## Saturday, May 10, 2014

### Understanding risk and the NFL draft

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