts the run/pass balance of
the Chicago Bears, we first find his x. To do so, we will consider Cutler’s
effect on the Broncos’ offense in 2007, his first year as a starter. We begin
using the data from the 2006 Broncos offense to calculate Table 6, Denver’s
2007 improvement in passing model, in a manner similar to our development
of Table 4.
Defense
Defend Run Defend Pass
Offense Run 2.73(1 + δx) 4.25(1 + δx)
Pass 4.86(1 + x) 3.33(1 + x)
Table 6: The 2007 Denver Broncos Improvement in Passing Model
In 2007, the Broncos gained an average of 4.57 yards per play. Thus,
the x-value that we seek for Jay Cutler is the solution to V ∗ ( 1,x)
= 4.57,
2
where V ∗ is as given in (7). Solving, we obtain x ≈ 0.279.
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