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


FirstChoice Pick

SecondChoice 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 firstchoice picks significantly
different than the variance performance of secondchoice picks over the 1970 to
2002 period? Conduct the hypothesis
test.
Discussion:
Is a comparison of the variance of career touchdowns for firstchoice QB
picks and secondchoice QB picks an appropriate way to measure the relative
risk of firstchoice and secondchoice QB picks? What statistics would better measure performance
risk for these two groups?
Analysis:
Question: Use the Ftest 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
(S_{1})^{2}/(S_{2})^{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 pvalue
for the Fstatistics is 0.104.
Interestingly,
I didn’t look this up in a stat book. I
found a free pvalue calculator for the F distribution on the Internet. Link is below.
The
variance of firstchoice picks is not statistically different than the variance
of secondchoice picks for a pvalue of 0.10.
Discussion: The variance of career touchdowns across
draft choices is NOT a good measure of performance risk. The high variance for firstchoice picks
is the result of more superstars among the firstchoice picks than among the
secondchoice 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 firstQB and secondQB choices. I looked at the proportion of QBs in each
sample with fewer than 25 TDs. The
difference between 24.2% for the firstchoice QBs and 39.4% for the
secondchoice QBs is substantial.
In many
respects the measurement of QBpick 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 firstchoice picks stems from the existence of more QBs with a
larger number of touchdowns among firstchoice 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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