When it’s Hot, Does Smoke Catch Fire?

Ten races into the NASCAR Sprint Cup season, Tony Stewart has put up some rather pedestrian numbers so far. With only two top 5s and four top 10s Smoke, as he is affectionately known throughout NASCAR circles, currently sits 21st in the point standings. His average finish of 19.8 is well above his career average of 12.9, yet some fans don’t seem to be worried. The reason? Memorial Day is fast approaching and as legend has it when the temperature heats up Smoke starts to catch fire. Throw in the added fact that under NASCAR’s 2014 rules a single win will probably qualify a driver for the chase, and many fans are betting that Tony picks up at least one win sometime between now and the last race before the chase cutoff at Richmond. But, will Tony pick up that win? Is there any merit to the legend that summer heat helps Smoke catch fire?

We’ll start simple and look at average finishes overall. From 1999 through 2013 Smoke has an average finish of 14.91 before Memorial Day and 11.66 after. If we just limit it to “the summer heat” where we look between Memorial Day and Labor Day, the gap tightens just a bit. During the summer Tony averages 11.74 compared to 13.38 during cooler times of year. We can use a statistical test to test for significant difference. In doing so, despite the large sample size (N = 521), the data are highly non-normal so a Student’s t-Test is not the appropriate test to apply in this situation. Instead we use a nonparametric test called the Wilcoxon-Mann-Whitney test which allows us to test for significance even though the data violates the normality assumption. Doing so gives p-values of 0.0006 and 0.0325, indicating Smoke’s improved post-Memorial Day and summertime performance is not just random noise, and is in fact not a myth.

Stewart's finishes before vs. after Memorial Day (left) and spring/fall vs. summer (right) with Wilcoxon-Mann-Whitney test for significance.
Stewart’s finishes before vs. after Memorial Day (left) and spring/fall vs. summer (right) with Wilcoxon-Mann-Whitney test for significance.

However, we can take this analysis farther. First, let’s remove the impact of mechanical failures, which the great majority of the time is not the driver’s fault (there can be situations where the driver abuses the car causing a tire or other mechanical failure, but they tend to be few and far between). We leave in races where accidents have caused a DNF (did not finish) because there are times this is the driver’s fault and times the driver is simply caught up in someone else’s wreck. Since there is no way to differentiate fault, we play it safe and leave accidents in. In doing so, Smoke now has average finishes of 14.01 before and 11.39 after Memorial Day respectively, and 12.73 and 11.51 in spring/fall and summer respectively. In both cases, removing mechanical failures has tightened the gap. However, applying Wilcoxon-Mann-Whitney still gives p-values of 0.0024 and 0.0561 respectively, once again implying Smoke’s finishes tend to be better after Memorial Day and during summer. Moving forward, the rest of this analysis has DNFs from mechanical failures removed.

It’s fair to ask the question, “well isn’t Tony Stewart simply better at some tracks than others, and the tracks he’s better at tend to fall in the summer?” Here’s where it gets interesting. Looking at the 14 tracks that Tony has raced on before and after Memorial Day, Tony has averaged 1.15 positions worse than his average finish at each track before Memorial Day. After Memorial Day, Smoke has finished 1.03 positions better than his average finish at each track, meaning Tony finishes almost 2.2 positions better compared to his track average before Memorial Day than after. This difference is statistically significant (p = 0.0225). However, if we look at the 9 tracks that have had summer and spring/fall races Tony finishes near his track average regardless of time of year (0.14 worse in spring/fall, 0.22 better in summer). This small difference could be purely random chance (p = 0.4895). Thus, it’s easy to conclude that since Tony does better after Memorial Day, but no better between Memorial Day and Labor Day, it stands to reason he does best after Labor Day.

Stewart's finish against track average for before vs. after Memorial Day (left) and spring/fall vs. summer (right) with Wilcoxon-Mann-Whitney test for significance.
Stewart’s finish against track average for before vs. after Memorial Day (left) and spring/fall vs. summer (right) with Wilcoxon-Mann-Whitney test for significance.

As it turns out, Smoke does indeed perform best late in the season. Now we divide the season into three segments, “Beginning”, consisting of races before Memorial Day, “Middle”, consisting of races between Memorial Day and Labor Day, and “End”, for races after Labor Day. For tracks that are not confined to one time of year he outperforms his track average by 1.21 positions at the end of the season, best of the three groups. This is one position better than the middle of the year, and 2.36 positions better than the beginning of the year against his track averages. The difference between beginning and end of year finishes produces the only result of significance (p = 0.0236).

Stewart's finishes against track average for beginning, middle, and end of year with Kruskal-Wallis (multiple means version of Wilcoxon-Mann-Whitney) test for significance.
Stewart’s finishes against track average for beginning, middle, and end of year with Kruskal-Wallis (multiple means version of Wilcoxon-Mann-Whitney) test for significance.

In other words, we can conclude, yes Tony Stewart does perform better after Memorial Day than before, but that is because stating it this way includes the end of the year. Instead, it is more correct to say he performs best at the end of the year, outperforming his track averages the most as the season winds down.

So, will Smoke similarly heat up this year? Under NASCAR’s new rules, winning matters most. Before Memorial Day Smoke has won 6 times in 174 races for a win ratio of 3.45%. After Memorial Day, he boasts a 12.54% win ratio. Considering there are 16 races left before the chase then at a similar 12.5% winning clip Smoke’s expected value is 2 wins before the chase in an average year. However, this has been no ordinary year so far for Smoke. Through 10 races, the 2014 season has been his worst start to date. Smoke has finished on average 8 spots worse than his track average in 2014. By comparison, his second worst start through 10 races was in 2007 where he averaged 4.9 spots worse than his track average. Applying the eight extra positions to Tony’s expected finish at each track, but crediting him for a post-memorial day bonus on all the tracks after Charlotte, we can try to calculate his expected wins. In doing so, the data for (actual finish – track average finish) needs to be transformed since it is highly non-normal. I first shifted the data so it is all positive valued and then I applied a Box-Cox transformation to produce a near-normal distribution of data. From here, we can calculate the expected win value for each of the 16 remaining races since we have the transformed mean and standard deviation for his actual finishes around his average track finish. When all is said and done, Tony’s new expected wins value is 0.1275 wins before the chase, a far cry from the 2.0 expected wins. This equated to about an 12% chance that Tony wins at least one race. Not too great.

Histogram of difference between actual finish and track average finish showing significantly skewed distribution of data
Histogram of difference between actual finish and track average finish showing significantly skewed distribution of data

Tony will have to step up his game if he wishes to make the chase. The data suggests he has only marginally improved performance in the middle of the year rather than the “as the summer heats up so does Tony” myth that is out there. Lucky for him, all it takes is one win, and if he does manage to significantly improve performance or grab an unexpected win with subpar performance to make the chase, all bets are off. Tony at the end of the year is a vastly different Tony than the beginning of the year as the data proves. Smoke could very well contend for the title if he simply makes the chase.

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