Further
analysis of first and second choice QB draft picks
Some
previous posts examined differences in the average and median career touchdowns
for first and second choice QB draft picks.
This post looks at the variance and the risk associated with different
picks. I attempt to add insight about
the draft for quarterbacks and the nature of risk.
Data:
The questions in this post require analysis of the descriptive data
presented below. The raw data spanned
the 1970 to 2002 time period. The sample
size is 33 years.
Descriptive Statistics on Number of Touchdowns for
First and Second Choice
QB Picks
|
||
First-Choice Pick
|
Second-Choice Pick
|
|
Average
|
129.5
|
77.6
|
Median
|
124.0
|
44.0
|
Min
|
1.0
|
0.0
|
25th Percentile
|
33.0
|
11.0
|
75th Percentile
|
174.0
|
125.0
|
Max
|
491.0
|
363.0
|
STD
|
109.3
|
87.2
|
Range
|
490.0
|
363.0
|
Interquartile Range
|
141.0
|
114.0
|
# of QB S with fewer than
25 career TDs
|
8.0
|
13.0
|
% of QBs with fewer than 25 career TDS
|
24.2%
|
39.4%
|
Sample
Size
|
33.0
|
33.0
|
See my
previous post for the raw data.
Question:
Is the variance career touchdowns of first-choice picks significantly
different than the variance performance of second-choice picks over the 1970 to
2002 period? Conduct the hypothesis
test.
Discussion:
Is a comparison of the variance of career touchdowns for first-choice QB
picks and second-choice QB picks an appropriate way to measure the relative
risk of first-choice and second-choice QB picks? What statistics would better measure performance
risk for these two groups?
Analysis:
Question: Use the F-test for equality of
variances. See the reference below.
The sample
variances are the square of the sample standard deviations. The test statistic used to test the hypothesis
that the population variances are identical is the ratio of the sample
variances
(S1)2/(S2)2
is 11,956/7597 which is 1.57.
The test
statistic follows the F distribution with 32 degrees of freedom for both the
denominator and numerator.
The p-value
for the F-statistics is 0.104.
Interestingly,
I didn’t look this up in a stat book. I
found a free p-value calculator for the F distribution on the Internet. Link is below.
The
variance of first-choice picks is not statistically different than the variance
of second-choice picks for a p-value of 0.10.
Discussion: The variance of career touchdowns across
draft choices is NOT a good measure of performance risk. The high variance for first-choice picks
is the result of more superstars among the first-choice picks than among the
second-choice picks.
Risk,
properly measured, does not increase in a population because of good performances
at the upper end of the spectrum. Risk
should measure the likelihood of poor performance
The table
contains two useful measures of risk.
First, the
coefficient of variation (the ratio of the standard deviation to the mean)
adjusts for the higher variance associated with some high values that increase
the mean career touchdowns.
Second, the
probability of only getting a few career touchdowns is a direct measure of
unsuccessful picks among first-QB and second-QB choices. I looked at the proportion of QBs in each
sample with fewer than 25 TDs. The
difference between 24.2% for the first-choice QBs and 39.4% for the
second-choice QBs is substantial.
In many
respects the measurement of QB-pick risk is similar to the measurement of
financial risk in a portfolio of stocks.
The use of the standard deviation – the most commonly used statistic for
the measurement of portfolio risk – seems silly because a high standard
deviation might stem from superior performance among a few stocks.
A portfolio
with Google in it in the early 2000s would have a high standard deviation. Would this portfolio be less risky if it had
not contained Google?
The higher
variance of first-choice picks stems from the existence of more QBs with a
larger number of touchdowns among first-choice QBs. Second choice QB picks are more risky because
they are more likely to have a relatively short career with little production.
Authors Note:
I hoped to have some work done comparing running backs to quarterbacks
prior to the NFL draft. Work has been
delayed because I am moving to Denver.
#NFL DRAFT
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