From the Blog

# Can anyone win at Daytona?

It’s common knowledge to the average NASCAR fan that races at Daytona and Talladega are different from other races.  In both cases, restrictor plates are placed in each car near the engine in order to slow the cars’ top speeds down to around 200 mph.  Limiting the airflow to the engine decreases horsepower and speed by reducing the oxygen content in the combustion process.  For this reason, NASCAR seems to level the playing field at Daytona and Talladega, and announcers love to promote the fact that “anyone can win.”  Is this true?  Can anyone win?  Many drivers have claimed they would rather be in second place going into the final lap.  Is it better to lead the entire race, or just sit back and wait to make your move towards the end?  Or does it really even matter at all?

We looked at data from previous races at Daytona in recent years in order to gain insight on whether or not a driver’s position throughout the race is associated to where he (or Danica) finishes the race.  Since drivers in the Sprint Cup Series have a ranking of 1-43 on any given lap, we used Spearman’s Rank Coefficient to test for a correlation.  The theory behind this statistic is simple; rank the cars on any given lap and see if the rankings themselves correlate to the final rankings.  The actual statistic looks a bit more complicated.

In this equation, $n$  is the number of drivers in the race, $R(x_{i})$ is rank of driver $i$ on lap $s$ , and $R(y_{i})$ is the rank of driver $i$  at the end of the race.  However, since there are no ties in the rankings, this rather large and complicated looking equation can be algebraically reduced to something much more simple.

Here, $d_{i}=R(x_{i})-R(y_{i})$ , car $i$ ’s rank on lap $s$  less its final rank.  When the race starts, $n=43$ , the number of drivers in the race.  For each sufficient lap, $n$  is equal to the total number of drivers still in the race.  So for instance, if someone crashes in the second lap and is subsequently in 43rd place for the rest of the race, it is evident that car will end in 43rd place, so there is no reason to include that car since the difference in rankings is zero.  Including this car in the correlation test will increase $r_{s}$ , the correlation coefficient, unnecessarily.

In each of the four races for which we gathered information, there was a green-white-checkered finish, basically just meaning there were extra laps added on so the race did not finish under caution.  Below is a graph of correlations of the rankings at the 2012 Coke Zero 400.  There were 160 laps in the race, and the race was under caution during laps 153-158.

As is evident from the graph, there is no correlation between the 10-laps-to-go rankings and the final rankings.  In fact, three of the four races we investigated at Daytona showed no correlation between these two lap rankings.  This indicates the position a driver was in with only ten laps to go had no significance to where he eventually finished the race.  In a sense, the goal of these races until the last ten laps should be just to stay in the race and not crash.

So what?  Couldn't this be true at any race?  It’s possible, but just to make sure the same results weren't true for non-restrictor plate races, or all races not held at Daytona or Talladega, we conducted the same statistical testing on the Quicken Loans 400 held at the Michigan International Speedway in Brooklyn, MI.  This track is two miles long and known to be one of the fastest tracks in NASCAR.  So is it very similar to races at Daytona and Talladega, but the Quicken Loans 400 is not a restrictor plate race.  As seen in the chart below, along with all of the other race information we gathered, with ten laps to go in the 2012 race, the correlation coefficient was .884, meaning there was a very strong positive correlation between the order of the cars with ten laps to go and the final rankings.  In fact, there was a positive correlation strong enough to pass Spearman’s Correlation Test throughout the entire race, even on the first lap.  There could be a lot said about these statistics alone, but for now we just take it to show that correlations typically do exist, even at race tracks that are similar to Daytona and Talladega.