Wednesday, February 4, 2009

Driver Skewness

Today's post is about skewness, an interesting property of distributions that you may remember learning about in your statistics courses.

Skewness measures how asymmetrical a distribution is. How can we apply this tool to enrich our understanding of driver performance? Intuitively, you would want a very positive skew, since that means most of your results are better (top 10s, top 5s, or even 1st place finishes). A negative skew would mean that you have most of your results on the far end of the spectrum (falling a lap or more down, DNFs, etc).

So if we measured some current and former drivers on the skewness of their career race results, what would we find? The full table appears below.

I think the results speak for themselves: skewness turns out to be a natural way to identify great drivers. As an example, it would be tough to argue that anyone else has outperformed Jimmie Johnson over the course of their career.

The table below also contains some surprises. For instance, it may be unexpected to see guys like Edwards and Hamlin this close to the top. Are they destined for great things ahead?

The simple statistic of "average finish" doesn't take into account the distribution of a driver's finishes. Skewness, however, takes that property into account, and thus might be the single best indicator of success in NASCAR.

Driver Skew
Jimmie Johnson 1.19
Dale Earnhardt, Sr. 1.16
Tony Stewart 1.10
Carl Edwards 1.02
Jeff Gordon 1.02
Denny Hamlin 1.00
Richard Petty 0.99
Mark Martin 0.95
Matt Kenseth 0.85
Clint Bowyer 0.76
Jeff Burton 0.72
Kevin Harvick 0.67
Dale Earnhardt, Jr. 0.66
Kyle Busch 0.59
Bill Elliott 0.57
Terry Labonte 0.56
Darrell Waltrip 0.55
Bobby Labonte 0.48
Greg Biffle 0.47
Sterling Marlin 0.36
David Ragan 0.32
Ken Schrader 0.25
Michael Waltrip 0.17
Kyle Petty 0.09
Ward Burton 0.08
Jeremy Mayfield 0.07
Joe Nemechek -0.15
Derrike Cope -0.25
Robby Gordon -0.28