Driver Average or Driver Median?

Why a NASCAR Drivers Average Is Not The Best Measurement

A NASCAR drivers average finish is a popular statistical benchmark used to determine how well a driver does at a certain track or track type. Look at these NASCAR stats sites:

They all have a column for ‘Average Start’ and ‘Average Finish’. I’ve got the same statistic scattered all over my pages as well.

Now, I’m a NASCAR fan and web design guy, not a statistician. But, I’ve been reading up on the difference between MEAN (aka AVERAGE) and MEDIAN (middle number).

What is MEAN?

Figuring the MEAN, or AVERAGE, of a group of numbers is simply adding them up and then dividing by how many numbers you added. For example, take Dale Earnhardt Jr‘s finishes at Daytona International Speedway.

1 + 1 + 2 + 3 + 3 + 3 + 6 + 7 + 8 + 13 + 13 + 29 + 35 + 36 = 160.

Divide 160 by 14 (the number of race results added up) and you get 11.429.

So, we say that Dale Jr’s AVERAGE Finish at Daytona is 11th.

What is MEDIAN?

Now, lets look at the MEDIAN of Dale Earnhardt Jr’s Daytona finishes. We’re going to knock a number off from each end until we are at the middle.

1 1 2 3 3 3 6 7 8 13 13 29 35 36.

We’re left with his 6th and 7th place finishes. Now, lets take the MEAN (or AVERAGE) of those two numbers. 6 + 7 = 13 and then 13/2 = 6.500 So, now we see that the MEDIAN finish for Dale Jr is about 7th. That’s 4 positions better than his AVERAGE finish of 11th.

Which is More Accurate?

I’m leaning more towards the MEDIAN number being the better statistic to look at.

Dale Earnhardt Jr at Daytona

In Dale Earnhardt Jr’s case, he has 8 of 14 finishes that are 7th or better. His next three worst finishes (8th, 13th & 13th) are all within 6 spots of his MEDIAN finish. Just looking at all 14 Daytona International race finishes for ‘Little E’, you can see that his three bad finishes (29th, 35th & 36th) are going to skew his overall results when looking at the AVERAGE.

It’s because of the unpredictability of a NASCAR race to result in a bad finish due to a wreck or mechanical problem that those outlying bad finishes can drastically change a drivers average.

Boris Said at Daytona

Think about a driver like Boris Said who currently has 3 Nextel Cup starts at Daytona. His finishes are 4th, 27th & 28th. Which appears more accurate?

  • His AVERAGE finish of 20th (4 + 27 + 28)/3
  • His MEDIAN finish of 27th (4, 27, 28)

I’m leaning toward the MEDIAN. Vital information for your fantasy race team when choosing who to run.

Wrapping Up

Once again, here is the definitions of MEAN and MEDIAN.

MEAN: The sum of a list of numbers, divided by the total number of numbers in the list.

MEDIAN: The ‘Middle Value’ of a list of numbers. If the list has an odd number of entries, the MEDIAN is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the MEDIAN is equal to the sum of the two middle (after sorting) numbers divided by two.